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Ground surface motions in the Fraser delta due to earthquakes 1979

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GROUND SURFACE MOTIONS IN THE FRASER DELTA DUE TO EARTHQUAKES BY DOUGLAS MONTAGUE WALLIS B i A i S C . , U N I V E R S I T Y OF B R I T I S H C O L U M B I A , 1975 A T H E S I S SUBMITTED IN P A R T I A L F U L F I L L M E N T OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF A P P L I E D S C I E N C E US THE FACULTY OF GRADUATE STUDIES (Department of Civil Engineering) We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF B R I T I S H COLUMBIA A p r i l , 1979 <c) DOUGLAS MONTAGUE WALLIS, 1979 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e - f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department The U n i v e r s i t y o f B r i t i s h Columbia 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 Date dPc* 2 7? • E - 6 B P 75-51 I E ABSTRACT The purpose of this thesis i s to investigate the potential ground surface motions i n the Fraser Delta due to earthquakes. The geological history of the area i s reviewed and information concerning the nature of the thick s o i l deposits that form the Delta i s presented. The dynamic properties of the Delta s o i l s are calculated and a model of the deposit i s developed for use with e x i s t i n g computer analysis based on wave propagation theory. The computer analysis method involves the computation of the ground motions as a v e r t i c a l l y propagating shear wave passes from bedrock, through s o i l layers, to the surface. The accuracy of the model was checked at three s i t e s by comparison of the surface motions computed using a recorded bedrock object motion with the ground surface motion recorded during the same earthquake. The close c o r r e l a t i o n between the computed and recorded motions confirms the v a l i d i t y of the analysis method and the s o i l model. The surface motions r e s u l t i n g from larger, maximum probable, earthquakes are computed. It was found that the thick s o i l deposits of the Delta a f f e c t both the ground accelerations and the period of the peak s t r u c t u r a l accelerations. Under the influence of low magnitude earthquakes the maximum accelera- tion i s larger on the surface of the deep s o i l deposits than i t i s on nearby bedrock outcrops, while for large magnitude earthquakes the reverse i s true. During large magnitude earthquakes, short buildings with periods of 0.25 sec. w i l l experience greater accelerations i f they are founded on bedrock than they w i l l i f f o u n d e d o n t h e t h i c k s o i l d e p o s i t s o f t h e D e l t a . T a l l e r b u i l d i n g s w i t h p e r i o d s o f a b o u t o n e s e c o n d w i l l e x p e r i e n c e f a r g r e a t e r a c c e l e r a t i o n s i f t h e y a r e f o u n d e d o n d e e p s o i l d e p o s i t s t h a n t h e y w o u l d i f f o u n d e d o n b e d r o c k . C o m p a r i s o n o f S t a n d a r d P e n e t r a t i o n T e s t d a t a i n t h e F r a s e r D e l t a w i t h e m p i r i c a l r e l a t i o n s i n d i c a t e s t h a t u n d e r l a r g e m a g n i t u d e e a r t h q u a k e s l i q u e f a c t i o n i s l i k e l y i n . t h e u p p e r f e w m e t e r s o f t h e D e l t a s a n d d e p o s i t s , b u t i s u n l i k e l y b e l o w t h e 6 o r 9 m e t e r d e p t h . - i v - TABLE OF CONTENTS PURPOSE AND SCOPE 1 CHAPTER 1 INTRODUCTION TO THE AREA OF STUDY 3 1-1 Physical Setting 3 1-2 Pre Pleistocene History 6 1-3 Pleistocene History 7 1- 4 Post G l a c i a l History 10 CHAPTER 2 SOIL CHARACTERISTICS OF THE FRASER DELTA,. . 12 2- 1 S o i l Type and Extent 12 2-2 S o i l Data requirements 17 2-3 S o i l Data Source and Accuracy 18 2-4 Water Content 20 2-5 Atterberg Limits 21 2-6 Compression Index 24 2-7 Undrained Shear Strength 25 2-8 Dry Density of Sand 27 2-9 Standard Penetration Test 28 2-10 Relative Density of Sands 39 2- 11 F r i c t i o n Angle of Sands 4 8 CHAPTER 3 DYNAMIC ANALYSIS 51 3- 1 Type of Analysis 51 3-2 S o i l P r o f i l e s and Dynamic Properties 56 3-3 Pender Island Earthquake Correlation 68 3- 4 Seismicity and the Design Earthquake 73 CHAPTER 4 RESULTS 81 4- 1 Pender Island Earthquake Correlation 81 4-2 Analysis Using the Design Earthquake 87 CHAPTER 5 COMMENT ON THE LIQUEFACTION POTENTIAL OF THE FRASER DELTA 9 5 CHAPTER 6 CONCLUSIONS AND SUGGESTIONS FOR FUTURE RESEARCH 99 6-1 Conclusions 99 6-2 Suggestions for Further Research 101 LIST OF REFERENCES 190 - v - APPENDIX 1 19 5 APPENDIX 2 196 APPENDIX 3 19 8 - v i - LIST OF TABLES Relative Density Data - v i i - • LIST OF FIGURES Figure Page 1-1- 1 Index Map of Fraser Lowland 103 1-1- 2 Physiographic Regions 104 1-1-•3 Recent . S u r f i c i a l Deposits 105 1-1- 4 Depth to G l a c i a l T i l l 106 1-1- 5 Depth to Bedrock 107 1-2- 6 Geolog i c Time Scale 108 2-1- 1 D i s t r i b u t i o n of S u r f i c i a l S o i l Types 109 2-1- 2 S u r f i c i a l S o i l P r o f i l e s 110 2-4- 1 Clay: Water Content vs Depth 111 2-4- 2 S i l t : Water Content vs Depth 112 2-4- 3 Peat: Moisture Content vs depth 113 2-5- 1 Clay: L i q u i d Limit and P l a s t i c Limit vs Depth 114 2-5- 2 S i l t : L i q u i d Limit and P l a s t i c Limit vs Depth 115 2-5- 3 S i l t : P l a s t i c i t y Index vs Depth 116 2-5- 4 Clay: P l a s t i c i t y Index vs Depth 117 2-5- 5 P l a s t i c i t y Chart 118 2-6-•1 S i l t : Compression Index vs Depth 119 2-6- 2 Clay: Compression Index vs Depth 120 2-7-•1 Clay: Undrained Shear Strength vs Depth 121 2-7- 2 S i l t : Undrained Shear Strength vs Depth 122 2-8- 1 Sand: Dry Density vs Depth 123 2-9- 1 Blow Count vs Depth i n Sand (Typical) 124 - v i i i - Figure ; Page 2-9-2 C o e f f i c i e n t of Relative Curve Smoothness vs 125 Depth f o r SPT i n sand: Comparison between Blow counted from 0 to 0.3m. and from 0.15m -0.4 5m on each sample. Data from 3 s i t e s . 2-9-3 C o e f f i c i e n t of Relative Curve Smoothness vs 126. Depth for SPT i n Sand: Comparison between Blows Counted from 0 - 0.3m and from 0.3 - 0.6m on each Sample, Data from 3 s i t e s . 2-9-4 Comparison of SPT Blow Counts Recorded i n f i r s t 127 0.3m with those recorded from 0.15m - 0.4 5m on Sample of sand, Data from 3 s i t e s . 2-9-5 Comparisons of SPT Blow Counts Recorded i n 128 F i r s t 0.3m with those recorded from 0.3 to 0.6m. on Same Sample of Sand, Data from 3 s i t e s . 2-9-6 Comparison of SPT Blow Counts Recorded i n the 129 F i r s t 0.3m with those recorded at other p o s i t i o n s on the same sample of sand. 2-9-7 Comparison s i t e : Blow Count vs Depth i n Sand. 130 Blow Counts Recorded for Penetration from 0 - 0.3m. 2-9-8 Comparison S i t e : Blow Count vs Depth i n Sand. 131 Blow Counts Recorded for Penetration from 0.15- 0.45m. 2-9-9 Comparison S i t e : Blow Count vs Depth i n Sand 132 2-9-10 Roberts Bank: Blow Count vs Depth i n Sand 133 - i x - Figure Page 2-9-11 Sturgeon Bank: Blow Count vs Depth i n Sand 134 2-9-12 Tilbury Island: Blow Count vs Depth i n Sand 135 2-9-13 Sea Island: Blow Count vs Depth i n Sand 136 2-9-14 Ladner: Blow Count vs Depth i n Sand 137 2-9-15 Annacis Island: Blow Count vs depth i n Sand 138 2-9-16 Annacis Island: Blow Count vs Depth i n Sand 139 2-9-17 Richmond: Blow Count vs Depth i n Sand 140 2-9-18 Head of Delta, Blow Count vs Depth i n Sand 141 2-9-19 Byrne Rd: Blow Count vs Depth i n Sand 14 2 2-9-20 Lulu Island: Blow Count vs Depth i n Sand 143 2-9-21 North Richmond: Blow Count vs Depth i n Sand 144 2-9-22 Summary, Blow Count vs Depth i n Sand 145 2-10-1 Blow Count-Relative Density Relationships 14 7 2-10-2 Blow Count-Relative Density Relationships 148 2-10-3 Grain Size Curves for the S o i l s Used to Develop 149 the Blow Count-Relative Density Relationships 2-10-4 Grain Size Curves for Typical Fraser Delta S o i l s 150 2-10-5 Relation Between Relative Density and Blow Count 151 with Depth at a P a r t i c u l a r Site 2-11-1 Sand: F r i c t i o n Angle vs Dry Density 152 2- 11-2 V a r i a t i o n of Blow Count with Depth and F r i c t i o n 153 3- 1-1 Hysteretic Stress-Strain Path 154 3-1-2 D e f i n i t i o n of Shear Modulus and Damping 154 3-2-1 Sites Chosen for Dynamic Analysis 155 3-2-2 Roberts Bank: S o i l P r o f i l e and S o i l Model 156 3-2-3 Annacis Island: S o i l P r o f i l e and S o i l Model 157 3-2-4 Brighouse: S o i l P r o f i l e and S o i l Model 158 - x - Figure Page 3-2-5 Roberts Bank: Maximum Shear Modulus 159 3-2-6 Annacis Island: Maximum Shear Modulus 160 3-2-7 Brighouse: Maximum Shear Modulus 161 3-2-8 Roberts Bank: Maximum Damping Ratio 16 2 3-2-9 Annacis Island: Maximum Damping Ratio 163 3-2-10 Brighouse Maximum Damping Ratio 16 4 3-2-11 Modulus Reduction Curves 165 3-2-12 Damping Reduction Curves 166 3-4-1 D i s t r i b u t i o n of Earthquakes i n S t r a i t of 167 Georgia-Puget Sound Area from Milne et a l (1978) 3-4-2 Major Faults and Lithospheric Boundaries i n 16 8 Western B.C. 3-4-3 S t r a i n Release vs Time i n Continental Area 168 3-4-4 Magnitude vs Time Relation for Georgia S t r a i t - 169 Puget Sound Area, from Milne et ajL (1978) . 3-4-5 Predominant Periods for Acceleration i n Rock 169 from Seed, I d r i s s and Kiefer 1969. 3- 4-6 Average Values of Maximum Acceleration i n Rock 170 from Schnabel and Seed 1972 4- 1-1 Annacis Island: Response Spectra of Computed 171 and Recorded Surface Motions Due to Pender Island Earthquake 4-1-2 Brighouse: Response Spectra of Computed and 172 Recorded Surface Motions due to Pender Island Earthquake 4-1-3 Roberts Bank: Response Spectra of Computed and 173 Recorded Surface Motions due to Pender Island Earthquake - x i - Figure Page 4-1-4 Annacis Island:- Response Spectra of Motions 174 Computed within the S o i l P r o f i l e due to Pender Island Earthquake 4-2-1 Response Spectra of Design Earthquake scaled 175 to Maximum Acceleration of 0.25g. 4-2-2 Annacis Island: Response Spectra of Surface 176 Motions for Design Earthquake scaled to Amax= 0 . 1 6 g . 4-2-3 Annacis Island: Response Spectra for Surface 177 Motion for Design Earthquakes scaled to Amax -° ' 2 5 9 - 4-2-4 Annacis Island: Response Spectra of Surface 178 Motions for Design Earthquakes Scaled to Amax = 0' 3 39- 4-2-5 Brighouse: Response Spectra of Surface Motions 179 for Design Earthquake Scaled to ̂ ^ = 0 . 16g. 4-2-6 Brighouse: Response Spectra of Surface Motion 180 to Design Earthquake Scaled to A =0.25g. 4-2-7 Brighouse: Response Spectra of Surface Motions 181 for Design Earthquake Scaled to A m a x=0.33g. 4-2-8 Brighouse: Mean of the Response Spectra for 182 Three Design Earthquakes of a P a r t i c u l a r A m a x 4-2-9 Annacis Island: Mean of the Response Spectra 183 for Three Design Earthquakes of a P a r t i c u l a r ^ n a x 4-2-10 Brighouse: Response Spectra of Surface Motions 184 for Desiqn Earthquake Scaled to A =0.25g. and 3 ^ max J Object Motion applied to Top of G l a c i a l T i l l - x i i - Figure Page 4-2-11 Annacis Island: Response Spectra of Surface 185 Motions for Design Earthquake Scaled to A . =0.25g. and Object Motion applied to max . J Top of G l a c i a l T i l l . 4-2-12 Annacis Island: Mean Response Spectra-Object 186 Motion and Surface Motion for A =0.25g max 2 4- 2-13 Maximum Acceleration on Rock vs Maximum 187 Acceleration at Ground Surface 5- 1 Blow Count - Liquefaction Potential Relations 188 5-2 Liquefaction Potentials of the Fraser Delta 189 - x i i i - ACKNOWLEDGEMENTS The Writer wishes to express his thanks to his research supervisor Dr. P.M. Byrne for his guidance during this research. He further wishes to express his appreciation to Dr. R.G. Campanella for his valuable suggestions. Data on the s o i l properties i n the Fraser Delta were kindly made available by Cook, Pickering and Doyle Limited, MacLeod Geotechnical Limited, B r i t i s h Columbia Hydro, and the Vancouver o f f i c e of the Geological Survey of Canada. Time h i s t o r i e s of l o c a l earthquake motions were provided by Dr. W.G. Milne of the P a c i f i c Geoscience Centre/Department of Energy, Mines and Resources. The Writer would also l i k e to express his appreciation to the National Research Council of Canada and Golder Brawner and Associates who provided f i n a n c i a l support for this investigation. -1- PURPOSE AND SCOPE The Fraser River Delta i s an area that i s growing rapi d l y to meet i n d u s t r i a l and r e s i d e n t i a l demands. I t i s a populated region i n the most seismicly active zone i n Canada. Design of engineering structures should incorporate the e f f e c t s of possible earthquakes. An earthquake can produce additional forces which must be r e s i s t e d by the s t r u c t u r a l members and foundation. I t can also reduce the strength of the foundation s o i l by processes such as l i q u e f a c t i o n . To assess the e f f e c t s of the earthquake induced forces on the structure, the c h a r a c t e r i s t i c s of the earthquake must be known. These c h a r a c t e r i s t i c s can be expressed i n terms of a response spectra. I t i s well documented that the ground surface motions i n areas of deep s o i l deposits are greatly affected by the type and extent of the s o i l s present. Mathematical methods are i n existance which allow the ground motion c h a r a c t e r i s t i c s i n deep s o i l deposits to be modelled under the influence of an earthquake. These modelling .techniques require knowledge of the dynamic properties of the - s o i l . This study i s developed i n three stages. In the f i r s t stage, available data describing the extent of the s o i l deposits and t h e i r engineering properties were col l e c t e d and analyzed to produce s o i l p r o f i l e s describing the dynamic s o i l properties of three s i t e s i n the Fraser Delta. The second stage involved using e x i s t i n g methods of dynamic analysis to f i n d the degree of accuracy with which the analysis method, using the properties determined i n stage one, agreed with the observed behaviour i n situations where -2- the surface response was known. In the t h i r d stage the model was used to predict the ground response to larger, maximum probable, earthquakes. -3- CHAPTER 1 INTRODUCTION TO THE AREA OF STUDY 1-1 Physical Setting The Fraser River Delta occupies an area i n the southwest corner of mainland B r i t i s h Columbia that stretches eastward from the S t r a i t of Georgia a distance of 23 kilometers, and northward from Boundary Bay a distance of 16 kilometers (figure 1-1-1). The most dominant geomorphological feature of the delta area i s the Fraser River, which emerges onto the delta at New Westminster through a narrow gap i n Pleistocene sediments, and s p l i t s into two major channels. On the eastern delta front, gently sloping t i d a l f l a t s extend westward 6 kilometers into the S t r a i t of Georgia, to the delta fore-slope, where the slopes are steeper. On the southern front, to the east of the Point Roberts upland, the t i d a l f l a t s extend southward into Boundary Bay. The Fraser Delta forms the western part of the Fraser Lowland, which stretches eastward from Vancouver, and north-eastward from Bellingham, Washington to define a triangular area with i t s apex 105 kilometers east of the S t r a i t of Georgia. The Fraser Lowland i s bounded on the north by the Coast Mountains and on the east by the Cascade Mountains (figure 1-1-2). I t forms the eastern part of a major physiographic region, the Georgia Depression. The Georgia Depression i s part of a li n e a r s t r u c t u r a l depression which runs from Alaska through Hecate S t r a i t , Georgia S t r a i t , and the Willamette-Puget Lowland to the Great Valley of C a l i f o r n i a . -4- The s u r f i c i a l deposits of the Fraser Lowland consist of late g l a c i a l and p o s t - g l a c i a l deposits, overlying older rock formations of i r r e g u l a r topography. These older formations outcrop at several locations i n ;bhe lowland. The delta i s an area of low r e l i e f and low elevation where p o s t - g l a c i a l sands, s i l t s , and clays, to depths of up to 210 meters o v e r l i e Pleistocene deposits e x i s t i n g to depths of over 800 meters (700 meters at Boundary Bay). Figure 1-1-3 shows the location of the s u r f i c i a l s i l t , sand and gravel deposits i n the western Fraser^Lowland. Areas of peat deposits have not been marked since these are generally less than 8 meters thick. A more detailed breakdown of the s u r f i c i a l deposits can be seen on maps by Johnston (1923), Armstrong (1956,1957,1960). Figure 1-1-4 shows areas of t i l l outcrop, and approximate contours of the buried contact between the upper t i l l surface and the over-lying , more recent deposits. The bed- rock outcrops and the approximate bedrock contours are shown i n figure 1-1-5. Figures 1-1-3, 1-1-4, and 1-1-5 have been adapted from unpublished maps compiled by A. Jerkevics. The remainder of the lowland consists of low, flat-topped h i l l s or uplands separated by wide, flat-bottomed valle y s , Most of these uplands are composed of Pleistocene deposits of g l a c i a l or Glaciomarine o r i g i n ; though some, such as Capitol H i l l and Burnaby Mountain have bedrock cores and a few are raised marine delta (Armstrong 1957). -5- The recent and Pleistocene deposits o v e r l i e Tertiary and Cretaceous rocks which extend to depths of up to 4600 meters (Holland 1976). To the east of the lowland the Tertiary and Cretaceous rocks are reduced i n thickness and o v e r l i e Pre- Tertiary metamorphics with ultrabasic intrusions,and paleocene formations. In the south,, the contact between the older and younger rocks i s obscure and probably involves a f a u l t r e l a t i o n s h i p (Hopkins 1966) . The western boundary of the bas-in i s open to the S t r a i t of Georgia. To the north the Tertiary and Cretaceous rocks reduce i n thickness and o v e r l i e C r y s t a l l i n e Complex. The Coast C r y s t a l l i n e Complex i s the g r a n i t i c unit which forms the mountains that r i s e abruptly north of Vancouver to between 1500 and 2100 meters. I t has been described extensively by Roddick (1965). This same unit underlies the Paleozoic and Mesozoic strata that bound the Fraser Lowland to the south and east (McTaggert 1977). The Fraser Delta i s presently growing due to the accumulation of r i v e r sediments on the delta front. The Fraser River i s the largest r i v e r i n B r i t i s h Columbia, with an outflow varying from 800 m3/s to 10,000 m3/s (Hoos and Packman 1974), drawn from a drainage area of 270,000 square kilometers. The r i v e r c a r r i e s 20 m i l l i o n cubic meters of sediment per year. These sediments are deposited to form t i d a l f l a t s having slopes varying from 1 to 3.5 degrees (Mathews and Shepard 1962). A c r i t i c a l examina- tion of the growth patterns of the present delta i s important, since i t may reveal patterns of sediment d i s t r i b u t i o n that w i l l - 6 - aid the interpretation of the s o i l types and the v a r i a b i l i t y i n the buried delta deposits. I n f i l l i n g of abandoned channels, gulley formation by active channels and slumping are three mechanisms that disrupt the uniform deposition of the sediments. The S t r a i t of Georgia i s r e l a t i v e l y protected from the waters of the P a c i f i c Ocean, but i t s r e s t r i c t e d passages and the t i d a l nature r e s u l t i n currents which contribute to the shaping of the de l t a . The i r r e g u l a r i t y of these shaping forces and the possible non- uniformity of i s o s t a t i c rebound within the Fraser Lowland area (Mathews, Fyles and Nasmith 1970),, indicate the pr o b a b i l i t y of a complex growth pattern. Scotton (1977) suggests that t h i s i s quite l i k e l y , even though he found no difference i n the.engineering properties of samples of a p a r t i c u l a r s o i l type but of possible age difference. This suggests that o n c e " c l a s s i f i e d by type, the properties of the delta s o i l deposits w i l l be well bounded. 1-2 Pre Pleistocene History In Lower Cretaceous times (see appendix 1 for geologic time scale) the area which i s now the Fraser Lowland was a marine basin having volcanic islands (figure 1-2-5). This resulted i n . the formation of bedrock which was both volcanic and sedimentary i n nature. Magma rose from depths within the earth and s o l i d i f i e d to form coarse c r y s t a l l i n e , igeneous rocks, composed mainly of quartz d i o r i t e and granodiorite. The older volcanic and sedimentary strata were incorporated into the magma as roof pendants and inclusions. During t h i s process some r e c r y s t a l i z a t i o n occurred, -7- forming metamorphic rocks. As cooling took place, cracking of the rock mass allowed the underlying magma to r i s e into the c r y s t a l i z e d rocks to form dykes and s i l l s . This complex structure i s c a l l e d the Coast C r y s t a l l i n e Complex (Formerly known as the Coast Range Batholyth). In Upper Cretaceous and Lower Tertiary times the Coast C r y s t a l l i n e Complex was elevated above sea l e v e l and an erosional period started. The eroded material was washed towards the P a c i f i c Ocean. By Lower Tertiary times these sediments had become cemented by groundwater, and compressed to form conglomerate, sandstone, s i l t s t o n e and shale. During t h i s period, volcanic a c t i v i t y resulted i n the formation of dykes and s i l l s . The Burrard and K i t s i l a n o Formations, which outcrop on the Burrard Peninsula, north of the present Fraser Delta, are two such sedimentary formations. Johnston (1923), who f i r s t defined these two formations, was not convinced that there was a prolonged time break between the two formations, and Roddick (1965) now considers them a single unit. Similar formations, with thicknesses of over a thousand meters, underly the present d e l t a . In Late Tertiary times, u p l i f t of the basin occurred and the sedimentary sheets were eroded i n the north to form a broad peneplain sloping down to what i s now the delta area. 1-3 Pleistocene History The Fraser Lowland has undergone at l e a s t three major and one minor ice advance (figure 6). These advances can be distinguished by the sequence.of s o i l deposits layed down during and af t e r each g l a c i a l advance. In the Pre-Olympia period, the Semour and Semiamu Groups are the only recognizable Pleistocene deposits. They may -8- o v e r l i e g l a c i a l and i n t e r g l a c i a l sequences (Danner 1968), or non-glacial Pliocene deposits. The Semour and the Semiamu advances produced two of the three t i l l layers that are found underlying the present Fraser Delta, and which can be seen on exposed r i v e r banks and sea c l i f f s i n the. Fraser Lowland.. . Throughout this work the term ' t i l l ' i s used as a shorter version of ' g l a c i a l t i l l ' , which i s a very compact, unsorted mixture of sand, s i l t , clay and stones, deposited d i r e c t l y beneath the g l a c i e r i c e . This excludes from the ' t i l l ' c l a s s i f i c a t i o n as used herein, material of the same composition which has been deposited through water from f l o a t i n g i c e , and which i s sometimes c a l l e d glacio-marine t i l l . The Olympia Interglaciation, which started about 50,000 years ago, and followed the Semour and Semaimu advances i s the period when the major part of the presently e x i s t i n g non-glacial Quadra sediments were layed down. The Point Grey c l i f f s date to this time (Armstrong 19 56), and are part of a flood p l a i n that may have extended to Vancouver Island. The l a t e r phases of the Olympia Inter g l a c i a t i o n were periods of erosion for many areas. Much of the topography of the Burrard Peninsula and of other areas of the Fraser Lowland were then shaped close to the i r present configuration. The Olympia Inte r g l a c i a t i o n was followed by the Fraser Glacia- ti o n , which started about 18,000 years ago. The f i r s t advance of the g l a c i e r , the Vashon Stade, was the t h i r d of the major ice advances that shaped the topography of the Fraser Lowland. I t dis t r i b u t e d outwash, t i l l and glacio-marine d r i f t over the Quadra" sediments. Surrey T i l l and Newton Stoney Clay are two such deposits that are present i n Surrey to depths of 9 meters (Armstrong 1956). The retreat of the ice occurred predominantly through wasting. The -9- ice thinned and floated, laying down the glacio-marine deposits. As i n the Semour g l a c i a t i o n , the land was depressed by the weight of the 2100 meters of i c e . The Vashon Stade was followed by the Everson Interstade, which started about 13,000 years ago, and subdued the topography by i n f i l l i n g . Mathews et a l (19 70), subdivided the Everson Inter- stade into Post Vashon Emergence and the Pre-Sumas Subsidence. During the Post-Vashon Emergence, which marked the removal of the weight of i c e , the sand and gravel deposits of the Capillano Group were layed down. During the Pre-Sumas Subsidence the g l a c i o - marine Watcom deposits were layed down. The Everson Interstade was followed by the Sumas Stade, which was a minor advance i n which the ice approached to within 40 kilometers of Vancouver. I t started about 11,500 years ago, and lasted for about 1,500 years. I t has been estimated that at this time , the land under present day Richmond was depressed by about 210 meters (Blunden 1973), so that Sumas deposits were layed down as glacio-marine layers of sand, s i l t , clay and unsorted material. I t should be noted that estimates both of the times of the g l a c i a l periods and of the position of the land surface r e l a t i v e to the ocean, w i l l depend on the methods by which these values were obtained. 1-4 Post G l a c i a l (Recent) History After the Sumas Glaciation, which ended between 10,000 and 8,000 years -ago, came a period of i s o s t a t i c adjustment: the Sumas Emergence. This u p l i f t of about 150 meters produced the terraces -10- and beaches on the present day Vancouver North Shore, and subjected the former deep-water deposits of the Fraser River to wave erosion. By 7000 BP (Before Present) the mouth of the Fraser advanced from i t s end-of-Pleistocene position at present-day New Westminster to the position now occupied by Twigg Island. By this time, the southward flow of the Fraser to Boundary Bay had stopped (Blunden 1973). At 2500 BP the land rose about 3 meters r e l a t i v e to the ocean, u p l i f t i n g the s a l t marshes o f f Lulu Island to form Sea Island. The surface of the present delta i s composed of sand and s i l t deposits with some clay, and large areas of peat, the l a t t e r up to 8 meters deep. Due to the method of growth of the delta there exi s t abandoned r i v e r channels which have become i n f i l l e d with sand and s i l t and covered with more recent deposits. The present channels are being kept stable by dredging, dyking and using j e t t i e s to control the currents. The present delta front i s growing due to the deposition of the r i v e r sediments. Johnston (19 23) estimated the rate of delta extension to be 3 meters per year, while Mathews and Shepard, (1962) in a more extensive survey o f f Main Channel, found the rate there to vary on average from 2.3 meters per year at the 6-meter depth to 8.5 meters per year at the 90-meter depth. This increased growth rate at depth means that the slope of the delta front i s more shallow now than i t was 30 years ago. Mathews and Shepard indicate that this may be due to the reduced amount of sand-size sediment deposited, as a r e s u l t of man's dredging a c t i v i t i e s i n the -11- r i v e r channels. Luternauer (1975) has pointed out. that the underwater topography and rate of growth at any p a r t i c u l a r spot on the delta front i s highly variable. Some parts are advancing at various rates while other parts are stable. CHAPTER 2 SOIL CHARACTERISTICS OF THE; FRASER DELTA • 2-1 S o i l Type arid Extent The present delta consists predominantly of loose sand s i l t and clay deposits resting i n a deep basin formed of Pleistodene deposits overlying bedrock. S u r f i c i a l deposits can be i d e n t i f i e d by careful mapping, however the v a r i a t i o n of the s o i l s with depth i s more d i f f i c u l t to determine. By mentally pi c t u r i n g the delta as being composed of an i n f i n i t e number of elements i n three dimensional space, one can see that extensive s u r f i c i a l mapping w i l l only reveal the nature of the elements on one plane i n this space. Knowledge of the t h i r d dimension can only be obtained by probing v e r t i c a l l y . This can be done using d i r e c t d r i l l i n g and sampling methods, or i n d i r e c t geophysical methods. If undisturbed samples could be recovered from the t o t a l length of the d r i l l hole, the nature of a single l i n e of elements in t h i s three dimensional space would be known. This i s an expensive procedure for a r e l a t i v e l y small amount of information. For reasons of cost, most d r i l l i n g w i l l be done with the aim of recovering r e l a t i v e l y undisturbed samples every 1.5 or 3 meters, and noting intermediate changes i n the s o i l s by watching the cuttings being brought to the surface with the d r i l l i n g f l u i d . This method obviously cannot i d e n t i f y a l l the elements on a p a r t i c u l a r l i n e . Geophysical surveys generally involve making traverses along the ground surface: hence the examination i s of s o i l elements defining part of a v e r t i c a l plane. Unfortunately these geophysical methods are capable only of recognizing major changes i n s p e c i f i c s o i l properties, and then only i f the surveys are related to bore- hole data. In terms of the model of elements i n space, th i s means that we know something about the elements on the top plane, but very l i t t l e about elements on other planes, p a r t i c u l a r l y those near the bottom of the space. Knowledge of the processes by which these delta deposits were layed down and the processes which have since shaped them w i l l prove invaluable when trying to deduce the nature of the delta deposits from the small amount of data avai l a b l e . The depth of bedrock i s not well known. Figure 1-1-5 indicates that bedrock l i e s at depths generally over 300 meters throughout-most of the d e l t a . In the northern part of the delta, where the sedimentary rocks slope up to form the Burrard Peninsula, the depths are s l i g h t l y less, probably i n the 210 or 240 meter depth range. A remarkable feature i s the i r r e g u l a r i t y of the buried contact between the bedrock and the Pleistocene deposits. This can be seen both from the i n d i v i d u a l points that were obtained from bore holes, ranging from 250 to 700 meters, and from the more detailed contours to the east of the del t a . These contours were obtained by consultants who correlated detailed geophysical work with borehole data. The i r r e g u l a r bedrock topography would be. the r e s u l t of erosion that took place during the u p l i f t i n -14- Oliogocene and Miocene ages, and the g l a c i a t i o n i n the Pleistocene Age. Above the bedrock l i e the Pleistocene deposits. Figure 1-4 shows that the depth to the top of these deposits i s l i k e l y to be over 120 meters, and i s probably about 210 meters throughout most of the de l t a . The contact between the Pleistocene and the recent deposits slopes upward i n the north, u n t i l the Pleistocene deposits reach the surface on the southern part of the Burrard Peninsula. They also reach the surface to the east i n Surrey and White Rock, and the south on the Point Roberts Upland, which must have been an islan d i n early Pleistocene times. Despite the f a c t that Annacis Island i s close to both the high New Westminster and Surrey areas of Pleistocene deposits, the top of the Pleistocene deposits i s several hundred feet below ground surface there. This i s because a channel had been eroded by the Fraser River. I t i s evident from the discussion of g l a c i a l history that these Pleistocene deposits could consist of up to three layers of g l a c i a l t i l l , possibly separated by i n t e r g l a c i a l deposits of sands, s i l t s , and clays. At any p a r t i c u l a r location, the existence of a complete p r o f i l e with layers of each deposit type i s unlikely, because of the e f f e c t s of erosion. Above the Pleistocene sediments l i e the recent deposits. To obtain an understanding of the sequencing of the beds i t i s important to consider the stages i n (the growth of the de l t a . At the end of Pleistocene times, the waters of the Fraser River -15- emerging from their narrow channel at New Westminster, slowed as they spread out into what was then a part of the S t r a i t of Georgia. The heavy sand-size p a r t i c l e s would quickly be dropped to form the near-horizontal top-set beds as the v e l o c i t y and sediment carrying capacity were reduced. As the v e l o c i t y was further reduced with distance from the r i v e r mouth, s i l t - s i z e p a r t i c l e s were layed down with the smaller sand sizes. At some distance from the mouth, an increase i n slope would occur as increasingly f i n e r grained s o i l s were deposited i n the r e l a t i v e l y s t i l l waters to form the near-horizontal bottom-set beds. This method of development would lead one to expect a s o i l p r o f i l e i n the delta that consists of sands near the surface, grading down to s i l t s i n the middle layers, and clays at depth. This generalized p r o f i l e would be affected by any perturba- tions to such a uniform, i d e a l i z e d system. The flow v e l o c i t y and volume of the Fraser was not constant, so the amount of sediment available to be added to the delta and the distance from the mouth to the spot where a p a r t i c u l a r p a r t i c l e - s i z e drop would vary with time. Seasonal variations of thi s type r e s u l t i n the varves that have been observed i n d r i l l holes on the de l t a . Variations i n bottom topography and ocean currents would modify the shape of the advancing delta. I s o t a t i c rebound and eustatic s h i f t s would change the flow patterns of the r i v e r , and r e s u l t i n a l t e r a t i o n i n the model patterns by erosion. Abandoned r i v e r channels would f i l l with material that was of a d i f f e r e n t nature than that found i n the surrounding lands. An example of thi s i s the old channel that exists on Lululsland to the north-west of -16- Annacis Island and the present southern channel.(Armstrong 1956) It i s from 0.8 to 1.6 kilometers wide and about 6 kilometers long. It can be seen on maps of the s u r f i c i a l deposits because the channel was active 'recently enough to be covered by a small thickness of floodplain s i l t instead of peat. The major part of the recent delta deposits conform generally to the basic p r o f i l e described, and i s thus explicable on the basis of the delta's growth mechanism. There are s u r f i c i a l flood- p l a i n and swamp deposits to shallow depths, usually less than 8 meters, underlain generally by sands to depths of about 30 meters. Under the sand there i s s i l t , which i s underlain by clays at depth. In the Point Roberts area the t i l l layers r i s e up to the surface. The surrounding deposits consist of sands and s i l t s , presumably because the clays s e t t l e d i n the deep water that surrounded th i s one-time i s l a n d . The s u r f i c i a l deposits of the delta area have been described by Armstrong (1956), and those of Richmond have been described i n more d e t a i l by Blunden (1973) . Since the description of s u r f i c i a l deposits i s peripheral to the central purpose of thi s paper, only b r i e f and generalized reference w i l l be made to the i r d i s t r i b u t i o n . The western half of the delta has s u r f i c i a l deposits which consist of material ranging from clays to sandy s i l t s , to depths of up to 4.5 meters, overlying sand or s i l t y sand. Generally this top layer i s graded, with the fi n e r material being found further inland. The western half of the delta i s covered to a large degree by s u r f i c i a l peat layers. These peat layers may be up to 8 meters deep and generally o v e r l i e sand s i l t y sand. Some -17- of the thinner peat layers overly a thin c l a y e y - s i l t layer which rests on the thick sand or s i l t y sand layer. Peat seams are often found i n layers of other material within 4.5 meters of the surface. Blunden (19 73) indicated that i n some areas tlie variable s u r f i c i a l layer o v e r l i e s clay rather than the sand or s i l t y sand usually found. Figures 2-1-1 and 1-1-2 shows generalized s o i l p r o f i l e s of the s u r f i c i a l deposits, and t h e i r d i s t r i b u t i o n within the de l t a . 2-2 S o i l Data Requirements To model the behaviour of a s o i l deposit under the influence of dynamic ex c i t a t i o n the s t r e s s - s t r a i n behaviour of the s o i l under the p r e v a i l i n g f i e l d conditions must be known. C y c l i c testing i n the laboratory has provided an understanding of the general type of behaviour that can be expected over a range of conditions for various s o i l types. The mathematical analysis must incorporate a model of these s t r e s s - s t r a i n c h a r a c t e r i s t i c s that successfully duplicates the behaviour of the s o i l over the stress range anticipated, to a degree of accuracy consistent with the type of analysis. The possession of a r e a l i s t i c s t r e s s - s t a i n law, and a method of analysis with which i t can be used does not i n i t s e l f allow analysis of a f i e l d problem. The c h a r a c t e r i s t i c s )df the s o i l p r o f i l e must be known well enough that the s o i l s t r e s s - s t r a i n law can be determined. This could be done by d i r e c t laboratory testing of the s o i l , or empirically, through a knowledge of more ea s i l y obtainable properties. Unless the problem involves a c r i t i c a l i n s t a l l a t i o n i n a s p e c i f i c area, d i r e c t laboratory testing for s t r e s s - s t r a i n r e l a t i o n s i s not p r a c t i c a l because of the d i f f i c u l t y i n obtaining representative undisturbed samples and the extensive and costly testing procedure. The c a l c u l a t i o n of the s t r e s s - s t r a i n c h a r a c t e r i s t i c s , generally expressed i n terms of shear modulus and damping at various s t r a i n l e v e l s from other more e a s i l y obtainable properties, i s the method that was used i n t h i s study. This method i s p a r t i c u l a r l y suited becasue of the large areal extent of the delta, and the existence of s o i l data from engineering projects. 2-3 S o i l Data Source and Accuracy The development of s o i l p r o f i l e s , which presented the c h a r a c t e r i s t i c s of the s o i l layers adequately for a dynamic analysis, was undertaken i n three stages. The f i r s t stage involved the c o l l e c t i o n of e x i s t i n g data.. These data consisted mainly of the borehole logs and the results of laboratory tests which had been undertaken by l o c a l geotechnical consultants as part of s i t e investigations for engineering projects, and were made available through the generosity of these firms. Where data was not available, either because the engineering property was not one which was commonly tested for, or because the tests were not performed i n the p a r t i c u l a r area where the information was needed, a r e a l i s t i c estimate of the desired property had to be obtained. This operation constituted the second.stage. These properties were estimated through an interpretation of the available data and a knowledge of the ori g i n s of the deposits. The t h i r d stage -19- involved the use of the standard engineering properties that had been obtained i n the f i r s t two stages to develop p r o f i l e s of the s o i l which characterized t h e i r dynamic behaviour. E s s e n t i a l l y , t h i s entailed determining the shear modulus and damping r a t i o of the s o i l layers when subjected to a range of shear s t r a i n s . These two functions describe the s t r e s s - s t r a i n behaviour of the s o i l i n a way that enables mathematical modelling of the s o i l when subject to earthquake-induced ground motions. The engineering properties which are presented here range from fundamental s o i l properties such as f r i c t i o n angle, to index properties such as Atterberg l i m i t s or blow count from the Standard Penetration test which have been correlated empirically with the more fundamental properties. The data that i s portrayed on the borehole logs has been subjected to several potential sources of error before being developed into t h i s presentable form. The l a t e r a l v a r i a b i l i t y of the s o i l should be considered. The log obtained from one d r i l l hole i s assumed to be representative of the immediately surrounding area. While t h i s i s l i k e l y to be true when considering the general form and properties of the s o i l , i t may not be true when looking at d e t a i l s of the p r o f i l e because of the s o i l v a r i a t i o n r e s u l t i n g from the i r r e g u l a r delta growth. Normal d r i l l i n g procedures do not provide the observer with a complete representation of the s o i l , even at the p a r t i c u l a r s i t e being tested. Samples of the s o i l are usually taken at int e r v a l s greater than one meter. The v a r i a t i o n of the s o i l between the points -20- of sampling i s interpreted by the d r i l l e r by q u a l i t a t i v e l y noting the rate of advance of the b i t and the type of material being returned as cuttings. Samples may not be representative of the layer within which they l i e , and are disturbed to varying degrees, depending on the sampling procedure and the degree of care exercised by the d r i l l e r . In the testing of the samples there i s opportunity to introduce error through improper handling or the use of non-standard procedure. In s i t u testing eliminates the problems of t r y i n g to procure an undisturbed sample, but adverse f i e l d conditions make i t d i f f i c u l t to obtain high quality r e s u l t s . Even i f credible r e s u l t s are obtained there may be doubt as to whether the t e s t i t s e l f i s meaningful* Having the d r i l l e r s logs, the laboratory c l a s s i f i c a t i o n of the samples, and the r e s u l t s of any f i e l d or laboratory tests performed, the engineer must use his experience and knowledge of the area to prepare his interpretation of the s o i l p r o f i l e . S i m i l a r l y , the available data had to be interpreted for the research purposes of t h i s project. 2-4 Water Content Water content data i s r e l a t i v e l y easy to obtain for p l a s t i c s o i l s since i t involves measuring the wet and dry weight of a sample, which may be disturbed so long as i t i s not allowed to drain. Water content i s a useful parameter to check i n the c l a s s i f i c a t i o n procedure. In fine-grained samples procured below the water table where 100% saturation can be assumed i t gives the void r a t i o of the -21- s o i l , when multiplied by the s p e c i f i c gravity of the s o l i d s . In cases where the consolidation c h a r a c t e r i s t i c s of the s o i l can be determined, comparison with the actual change i n void r a t i o determined from the f i e l d water content w i l l indicate whether the s o i l type and the method of deposition are constant with depth. The v a r i a t i o n of water content with depth for the clay s o i l s i s shown i n Figure 2-4-1. The water content varies l i n e a r l y from 45% at the surface to 29% at a depth of 30 meters. Samples with organic content have water contents greater than the mean. This, and the p o s s i b i l i t y that water table f l u c t u a t i o n has produced an over-consolidated desiccated layer, accounts for the larger v a r i a t i o n of the moisture content at the surface of the deposit. The water content p r o f i l e i n the s i l t s o i l s has the same form as the clay p r o f i l e , varying from an average of 41% at the surface to 26% at a depth of 60 meters as shown i n figure 2-4-2. The presence of organic material and clays near the ground surface, results i n the larger scattering of the near surface samples towards higher water contents. The water content of the peat s o i l s i s highly variable, as shown i n figure 2-4-3. Generally, seams less than 0.3 meters thick have water contents varying from 100 to 250%. Seams from 0.3 to 1.0 meters thick have water contents varying from 250% to 600%. The larger layers have moisture contents.varying from 600% to 1150%. 2-5 Atterberg Limits The l i q u i d l i m i t and p l a s t i c l i m i t are useful parameters i n the c l a s s i f i c a t i o n of fine-grained s o i l s , p a r t i c u l a r l y clays. As -22- part of the test procedure the samples are remolded, so the disturbed samples recovered during the Standard Penetration Test are suitable for analysis. The tests do not y i e l d r e s u l t s d i r e c t l y i n terms of fundamental s o i l properties, but experience has led to re l a t i o n s which indicate the general c h a r a c t e r i s t i c s of the s o i l . Figure 2-5-1 shows the l i q u i d and p l a s t i c l i m i t s for the clay s o i l s under study plotted against depth. Both are constant with depth, the l i q u i d l i m i t having a mean value of 34% and the p l a s t i c l i m i t a mean value of 22%. A pl o t of the l i q u i d and p l a s t i c l i m i t s with depth for the s i l t s o i l s i s shown i n figure 2-5-2. A close examination of the plot reveals that the points are better characterized by discontinuous v e r t i c a l l i n e s rather than by a continuous sloping l i n e . This feature points to the existence of at lea s t two d i s t i n c t s i l t types. The data plotted above the discontinuity i n the mean l i n e were obtained i n general from a d i f f e r e n t location i n the delta than the data plotted below the discontinuity so thi s phenomina i s unl i k e l y to be the r e s u l t of a sudden change i n the composition of the Fraser River sediments. The mean l i q u i d l i m i t i s about 40% i n the upper s i l t and 33% i n the lower s i l t . The mean p l a s t i c l i m i t i s 30% i n the upper s i l t and 23% i n the lower s i l t . The p l a s t i c i t y index i s defined as the difference between the l i q u i d l i m i t and the p l a s t i c l i m i t , and i s in d i c a t i v e of the range in water contents over which the s o i l retains i t s p l a s t i c i t y . Figure 2-5-3 shows a pl o t of the p l a s t i c i t y index i n the s i l t s o i l s , i t i s constant with depth., varying from 5% to 15%, with a mean of 9%. - 2 3 - Figure 2-5-4 presents a p l o t of the p l a s t i c i t y index i n the clay s o i l s . I t varies from 8% to 1 7 % and has a mean of 1 1 % . The p l a s t i c i t y index can be plotted.against the l i q u i d l i m i t of the s o i l s on the p l a s t i c i t y chart, as shown i n figure 2 - 5 - 5 . According to th e i r plotted position on the p l a s t i c i t y chart, the clay would be c l a s s i f i e d as an inorganic clay of medium p l a s t i c i t y , and the s i l t s as inorganic s i l t s of medium compressibility. These s o i l s , c l a s s i f i e d p r i n c i p a l l y on the basis of grain size, r e t a i n the i r c l a s s i f i c a t i o n when examined i n terms of p l a s t i c i t y . Though the mean values for the s o i l s p l o t quite d i s t i n c t l y on the p l a s t i c i t y chart, when the range of values i s considered, the areas defined overlap s u b s t a n t i a l l y . This i s p a r t i c u l a r l y true i n the case of the lower s i l t , which can almost be c l a s s i f i e d i n these terms as a clay. The l i q u i d i t y index i s defined as the difference between the natural water content and the p l a s t i c l i m i t , divided by the p l a s t i c i t y index. I t provides a measure of the softness of the s o i l i n i t s remolded state by showing how close the moisture content of the s o i l i n i t s natural state i s to the l i q u i d l i m i t . Using the straight l i n e mean relationships developed for the l i m i t s and indices, the l i q u i d i t y index of the clay i s calculated to range from a projected average of 2.0 at surface to 0.64 at a depth of 50 meters. The l i q u i d i t y index of the upper s i l t varies from 1.3 at the surface to 0.55 at a depth of 25 meters and the l i q u i d i t y index of the lower s i l t varies from 1.3 at 25 meters to 0.33 at 60 meters. Each deposit shows the same trend, changing from a very soft consistency i n the upper regions to a s t i f f e r one with depth. - 2 4 - 2 - 6 Compression Index The compression index i s the slope of the plot of void r a t i o versus the logerithum of confining pressure obtained from a consolidation test. As such i t i s in d i c a t i v e of the amount of settlement that can be expected to occur as the r e s u l t of a known increase i n e f f e c t i v e normal pressure. Figure 2 - 6 - 1 i s a plot of compression index against depth for the s i l t s . The presence of two d i s t i n c t s i l t types i s again revealed by a discontinuity i n the compression index values with depth. The upper s i l t has constant compression index with depth, varying from 0 . 2 0 to 0 . 4 0 about a mean of 0 . 3 1 . The p l o t shows the compression index of the lower s i l t to be constant with depth at a mean value of 0 . 2 1 , with data points i n the range from 0 . 1 5 to 0 . 2 6 . The data points from the sandy s i l t s p l o t generally i n the lower end of the th i s range, while those from the clayey s i l t s p l o t i n the upper end. The limited data obtained indicates the compression index of the sand to be almost an order of magnitude less than that of the s i l t , with a value of about 0 . 0 6 . The compression index of the clay i s constant with depth, varying from 0 . 3 3 to 0 . 4 8 with a mean value of 0 . 4 2 as shown i n figure 2 - 6 - 2 . The compression index of clays can also be estimated from the l i q u i d l i m i t using Skempton-'sr-. equation C c = 0 . 0 0 9 ( l i q u i d l i m i t - 1 0 ) . Using the mean l i q u i d l i m i t of 34%, this equation predicts a value of compression index of 0 . 2 2 . This predicated value i s less than the measured values. The reason may be that this clay i s more sensitive than those used by Skempton to define his rela t i o n s h i p between the compression index of remolded and undisturbed clays. The change i n void r a t i o that would r e s u l t from the c o n s o l i - dation of a homogenous s o i l deposit was calculated and compared to the actual void r a t i o change with depth, based on the water content. The void r a t i o i n clay calculated at 50 meters below the surface from the consolidation c h a r a c t e r i s t i c s d i f f e r s only 3% from that deduced from the measured water content. This good co r r e l a t i o n confirms the hypothesis that the clay deposits are normally consolidated and uniform i n structure and c o n s t i t u t i v e components with depth. A similar analysis gives a v a r i a t i o n of 11% i n the void r a t i o s at the 30 meter depth i n the upper s i l t , and an v a r i a t i o n of 20% at the 50 meter depth i n the lower s i l t . This larger v a r i a t i o n may be i n part the r e s u l t of having used a single straight l i n e to characterize the water content with depth instead of f i t t i n g separate l i n e s for the upper and lower s i l t s . An examination of the lower s i l t data reveals that the water content may change less with depth than i s indicated by the single straight l i n e f i t . 2-7 Undrained Shear Strength The undrained shear strength of s o i l s may be determined by performing a vane shear test or an unconfined compression test on an undisturbed sample. The torvane and pocket penetrometer can also be used to give quick results on small specimens, but are not as accurate. Figure 2-7-1 i s a plot of the undrained shear strength of clay with depth as determined by these methods. Below the 6 -26- meter depth the data can be characterized by a straight l i n e passing through the o r i g i n . By assuming a value for the unit weight of the s o i l , the slope of t h i s l i n e can be expressed i n terms of a r a t i o of the undrained shear strength (C) to the e f f e c t i v e overburden pressure (P). This clay has a C/P r a t i o of 0.19. The C/P r a t i o can also be estimated from Skempton's equation, C/P = 0.10 + 0.004 ( p l a s t i c i t y index), which gives a value of 0.14. These two estimates of the C/P r a t i o are i n good agreement considering the small number of data points at depth and that Skempton's equation i s generalized for a l l clays. Samples obtained i n the top 6 meters of the deposit deviate substantially from the straight l i n e C/P r e l a t i o n s h i p due to the overconsolida- tion e f f e c t of surface dessication. The shear strengths i n t h i s upper layer range up to 105 kPa. The undrained shear strength data for the s i l t s are shown plotted against depth i n figure 2-7-2.. As with the clay, a d i s t i n c t dessicated layer i s present above the 6 meter depth. Below the 6 meter depth, the data are widely scattered. The shallowly sloping l i n e having a C/P r a t i o of 0.30 i s f i t t e d to data determined i n one area using a pocket penetrometer, while the steeply sloping l i n e having a C/P r a t i o of 0.11 i s f i t t e d to data gathered over a s l i g h t l y larger area using various techniques. The larger v a r i a t i o n i n the r e s u l t s of the tests could be due both to the fact that the samples were from d i f f e r e n t areas of the delta and to the d i f f e r e n t tests and test techniques used. - 2 7 - The handling of the sample and the rate of testing w i l l a f f e c t the r e s u l t s because completely undrained conditions may not exi s t i n the s i l t - s i z e sample. Though Skempton's. equation was developed for clays, i t may be applicable to a ce r t a i n extent to these s i l t s because, as can be seen from the p l a s t i c i t y chart (figures 2 - 5 - 5 ) , the s i l t s can have a high clay content. The C/P r a t i o determined from Skempton's equation i s 0 . 1 4 , which l i e s between those defined by the two stra i g h t l i n e s . 2 - 8 Dry Density of Sand To measure the density of a s o i l a representative sample must be obtained i n such a way that the o r i g i n a l volume of the sample can be measured or calculated. The volume of a fine grained s o i l sample can be measured as i t i s extracted from the ground by the sampling t o o l , or i t can be calculated i n the laboratory by measuring the water content i f the s p e c i f i c gravity i s known, and the s o i l i s saturated. The water content of sand and therefore the volume cannot be determined from f i e l d samples handled using normal methods because the pore spaces are too large to prevent drainage of the sample before the wet weight can be determined. This means that the volume of sample must be measured d i r e c t l y i n the f i e l d during the sampling procedure. These measurements are d i f f i c u l t to obtain accurately. Figure 2 - 8 - 1 shows the dry density of sand samples taken from various locations i n the d e l t a . There i s no discernable trend with depth, the values ranging from 1 4 kN/m3 to 1 6 . 5 kN/m3, around a mean value of 1 5 kN/m3. -28- The void r a t i o i s related to the dry density by the equation: e = JfwGs -1 y d Here e i s the void r a t i o , Jfw i s the unit weight of water, JTd i s the dry density of the s o i l , and Gs i s the s p e c i f i c gravity. Using a s p e c i f i c gravity of 2.8, and the dry density values shown i n figure 2-8-1, the void r a t i o of the sand was calculated to range from 0.68 to 0.96 about a mean of 0.84 for those sands sampled. 2-9 Standard Penetration Test The standard penetration test involves counting the number of blows of a standard weight that are required to drive a standard sampler into the.bottom of a d r i l l hole. I t gives results i n terms of blow counts, which are dependent on more fundamental properties of the s o i l . Unfortunately, because of the many variables and sources of error involved i n the testing procedure and the absence of complete t h e o r e t i c a l understanding of the mechanism of soil-sampler i n t e r a c t i o n , the r e l a t i o n s h i p between the blow counts and these more fundamental properties i s not well developed. Exis t i n g correlations were developed using p a r t i c u l a r s o i l s and procedures and often under laboratory rather than f i e l d conditions, so that even i f the r e l a t i o n i s accurate under those p a r t i c u l a r conditions, i t i s u n l i k e l y to be uni v e r s a l l y representative. This means that the trends shown i n these correlations should be representative but that the actual -29- magnitudes cannot be found without s p e c i f i c s i t e testing to adjust the c r i t e r i a for s p e c i f i c s o i l s . Despite these disadvantages, the Standard Penetration Test (SPT) i s widely used for s i t e investigation of deep s o i l deposits because i t can be e a s i l y be performed using a standard d r i l l f i g and i t allows recovery of samples. These samples are disturbed but are suitable for use i n some tests and for c l a s s i f i c a t i o n . This laboratory information, obtained from from the SPT sample, when used with the blow count information, allows i n d e n t i f i c a t i o n of the s o i l layers and indicates the v a r i a t i o n within each layer of those properties which influence the blow count. S o i l properties determined from the blow counts of two standard penetration tests can d i f f e r because of the difference i n the state of the s o i l between the two tests, because of a va r i a t i o n i n procedure between the two tests, or because of inaccuracies i n the function used to correlate the blow count with those properties. T h e - f i r s t - i s the difference that we wish to observe, while the second and t h i r d must be regarded as errors, to be minimized. The state of the s o i l , as i t influences the SPT can be thought of i n terms of the stress regime, the strength c h a r a c t e r i s t i c s and the f a i l u r e mechanism. In i t s undisturbed form, the stress state of the s o i l can be described i n terms of an overburden pressure and a l a t e r a l pressure. This indicates the importance of the over consolidation r a t i o , which influences the l a t e r a l pressure and i s effected by the method of deposition of the s o i l and i t s stress -30- history. This stress state w i l l be altered l o c a l l y by the presence of the bore hole, but the magnitude and extent of th i s l o c a l v a r i a t i o n i s d i f f i c u l t to determine. The s o i l strength i s generally expressed i n terms of a cohesion and a f r i c t i o n angle, the values of which w i l l depend on the void r a t i o of the s o i l . The f a i l u r e mechanism which must occur i f the sampler i s to - penetrate into the s o i l , w i l l vary to some degree with s o i l properties. P a r t i c l e size, shape, gradation and orientation are important. In s i l t - s i z e s o i l s below the water table the small pore spaces i n h i b i t the flow of pore f l u i d , r e s u l t i n g i n p a r t i a l l i q u e f a c t i o n of the s o i l surrounding the sampler with each blow, so that the penetration resistance i s greatly reduced from that observed i n the more free draining sand samples. This reduction became s i g n i f i c a n t i n the data reviewed for t h i s work when the s o i l was composed of more than 20 percent s i l t . In a test such as the SPT, e n t a i l i n g an a r b i t r a r y procedure, variations i n the prescribed procedure can be considered errors only i n the sense that they w i l l prevent data obtained i n a non- standard way from being compared with the standard data. Modifications to the test procedure may well r e s u l t i n data which are more meaningful i n the p a r t i c u l a r sense for which that data i s required. In order to assess the accuracy with which any two data sets may be compared, i t i s important to have an understanding of those elements of procedure which can a f f e c t the re s u l t s of the test. Kovacs, Evans, and G r i f f i t h (19 77) undertook.a study to assess the e f f e c t of some of these variables on the measured blow counts. They found that the number of turns of rope around the cathead changed - 3 1 - the f r i c t i o n between rope and cathead, which i n turn affected the speed at which the weight could f a l l , and so; influenced, the amount of energy imparted to the top of the d r i l l s t r i n g . A larger number of wraps of the rope around the cathead reduces the energy imparted and increases the blow count for one foot of penetration. They found that new, s t i f f e r ropes, when released from the cathead, formed loops with a larger radius of curvature than older ropes, reducing f r i c t i o n and increasing the energy imparted. The cathead speed and the mechanism by which the operator released the rope were also found to have an e f f e c t on the energy imparted. These are only some of the sources of v a r i a t i o n i n -the amount of energy imparted to the top of the d r i l l s t r i n g . Though the eff e c t s of these variations could be lim i t e d b y - c a l l i b r a t i n g each d r i l l r i g to a standard impact energy, th i s does not help when comparing old test r e s u l t s , and w i l l not aid i n solution of some of the other problems which have the i r o r i g i n below the ground. Rod length w i l l influence blow count. Gibbs and Holtz (1957) found that the blow count was increased when using a long rod i n a deep hole through loose sands because of the weight of the rod, but was decreased when using a long rod i n dense sands because of the energy l o s t due to the flexure and whipping of the rods. The types of rods used and the i r physical condition w i l l also influence the blow count because of the v a r i a t i o n i n weight, and the differences i n s t i f f n e s s and size o f . e c c e n t r i c i t i e s . The blow count i n the STP i s generally recorded over three increments of 0.15 meters, making the t o t a l penetration of the sampler 0.45 meters. If the d r i l l e r does not exercise care i n -32- cleaning out the bottom of the hole, the loose disturbed s o i l found there w i l l r e s u l t i n low i n i t i a l blow counts which do not characterize the s o i l . U n c h a r a c t e r i s t i c a l l y high blow counts may occur near the end of the 0.45 meter penetration i f the sampler i s over-driven or i f operation becomes obstructed by s o i l within the tube or casing. The ASTM designation D1586-67 describing the penetration t e s t indicates that the f i r s t 0.15 meter increment should be considered as a seating drive, and the number of blows required for the second and t h i r d increments of 0.15 meters should be considered the penetration resistance. Not a l l firms use t h i s procedure. Schnable (1971) suggests that a more l o g i c a l procedure would be to seat the sampler with a few l i g h t taps, and then to record the blow count on the f i r s t 0.3 meters of penetration. He points out that this method requires a s k i l l f u l d r i l l e r , however the whole method i s such that the r e s u l t s of the test w i l l only be s i g n i f i c a n t i f i t i s performed by a s k i l l f u l and experienced d r i l l e r . Schnable must be assuming that the bulb of s o i l affected by the stress r e l i e f i n the bottom of the d r i l l hole i s small enough i n extent and magnitude that the blow count measured there i s not affected by t h i s phenomenon any more that i t i s i n the deeper two 0.15 meter increments. This assumption seems to be supported by the data shown by Schmertmann (1971). He used a ' f r i c t i o n cone SPT formula* with data c o l l e c t e d from cone 1 . .... . penetration tests i n the form of the f r i c t i o n a l and end bearing components of resistance to predict the blow counts i n each of the three 0.15 meter increments that would be expected from a SPT i n the same s o i l . These values were compared with the actual blow count values that -33- were obtained from a c a r e f u l l y executed SPT i n an adjacent hole. The r a t i o of the blow counts i n the f i r s t increment to those i n the t h i r d increment, and those i n the second increment to those i n the t h i r d increment i n loose to medium sands was respectively 0.61 and 0.80 for the predicted values, and 0.63 and 0.81 for the observed values. The excellent agreement of both sets of r a t i o s not only indicates the v i a b i l i t y of Schmertmann1s ' f r i c t i o n cone SPT formula' but also shows that under the controlled testing procedure used, the blow counts i n the f i r s t 0.15 meter increment were not abnormally low. The increase i n the blow count over the three increments i s more probably due to the way that the sampler mobilizes the penetration resistance i n a combination of side f r i c t i o n and end bearing, rather .than due to a change i n s o i l strength with depth. Much of the SPT data c o l l e c t e d for this study included blow counts reported over the f i r s t 0.3 meters of penetration. Though data presented i n this way i s v a l i d i t cannot be compared d i r e c t l y with data recorded over the 0.15 to 0.4 5 meter penetration range. To f a c i l i t a t e data comparison and to permit the use of relationships which have been developed to correlate the blow counts i n the 0.15 to 0.4 5 meter range with more fundamental s o i l properties, a r e l a t i o n - ship was developed to allow the blow counts recorded over the f i r s t 0.3 meters of penetration to be expressed as equivalent blow counts i n the 0.15 to 0.45 meter penetration range. A t y p i c a l p l o t of blow count versus depth for a sand layer i s shown i n figure 2-9-1. One curve shows the v a r i a t i o n of blow count recorded over the f i r s t 0.3 meters of penetration while the other i s a plot of the blow count recorded from 0.15 to 0.45 meters -34- on the same sample. These two curves are roughly p a r a l l e l . To assess the degree of correspondence between the two curves, a method of comparison was needed which would not compare the two curves with an a r t i f i c i a l curve of some a r b i t r a r y shape, but with each other. The change i n blow count between successive tests was used as a method of comparing the curves. I t was assumed that the v a r i a t i o n of the blow count would be l i n e r a l l y proportional to the magnitude of the blow count, so the change in blow counts between two successive tests was normalized by d i v i d i n g - i t by the average of the two values. The r a t i o of these normalized differences was c a l l e d the ' c o e f f i c i e n t of r e l a t i v e curve smoothness1 and was plotted against depth. This c o e f f i c i e n t , developed from blow counts recorded from 0 to 0.3 meters and those from 0.15 to 0.4 5 meters, i s shown i n figure 2-9-2, and the c o e f f i c i e n t from those recorded from 0 to 0.3 meters and those recorded from 0.3 to 0.6 meters i s shown on figure 2-9-3. The points are scattered, but evenly d i s t r i b u t e d around the axis where the c o e f f i c i e n t of r e l a t i v e curve smoothness i s equal to 1. This suggests the v a l i d i t y of the normalizing procedure. Points p l o t t i n g to the l e f t of the axis show that the blow count curve for penetration from 0 to 0.3 meters i s smoother than that for penetration from 0.15 to 0.4 5 meters. This could be due to loose s o i l i n the bottom of the d r i l l hole which would give a reduced but constant number of blows i n the f i r s t few inches which would not show i n the 0.15 to 0.45 meter reading. I t could also be due to the jamming of the sampler i n the l a s t few inches, -35- which would r e s u l t i n an abnormally high blow count i n the 0.15 to 0.45 meter reading. When the points p l o t to the r i g h t of the axis, i t indicates that the blow count for curve penetration from 0.15 to 0.45 i s smoother than that for penetra- tion from 0 to 0.3 meters. This could be due to i r r e g u l a r or improper cleaning of the d r i l l hole before the sampler was placed, which i s i n d i c a t i v e of poor d r i l l i n g technique. Because of the crudeness of the analysis, the v a r i a t i o n i n the points away from the axis would be s i g n i f i c a n t only when several consecutive points exhibited the same trends. With the exception of one set of data shown i n figure 2-9-3 th i s i s not the case. The points l i e scattered about the axis, i n d i c a t i n g that a simple r e l a t i o n s h i p between the blow count asecorded when penetrating from 0 to 0.3 meters and from 0.15 to 0.4 5 meters should e x i s t . To reveal this r e l a t i o n s h i p , the difference between the blow count recorded during penetration from 0 to 0.3 meters and that recorded from 0.15 to 0.45 meters was calculated and normalized by d i v i d i n g i t by the blow count from 0 to 0.3 meters. Expressed as a percentage th i s difference was plotted against depth i n figure 2-9-4. Figure 2-9-5 shows the r e s u l t s of the same procedure applied to the difference i n blow counts recorded from 0 to 0.3 and 0.3 to 0.6 meters. The best f i t s t r aight l i n e characterizing each data set was determined and replotted for convenience i n figure 2-9-6. The increase i n blow count recorded for penetration from 0.15 to 0.45 meters penetration over that recorded from 0 to 0.3 meters varied from 49% at the surface of the sand deposit to 37% at a depth of 30 meters. The increased blow count measured from 0.3 to 0.6 meters penetration over that measured from 0 to -36- 0.3 meters ranged from 66% at the surface to 53% at a depth of 30 meters. This decrease i n the 'per cent d i f f e r e n c e 1 with depth means that the f i r s t blow count increment, from 0 to 0.15 meters contributes proportionately more to the t o t a l reading, with depth, than does the l a s t increment from 0.3 to 0.45 meters. This phenomenon cannot be due to the presence of an i n i t i a l disturbed layer at the bottom of the d r i l l hole as t h i s would produce the opposite e f f e c t , the uniformly loose layer giving nearly constant blow count and increasing the 'per cent difference' with depth. The trend i s more reasonably related to the mechanism by which the penetra- tion resistance i s mobilized. Using the ' f r i c t i o n cone SPT formula' developed by Schmertmann (1971), the t o t a l penetration resistance developed at a p a r t i c u l a r depth of sampler embedment can be subdivided into the percentage due to end bearing, and that due to side f r i c t i o n , (appendix 2). For sands, th i s r e l a t i o n predicts that approximately 72% of the penetration resistance would be provided by end bearing at the 0.15 meter penetration l e v e l , while at the 0.4 5 meter l e v e l the end bearing component would be reduced to 46%. Because the resistance developed by end bearing i s more dominant i n the f i r s t 0.15 meter increment of each test, the reduction i n the 'percent difference' values with depth below the ground surface could be due to a disproportionate increase i n the resistance generated through end bearing. As the sampler i s driven, a compacted plug of s o i l i s formed ahead of i t . The end bearing resistance i s affected by the increased confining pressure at depth and also by the increased energy required to -37- compact the s o i l at depth. To check the usefulness of the r e l a t i o n developed between the blow count recorded from 0 to 0.3 meters and that recorded from 0.15 to 0.45 meters, data from one d r i l l e r describing the blow count from 0.15 to 0.45 meters was compared to data obtained by another d r i l l e r and i n the same area recorded from 0 to 0.3 meters but modified to give the equivalent.0.15 to 0.45 meter readings using the curve i n figure 2-9-6. Figure 2-9-7 shows the curve developed from the blow count recorded by one d r i l l e r for penetration from 0 to 0.3 meters i n each test. The curve describing the blow count data Recorded during penetration from 0.15 to 0.45 meters i s depicted i n figure 2-9-8. Figure 2-9-9 i s a comparison of these two curves and the curve modified from the 0 to 0.3 meter penetration curve to give the equivalent blow count for the 0.15 to 0.45 meter penetration. The comparison between the measured and modified curves showing the blow count for the 0.15 to 0.45 meter penetrations' sgood, p a r t i c u l a r l y considering that the two test sets were performed by d i f f e r e n t d r i l l e r s , each using th e i r own technique and equipment, and i n view of the fact that the d r i l l holes were not i n the same spot, even though close i n loca t i o n . Additional blow count information from d r i l l holes i n the Fraser Delta i s shown plotted against depth i n figures 2-9-10 to 2-9-21. A curve has been f i t t e d to each data set, and where necessary the conversion shown i n figure 2-9-6 has been applied to this curve express the data i n terms of the equivalent blow count from 0.15 to 0.45 meters of penetration on each sample. -38- The data i n each figure are widely spread from the mean due to i r r e g u l a r i t i e s i n the s o i l i t s e l f , and i n the testing procedure. In figure 2-9-12 data obtained by two d r i l l e r s i n the same a r e a are plotted together. One data set predicts higher blow counts with depth than does the other, pointing to a v a r i a t i o n i n the d r i l l i n g technique and equipment. Figure 2-9-15 i s composed of v e r t i c a l l i n e s indicating average blow counts over the depths defined by each l i n e , rather than points i n d i c a t i n g the measured blow count at a s p e c i f i c depth. Because of th i s presentation of averaged data, the curve f i t t i n g gives r e s u l t s which are less i n d i c a t i v e of the s o i l s present. Figure 2-9-11 shows a p l o t of blow count from d r i l l holes i n the Sturgeon Bank Sea Island area. Those samples closer to Sea Island generally show higher blow counts than those farther out on the banks, though a single curve i s used to characterize a l l the data. The curves representing the blow count for penetration from 0.15 to 0.45 meters are summarized i n figure 2-9-22. These are the curves that w i l l be u s e d to determine s o i l properties, since the correlations between s o i l properties and the SPT have been developed using sampler penetration from 0.15 to 0.4 5 meters. The curves are grouped together i n two major concentrations, with some lone curves in d i c a t i n g lower blow counts. The f i r s t group i s composed of curves which run roughly i n a straight l i n e from a blow count (N) of 14 at 6 meters to an N of 62 at 18 meters. This group i s composed of data from bore holes along the northern part of the delta, one s i t e on Sea Island, one south of Sea Island on Number Three Road, one near the head of the delta, and one south of the Oak Street Bridge. The second group i s composed of curves which run i n a straight l i n e from an N of 15 at 6 meters to an N of 3 5 at 18 meters. Below 18 meters the N value remains almost constant to the l i m i t of the data at 40 meters. This group i s composed of data from s i t e s throughout the central portion of the d e l t a . There are s i t e s on Annacis Island, on South Eastern Lulu Island, i n Ladner, and i n the Sturgeon Bank-Sea Island area. The curve characterizing the s o i l i n the Brighouse area of Richmond resembles the curves of group 2 to a depth of 12 meters, where the slope changes and N remains constant, or decreases s l i g h t l y with depth. The Tilbury Island curve shows a low N u n t i l a depth of 27 meters i s reached, where i t joins the second group of curves. The Roberts Bank curve depicts a very low N, ranging from 11 at a depth of 6 meters to 41 at a depth of 30 meters. Despite the trends that may seem to be apparent regarding the d i s t r i b u t i o n of the s o i l p r o f i l e types, i t would be a mistake to make generalizations, other than that the N value appears to be less on the banks than throughout the r e s t of the delta. This i s so because th i s data was c o l l e c t e d for the purpose of understanding the s o i l p r o f i l e at three p a r t i c u l a r locations rather than every- where i n the d e l t a . I t may however, on the basis of the wide d i s t r i b u t i o n of data, be reasonable to assume that the sand types shown here are t y p i c a l and representative of these throughout the delta. 2-10 Relative Density of Sands The r e l a t i v e density of a s o i l i s a measure of the density -40- of the s o i l r e l a t i v e to i t s most dense and most loose states. I t i s defined as follows: Dr = e -e max e —e max min where Dr = Relative Density e = i n - s i t u void r a t i o e void r a t i o of sample i n i t s loosest state max - e . = void r a t i o of sample i n i t s densest state min Accordingly, the larger the value of r e l a t i v e density the more dense the sample. A standard procedure for the test i s presented i n ASTM Designation D2049-69, however many firms use non-standard techniques. The errors inherent i n the r e l a t i v e density t e s t were investigated by Tavenas, Ladd, and LaRochelle (1972). In addition to the errors introduced by the use of non-standard technique, and the error i n determining the i n - s i t u void r a t i o from f i e l d volume measurements, they found that the formulation of the equation for r e l a t i v e density magnified laboratory errors which i n themselves were within reasonable bounds. They found that the v a r i a b i l i t y of the r e l a t i v e density was usually 10 times that of the maximum and minimum densities, giving errors i n the r e l a t i v e density i n the order of plus or minus 30 to 47%. Because of the d i f f i c u l t y i n determining the r e l a t i v e density and the large amount of data available from the SPT, correlations have been developed between the N value and r e l a t i v e density. Although this increases dramatically the amount of r e l a t i v e density information -41- that i s available, i t decreases the accuracy of such data. To develop the rel a t i o n s h i p , the r e l a t i v e density must be determined for s o i l s of known N value, knovnproperties and known state of stress. Such a complete re l a t i o n s h i p would be d i f f i c u l t to formulate and impractical for f i e l d a pplication where the important parameters a f f e c t i n g the r e l a t i v e density are not any better known than the r e l a t i v e density i t s e l f . For thi s reason the r e l a t i v e density and N value are generally correlated with the v e r t i c a l e f f e c t i v e stress only, though Saito (197 7) points out that the mean e f f e c t i v e p r i n c i p a l stress would be better, and de Mello (1971) i n his extensive state of the a r t report on the SPT indicated that important e f f e c t of the f r i c t i o n angle. Other errors are incorporated i n the r e l a t i o n through the laboratory determination of the r e l a t i v e density for the c o r r e l a - t i o n . The majority of the relations i n existence were developed by simulating f i e l d conditions i n the laboratory. This simulation i s not exact, so additional errors are introduced at thi s point. In addition to t h i s , there are a l l the errors inherent i n the SPT. Despite the problems involved i n the application of such empirical c o r r e l a t i o n s , they continue to be used because they give large volumes of inexpensive information. When using these correlations i t must be remembered that they were developed by testing a s p e c i f i c s o i l i n a p a r t i c u l a r fashion, so they should only be used q u a l i t a t i v e l y u n t i l the c r i t e r i a can be adjusted by l o c a l testing. De Mello (1971) warns of the danger inherent i n using these correlations b l i n d l y when he says ' i f any sand i s not -42- c l o s e l y similar to the (tested) sands, the chances of adequately representing the behaviour by analogy with the (test) results w i l l be very small.' Many researchers have developed relationships between the blow count of the SPT and overburden pressure at various values of r e l a t i v e density. In the Fraser River Delta, the water table i s generally within a few feet of the ground surface, and the sand deposits quite uniform. The dry density of the sand i s 3 shown i n figure 2-8-1 to be i n the range from 14.3 kN/m to 15.5 kN/m3, which suggests that a reasonable assumption for the 3 saturated unit weight would be 19.2 kN/m . Using t h i s value, the s o i l p r o f i l e can be idea l i z e d as one having buoyant unit weight 3 of 9.4 kN/m , constant with depth. This allows the blow count- r e l a t i v e density information to be plotted against depth as well as overburden pressure. Figures 2-10-1 and 2-10-2 show f i v e such r e l a t i o n s . Though the curves are similar i n trend there can be a 50% difference between the r e l a t i v e density values predicted for a sample at a p a r t i c u l a r depth and with a p a r t i c u l a r N value. If the SPT data i s to be used to advantage, i t i s important to determine which of these relationships best describes the sands present i n the del t a . To this end, these relationships can be examined on the basis of various c r i t e r i a . The experimental methods used to determine the relationships can be examined. The grain size curves of the test s o i l s can be compared to those of .samples from the f i e l d . Direct measurements of the r e l a t i v e density determined from f i e l d samples can be compared to predicted values. The v a r i a t i o n of r e l a t i v e density with depth can be checked for conformity with - 4 3 - the r e l a t i o n s predicted from a knowledge of the history of the deposit. The Bazaraa curves (1967) were developed from data, obtained i n the f i e l d , and would therefore be subject to the errors i n blow count and r e l a t i v e density measurement outlined previously. The other researchers t r i e d to simulate f i e l d conditions i n the laboratory. Though th i s allowed c a reful measurements to be taken i n a controlled environment, i t would not eliminate a l l the sources of error present i n the f i e l d and could introduce other errors through inaccurate modelling of the f i e l d conditions. The laboratory procedures involved d r i v i n g the sampler into a large container of s o i l which had been placed at some known r e l a t i v e density, and which could be subjected to a known v e r t i c a l stress by loading the plate covering the surface of the container. However, the container used to hold the s o i l could not produce precisely the same boundary conditions as those i n the f i e l d . Marcuson and Bieganousky (1977) improved an e a r l i e r method by using a container formed of alternating steel and rubber rings stacked to the required height, so that the container could deform s l i g h t l y i n the v e r t i c a l d i r e c t i o n when the top plate was loaded, thereby reducing the effects of the side f r i c t i o n . The placement of the s o i l at uniform density throughout the container i s d i f f i c u l t . The method of obtaining a known r e l a t i v e density varied between researchers, but i n some cases the density control was not good. In the laboratory, the ef f e c t s of the f r i c t i o n between the rod and the hole or casing were not reproduced, and the rod length; though varied to a ce r t a i n extent i n the testing -44- programs, would not correspond exactly to the f i e l d s i t u a t i o n . The majority of the tests were performed on a i r dried samples. Gibbs and Holtz (1957) performed a series of tests on submerged samples, but were uns a t i s f i e d with th e i r r e s u l t s , and recommended that the curves developed for the a i r dried sand be used for the submerged s i t u a t i o n . Marcuson and Bieganousky (19 77) performed the i r series of tests on submerged samples, but did not achieve complete saturation. One of the problems encountered i n te s t i n g the submerged samples i s that within the small testing tank, the pore pressure response system r e s u l t i n g from the dynamic loading would not duplicate that found i n the f i e l d . The grain size d i s t r i b u t i o n of the sands tested to develop the r e l a t i v e density-blow count re l a t i o n s h i p are shown i n figure 2-10-3 and the grain size d i s t r i b u t i o n of sand samples obtained from the Fraser Delta are shown i n figure 2-10-4. The samples were procured from the western part of the delta so these curves may not be representative of the t o t a l delta sand deposits. The sands used by Gibbs and Holtz (1957) and Schultze and Melzer (1965) compare poorly with the s o i l s i n the del t a . They are larger i n grain size and more well graded than the delta s o i l s . The sand used by Shultze and Menzenbach (19 61) compares more favourably, being more uniform and smaller i n grain s i z e . The sands used by Marcuson and Bieganousky (1977) are clo s e s t i n grain size to the samples from the d e l t a : they are s i m i l a r . i n uniformity, though they l i e i n the upper range of actual grain s i z e . With knowledge of the s o i l c h a r a c t e r i s t i c s and the v a r i a b i l i t y of the depositional environment, the shape of the curves r e l a t i n g -45- blow count to e f f e c t i v e overburden pressure for various values of r e l a t i v e density can be predicted. I t was found i n section 2-6 that the change i n void r a t i o with depth determined from the water content values i n the s i l t and clay s o i l s could be accounted for by the consolidation of the s o i l under the weight of the overburden. This indicates that the depositional environment has been constant throughout the time when these deposits were layed down. Accordingly, one would expect the sand deposits to d i f f e r i n density with depth i n a manner prescribed by the consolidation c h a r a c t e r i s t i c s of the s o i l . The values of r e l a t i v e density and dry density with depth which are shown i n table 2-9-1 were used with an assumed s p e c i f i c gravity i n the solution of simultaneous equations to y i e l d average values of maximum and minimum void r a t i o for the sand deposit. The analysis yielded an average maximum void r a t i o of 1.2 and an average minimum void r a t i o of 0.66. These values were used with the compression index of the sand to predict the change i n r e l a t i v e density that would occur with depth as a r e s u l t of the deposits consolidating under i t s own weight. Over a change i n depth of one logarithmic increment, say from 3 to 30 meters, the r e l a t i v e density was found to increase by an increment of 10.1%. The various r e l a t i v e density r e l a t i o n s shown i n figures 2-10-1 and 2-10-2 were checked to see whether they s a t i s f i e d t h i s c r i t e r i o n , by overlaying them on the average blow count curves shown i n figure 2-9-22. Recall that there were two general curve shapes, one where the N value increased l i n e a r l y to a depth of 18 meters and then remained almost constant with depth, and another where the -46- N value increased l i n e a r l y to a larger value at a greater depth. The former group of curves was examined f i r s t . The Schultze and Menzenback and the Bazaraa curves correspond most c l o s e l y to the predicted curve shape. These were followed, i n order of best f i t by the Marcuson and Bieganouski, the Gibbs and Holtz, and the Schultze and Mel.zer curves. When the theory describing the increase i n r e l a t i v e density with depth was applied to the l a t t e r group of curves poor correspondence was achieved with the r e l a t i v e density r e l a t i o n s . The Schultze and Melzer curves provided a better f i t than the others, but one that was not p a r t i c u l a r l y close. This suggests that the l a t t e r curve group represents p r o f i l e s where the s o i l s or the depositional environment were not uniform with depth, so that the r e l a t i v e density increases with depth more than could be expected from the consolidation of the deposit under i t s own weight. This phenomina could also be explained i f the sands i n t h i s l a t t e r group had a very high s i l t content so that the consolidation c h a r a c t e r i s t i c s would resemble those of the more compressable s i l t s , predicting a much larger increase i n r e l a t i v e density with depth. However, an examination of the d r i l l logs does not lend support to t h i s hypothesis. Actual f i e l d measurement of r e l a t i v e densities are c r i t i c a l in the selection of the r e l a t i v e density r e l a t i o n which best describes the s o i l s of the de l t a . The values of r e l a t i v e density from table 2-10.-1 are shown at the appropriate depths along with the plo t of N against depth for the d r i l l holes i n that area, from figure 2-9-22. The large v a r i a b i l i t y i n the r e l a t i v e density measurements i s more l i k e l y due to errors i n the measure- ment than to actual v a r i a b i l i t y i n the s o i l . The average r e l a t i v e density measurement i s 63%, so i t was assumed, from the knowledge of the shape of the curve, that the r e l a t i v e density would increase quickly from a value of 58% at a depth of 3 meters, to a value of 68% at a depth of 30 meters. On the basis of these values, and the r a t i o of the change i n r e l a t i v e density to the r e s u l t i n g change i n N value at various depths, as observed from the r e l a t i v e density r e l a t i o n s i n figures 2-10-1 and 2-10-2, the approximate l i n e s showing the change i n N value with depth for r e l a t i v e densities of 60% and 80% were constructed i n figure 2-10-5. These li n e s were compared with the r e l a t i v e density curves. The c o r r e l a t i o n with the Schultze and Menzenbach curves was very good. The Gibbs and Holtz curves gave a reasonable prediction, but the other r e l a t i o n s were less s a t i s f a c t o r y . Scotton (1977) performed a series of c a r e f u l l y controlled r e l a t i v e density measurements on the near-surface s o i l s at Sturgeon Bank. Using these and N values from nearby d r i l l holes, he concluded that the Bazaraa r e l a t i v e density r e l a t i o n s better described these s o i l s than the Gibbs and Holtz r e l a t i o n s . This i s consistent with the observation that the Gibbs and Holtz r e l a t i o n over-estimates the r e l a t i v e density calculated on the basis of the curve shape determined from the consolidation c h a r a c t e r i s t i c s , though the difference could be due i n part to the tests being performed on a d i f f e r e n t s o i l type. On the basis of these discussions, the Schultze and Menzenbach relations were selected as best describing the r e l a t i v e density -48- c h a r a c t e r i s t i c s of the delta sands. This r e l a t i o n i s much closer i n form to the Gibbs and Holtz than to the Bazaraa r e l a t i o n . At depths less than 4.5 meters, where the Schultze and Menzenback r e l a t i o n i s not defined, the r e l a t i v e density may be better described by the Bazaraa than the Gibbs and Holtz r e l a t i o n s . I t i s importaat to remember that t h i s choice of a r e l a t i v e density r e l a t i o n was based on a small number of r e l a t i v e density measure- ments and that the choice of this r e l a t i o n does not mean that i t i s the r e s u l t of the most accurate testing program. Rather, i t best describes the p a r t i c u l a r s o i l s i n the Fraser Delta. 2-11 F r i c t i o n Angle of Sands The angle of i n t e r n a l f r i c t i o n depends primarily on the r e l a t i v e density or void r a t i o of the s o i l , the grain size d i s t r i b u t i o n and the grain shape. Its d i r e c t dependence on the stress state of the s o i l i s small. The f r a c t i o n angle i s generally determined using the data from t r i a x i a l or shear tests to define the f a i l u r e envelope of the s o i l . Figure 2-11-1 i s a plot of f r i c t i o n angle against dry density for two sand types. One i s a fine to medium sand, and the other i s a s i l t y sand. Both s o i l types show the expected trend of increasing f r i c t i o n angle with increasing dry density. The s i l t y sand had a f r i c t i o n angle 5 or 6 degrees greater than the clean sand at the same dry density. De Mello (1971) suggests that the apparent f r i c t i o n angle may be more fundamental and more s i g n i f i c a n t parameter...to use i n correlations with the blow count of the SPT than the r e l a t i v e -49- density. I t may be possible to develop a single r e l a t i o n s h i p between the N value and f r i c t i o n angle with confining pressure which i s applicable to a l l sand types. Once the f r i c t i o n angle had been determined, the r e l a t i o n between i t and the r e l a t i v e density could be developed for each s o i l type. The curves developed by De Mello are shown i n figure 2-11-2 i n a form r e l a t i n g the N value and the depth -below surface for various values of f r i c t i o n angle. This was done using an average value for the s p e c i f i c gravity and assuming the s o i l to be saturated. De Mello's curves describing the fine sand, and the average of the fine and coarse sands are shown. The relations are i n the form of straight l i n e s because of the form of s t a t i s t i c a l analysis used. Shown with these relations are the plots of N value against depth for the s i t e s where the samples used to determine the f r i c t i o n angles shown i n figure 2-11-1. 3 Using the mean dry density from figure 2-8-1 of 14.9 kN/m , figure 2-11-1 indicates- that the fine to medium sand has a f r i c t i o n angle of 38.5 degrees. Using De Mello's r e l a t i o n with the mean of the fine and medium curves i n figure 2-11-2 res u l t s i n a predicted f r i c t i o n angle of 41 degrees for the penetration p r o f i l e shown. This i s a reasonable c o r r e l a t i o n . The s i l t y sand samples were taken from Roberts Bank, where no separate measurements of dry density were obtained, so the average dry density achieved i n the tests was used to give an anticipated f r i c t i o n angle of 37 degrees, from figure 2-11-1. Using the set of curves describing the fine sand i n figure 2-11-2 and the N p r o f i l e for the Roberts Bank area, a f r i c t i o n angle of 36 degrees was predicted. This i s a good cor r e l a t i o n , which tends to confirm that the N value can be related -50- more successfully to the f r i c t i o n angle than to. the r e l a t i v e density for a large range of s o i l types. CHAPTER 3 DYNAMIC ANALYSIS 3 - 1 Type of Analysis In areas of seismic a c t i v i t y , the design of engineering structures should incorporate some method of considering the effects of possible earthquakes. The method used to assess these e f f e c t s w i l l depend on the type and the purpose of the structure and the problems associated with i t s p o t e n t i a l f a i l u r e . Various c r i t e r i a are considered when attempting to characterize the effects of an earthquake on a p a r t i c u l a r structure. The maximum acceleration and the frequency content of the motion are important. The frequency content i s of p a r t i c u l a r i n t e r e s t as structures having a predominant period close to that of the earthquake w i l l expeience large deflections. Most buildings are designed to absorb the energy of the earthquake through the d u c t i l i t y of the i r members. For such designs, the duration of the strong motion and the duration of any large acceleration pulses are important, as the energy-absorbing capacity of the structure i s f i n i t e . To analyze the e f f e c t s of an earthquake on a structure, whether i t be a building, an earth structure, or a buried structure; the changing c h a r a c t e r i s t i c s of the motion and th e i r effects,can be followed from the source to the bedrock at the s i t e , through the s o i l layers to the surface, and through the building as a whole, - 5 2 - to i n d i v i d u a l members. This procedure involves a modelling process, which becomes increasingly d i f f i c u l t and c ostly as more stages are included. At some stage, a break i s made from consider- ation of the earthquake's dynamic ef f e c t s to consideration of the s t r u c t u r a l behavior i n terms of standard design methods. The National Building Code of Canada has divided the country into zones of varying seismic r i s k and defines the ground acceleration on rock or deep s o i l deposits that may be used to calculate equivalent horizontal i n e r t i a l loading. These loads are included with other loads i n the design of the members. The effects of a p a r t i c u l a r earthquake on a series of structures can be examined using a response spectrum. A response spectrum shows the r e l a t i v e magnitude of the various uniform harmonic waves that combine to give the complex motion of an earthquake record and can be thought of as a p l o t of v e l o c i t y , displacement, or acceleration response of a single-degree-of-freedom structure of varying natural frequency and a p a r t i c u l a r amount of damping to a s p e c i f i c earthquake. I t i s a function both of the earthquake and the structure. This form of presentation i s valuable because most structures can be roughly characterized by a natural frequency and damping. The response spectrum indicates whether the structure i s l i k e l y to undergo a large response r e l a t i v e to similar structures of other periods and gives an i n d i c a t i o n of the magnitude of the response for a p a r t i c u l a r earthquake. Methods e x i s t whereby the response spectra of potential earth- quakes can be predicted from the spectra of recordcJearthquakes. Housner produced a set of curves which represents the average response spectra of several recorded earthquakes for various percentages of c r i t i c a l damping. The curves can be scaled according to the magnitude of the earthquake that i s anticipated. Newmark developed a method where spectra are produced for a structure by applying to the ground spectra and m u l t i p l i c a t i o n factor which i s related to the structural damping. The ground spectra i s a curve drawn for convenience to represent the maxi- mum anticipated ground v e l o c i t y accelerations and displacement; He found that the v e l o c i t y , which i s related to the energy absorbed; the acceleration, which i s related to the forces experienced, and the displacement, which i s related to the di s t o r t i o n ; were c r i t i c a l design parameters i n d i f f e r e n t s t r u c t u r a l period ranges. The Newmark method produces a design curve that i s an envelope of analyzed cases. The next stage i n complexity involves modelling the s i t e to a n a l y t i c a l l y produce a spectrum which t y p i f i e s the building response. Using an earthquake record that i s representative of the motion on bedrock and a model describing the dynamic "properties of the s o i l , the re s u l t i n g ground surface motions can be mathematically determined and the surface response calculated. If c a r e f u l l y executed, this procedure should y i e l d a response spectrum that i s more t y p i c a l of the l o c a l s i t e conditions than the methods previously described. The f i n a l stage i n complexity involves l i n k i n g the structure and s o i l together through the use of f i n i t e elements and modelling the whole system to f i n d the actual response of the structure to a •particular earthquake on bedrock. The attempt of this method i s to - 5 4 - incorporate the effects of s o i l structure i n t e r a c t i o n . This i s desirable because the f r e e - f i e l d response of s o i l i s not the. same as the response of s o i l which underlies a building. F i n i t e element analysis i s also suited to problems where the s o i l cannot be modelled as semi-in f i n i t e horizontal layers. However, this method of analysis i s co s t l y , and for general problems may not y i e l d r esults which are any more r e l i a b l e than those obtained for the one-dimensional analysis. A good combination of p r a c t i c a l i t y and accuracy i s provided by the dynamic analysis of methods that use the properties of the s o i l deposits to produce a response spectrum on surface from an assumed earthquake motion at bedrock. Because of t h e i r complexity when applied to r e a l problems, these methods generally require the use of a computer. There are two general classes of programs; those which use a lumped mass model and those which provide a solution to the wave equation. The lumped-mass method uses a s o i l model consisting of discrete masses connected by s t i f f n e s s elements which characterize the properties of the various s o i l layers. The wave equation methods are based on the theory of one-dimensional wave propagation i n a continuous medium. Both of these classes of analysis are based on the assumption that the earthquake can be respresented by a shear wave propagating v e r t i c a l l y through horizontal s o i l layers. This assumption i s more v a l i d for deep than for shallow earthquakes. Computer programs based on the wave-equation methods use a fou r r i e r transform to develop the f o u r r i e r spectrum. Transfer functions which incorporate the dynamic e f f e c t of the s o i l deposit -55- are developed to produce a f o u r r i e r spectrum which describes the ground-surface motion i n the frequency domain., Because the f o u r r r i e r spectrum contains a l l the information describing the ground motion, i t i s possible to produce the predicted ground surface record i n the time domain i n the form of an acceleration record. In t h i s study, a wave propagation solution was employed to predict the surface motion c h a r a c t e r i s t i c s . The SHAKE program developed i n Berkley (Schnabel, Lysmer, and Seed, 19 72) was used, with a minor modification to allow the use of a greater range of dynamic s o i l properties. SHAKE uses an i t e r a t i v e visco- e l a s t i c method of analysis to solve a non-linear problem. When s o i l i s deformed i t follows a h y s t e r i t i c stress s t r a i n path, the shape of which i s dependent on the stress s t r a i n amplitude, as depicted i n f i g . 3-1-1. The SHAKE program approximates t h i s behaviour through the use of a secant shear modulus, and a damping r a t i o . As shown.in figure 3-1-2, the shear modulus i s defined by a str a i g h t l i n e through the end points of the stress loop, and the damping r a t i o i s related to the r a t i o of the area of the hysteresis loop and the area of a triangular area defined by the shear modulus and the end-point of the loop. The SHAKE program uses th i s equivalent li n e a r modulus and a viscous damping r a t i o to determine the s t r a i n amplitude which w i l l define a new modulus and damping r a t i o . The i t e r a t i o n continues u n t i l the solution s t a b i l i z e s . I t i s assumed that the average s t r a i n amplitude i s 65% of the peak experienced from the t o t a l earthquake amplitude record. The SHAKE program has -56- th e same l i m i t a t i o n s as other similar dynamic analysis i n that i t performs a one-dimensional analysis of horizontal semi- i n f i n i t e beds and uses an approximate mathematical solution. The input to the SHAKE program consists of a description of the s o i l p r o f i l e at the s i t e and an acceleration record to be used as the object motion on bedrock. The s o i l i s described i n terms of layers with similar dynamic properties, varying i n thickness from less than 2 meters near the surface to up to 50 meters at depth. The dynamic properties are presented i n terms of the maximum shear modulus determined at low s t r a i n amplitude; attenuation curves describing the reduction i n modulus experienced as the s t r a i n l e v e l increases, and the maximum damping r a t i o and i t s v a r i a t i o n with s t r a i n amplitude. 3-2 S o i l P r o f i l e s and Dynamic Properties The dynamic analysis i n thi s study was undertaken i n two stages. In the f i r s t stage of the analysis, the SHAKE program was used to predict the surface motions of several s i t e s i n the Fraser Delta. The 19 76 Pender Island earthquake was used as the bedrock input, and the dynamic properties at the s i t e s were calculated from the information gained i n the examination of the delta s o i l s . These motions were compared with the actual motions recorded for the 1 9 7 6 Pender Island earthquake at those s i t e s , to form an estimation of the accuracy of the modelling procedure and input parameters. With t h i s knowledge, the second stage of analysis could be undertaken. This involved subjecting the p r o f i l e developed i n the f i r s t stage to data representing earthquakes -57- of various magnitudes to assess the e f f e c t of large motions on the s i t e s . Because of the necessity of comparison between the predicted and measured earthquake i n the f i r s t stage, the s i t e s were limited to those where surface records for the 1976 Pender Island earth- quake had been obtained. Three s i t e s s a t i s f i e d t h i s c r i t e r i o n . They consist of one at Roberts Bank, one on Annacis Island and one i n the Brighouse area of Richmond, as shown i n figure 3-2-1. These s i t e s are widely spaced across the area of the recent delta, and their p r o f i l e s are representative of the s o i l s found through- out the d e l t a . The three p r o f i l e s that were developed and the s o i l models that were used for the computer analysis are shown i n figures 3-2-2, 3-2-3 and 3-2-4. Generally, the nature of the near-surface deposits i s well known from d r i l l holes i n the v i c i n i t y of the s i t e . Below depths of 45 meters to 60 meters, the nature of the deposits, and t h e i r properties have been gleaned from a few deep d r i l l holes and a knowledge of the history of the delta formation. The l a t e r aids i n the extrapolation of known s o i l c h a r a c t e r i s t i c s near surface to those at depth. Depths to the top of the t i l l deposits were estimated by projection of the t i l l surface slopes as indicated by d r i l l holes which intercepted the t i l l , and by c o r r e l a t i o n with a few i s o l a t e d deep holes. The depth to bedrock was estimated from a few deep d r i l l holes, and vibro-seismic p r o f i l e s . Figure 1-1-5 shows the large i r r e g u l a r i t y i n the bedrock surface, i n d i c a t i n g that the bedrock depths estimated could e a s i l y vary by 30 meters from the true depth. -58- The Brighouse p r o f i l e s consist of 3.7 meters of clayey s i l t overlying sand to about 45 meters. Below that i s s i l t grading downwards to clay. T i l l i s estimated to be §t 19 8 meters and bedrock at 305 meters. Because of the sequence of g l a c i a t i o n that effected the present Fraser Delta area, there i s a p o s s i b i l i t y that the t i l l could contain layers of i n t e r - g l a c i a l deposits of sand, clay or s i l t , though because of t h e i r lack of resistance to abrasion and errosion, these deposits may have been completely eliminated. The Roberts Bank p r o f i l e consists of 9.1 meters of sandy s i l t f i l l and s i l t overlying sand with some s i l t layers to about 60 meters. Below t h i s , s i l t i s expected to 107 meters, where t i l l i s estimated to occur, again with the p o s s i b i l i t y of i n t e r g l a c i a l deposits. Bedrock i s estimated to be at 228 meters. The Annacis Island p r o f i l e i s si m i l a r to the Roberts Bank p r o f i l e . I t consists of 6 meters of sandy s i l t overlying sand to about 37 meters with sandy s i l t to about 91 meters, where t i l l i s estimated to occur, possibly with some i n t e r g l a c i a l deposits. Bedrock i s estimated to be at 220 meters. The s o i l model consists of s o i l layers ranging from a few feet i n thickness at the surface, to 30 meters i n thickness at depth. This approach i s taken since a single value of each dynamic parameter must be selected to be representative of a l l the s o i l i n each layer. The layers are shown c l a s s i f i e d by the major soil-type they represent, as th i s w i l l determine the method used to derive the dynamic properties of the layer. The dynamic properties of the s o i l s shown i n the p r o f i l e are input i n terms of a maximum shear modulus, maximum damping r a t i o , and reduction curves which show the rel a t i o n s h i p between these maximum values and the s t r a i n l e v e l . The dynamic s o i l c h a r a c t e r i s t i c s have been determined from r e l a t i o n s developed by others using both laboratory and f i e l d tests. In the laboratory, the material being tested i s well known but i t i s d i f f i c u l t to apply test conditions that are representative of the s i t u a t i o n found i n the f i e l d , while i n f i e l d t esting the reverse i s true. Both laboratory and f i e l d tests can be sub- divided into two groups; those which attempt to measure the response of the s o i l system to dynamic ex c i t a t i o n , and those which measure the shear wave v e l o c i t y to the s o i l , from which' the modulus can be calculated. Common laboratory techniques for the measurement of the s o i l stress s t r a i n properties include the resonant column test, ultrasonic pulse tests, shake table tests and c y c l i c t e sts. The c y c l i c tests may be either t r i a x i a l , simple shear, or t o r s i o n a l . These c y c l i c tests can be either stress or s t r a i n controlled. Common f i e l d tests are seismic r e f r a c t i o n survey, cross hole survey, down hole survey, or surface-save techniques. These give the modulus i n d i r e c t l y through measurement of the shear wave v e l o c i t y . Vibro-seismic methods can also be used, as can the c y l i n d r i c a l i n s i t u test developed by Bratton and Higgins (1978), i n which accelerometers on a surface grid measure the response of the s o i l to an explosion and an i t e r a t i v e procedure i s used to determine the s o i l properties. Because of the lack of knowledge of the material being tested -60- in the f i e l d , most modulus and damping r e l a t i o n s have been developed from laboratory data. I t i s important, therefore, to e s t a b l i s h a co r r e l a t i o n between the f i e l d and laboratory data, which often d i f f e r because of the varying s t r a i n l e v e l s at which the tests were performed. The maximum shear modulus has been calculated for the s o i l layers i n the three p r o f i l e s from several r e l a t i o n s and i s shown i n figures 3-2-5, 3-2-6, and 3-2-7. Hardin and Black (1968) developed the relat i o n s h i p for cohesive and cohesionless s o i l s : G =1230(2.973-e)2 (OCR) k CT.* (psi) mdx — 1 + e where the factor K depends on the p l a s t i c i t y index of the s o i l as follows: P l a s t i c i t y Index K 0 0 20 .18 40 .30 60 .41 80 .48 100 or greater .50 The above equation relates the maximum shear modulus (G , . - , v ) to the void r a t i o (e) , the over consolidation r a t i o (OCR) , a factor related to the p l a s t i c i t y index (K). and the mean normal e f f e c t i v e stress (<r„). Seed and Idr i s s (1970) developed separate relations for sand and for clay. For sand they use the re l a t i o n s h i p : G =1000 (K,). ( V a ) h (psf) max * max - 6 1 - Here W0 i s the mean normal e f f e c t i v e stress and (K_) i s a factor 2 max which depends upon the r e l a t i v e density of the sand. For clay s o i l s the following relationship was developed: G =Su (K) (psf) Max c i Here, Su i s the undrained strength, and K i s a constant which ranges from 1100 to 4000 with an average of 2200. Ohsaki and Iwasaki (1973) bypass the steps required to ascertain the r e l a t i v e density by using the folowing formulation: GMax = 1 2 0 0 ( N ) * 8 (t/m2) They relate the maximum shear modulus d i r e c t l y to the standard penetration test blow count (N), Murphy et a l (1978) have developed a graphical re l a t i o n s h i p for the g l a c i a l t i l l used i n t h e i r study which relates the maximum shear modulus to the mean consolidation stress and maximum past pressure. The maximum shear modulae of the various layers i n the p r o f i l e s were calculated from these equations using the s o i l data presented i n Chapter 2. The p l a s t i c i t y index was read d i r e c t l y from the plots shown i n Chapter 2, as was the undrained shear strength, though the lack of information at depth made i t impossible to obtain a measure of the c ratio,-accurately enough to extrapolate P the s i l t data. The blow count data was taken d i r e c t l y from the curves of blow count for 0.15 to 0.45 meter penetration for the s i t e area i n question, as shown i n Chapter 2. The r e l a t i v e density values were computed from the blow count curves using the Schultze and Menzenback re l a t i o n s h i p . The void r a t i o s were.computed from the water content of the clays and s i l t s , and the r e l a t i v e densities of the sands. The void r a t i o data was extrapolated to depth by- assuming that the change i n void r a t i o was due only to consolida- tion of the material under the weight of the overburden, an assumption that was supported by the data c o l l e c t e d i n Chapter 2. This allowed the void r a t i o to be computed using the c o e f f i c i e n t of consolidation. In cases where the s o i l had been over consolidated by g l a c i a t i o n , the rebound of the s o i l was considered. The mean pr i n c i p l e e f f e c t i v e stress was computed from the void r a t i o , s p e c i f i c gravity and using an assumed value of the c o e f f i c i e n t of l a t e r a l pressure which varied from 0.6 for the soft clays to 0.4 for the t i l l s . The overconsolidation r a t i o was determined at the surface from the plots of undrained shear strength versus depth, and the c r a t i o . At depth the overconsolidation r a t i o was determined P from a knowledge of the g l a c i a l h i s t o r y . The engineering properties of the t i l l s were taken from the values presented by Klohn (1965), Radhakrishna and Klym (1974), Clarke (1966) and Murphy et a l (1978). The properties of the rocks are based on average values for the rock type anticipated, as presented by Clark (19 66). The values of maximum shear modulus computed using these methods are shown for the three s o i l p r o f i l e s i n figures 3-2-5, 3-2-6, and 3-2-7. It can be seen that despite the change i n s o i l type between layers, the modulus predicted by each method increases smoothly with depth, there being no major d i s c o n t i n u i t i e s , except where the t i l l and rock layers are encountered. In figure 3-2-7, for the Brighouse p r o f i l e the range of the maximum shear modulus was shown. This range was based on the maximum range anticipated i n those parameters which are used to calculate the modulus. The range, though large i s s t i l l smaller than the range between the modulus values determined by d i f f e r e n t methods, which suggests that e f f o r t s should be made to make a choice between the analysis methods used rather than concentrating on the possible errors i n the data. The plots show that the Ohsaki and Iwasaki method generally predicted the highest modulus, and the Hardin and Black method the lowest, with the Seed and Idriss method l y i n g i n between. This i s i n keeping with the findings of Anderson et a l (1978) , who compared these methods with values measured i n the f i e l d . They found that the Hardin and Black method underestimated the f i e l d value by a factor of 1.8, that the Seed and Idriss method underestimated the f i e l d value by 1.6 and the Ohsaki and Iwasaki method overestimated the f i e l d value by a factor of 1.4. The trends seen i n the p r o f i l e s calculated for the Fraser Delta s i t e s are si m i l a r to those found by Anderson et a l , but the magnitude of the v a r i a t i o n i s not as great. In the t i l l layer, the use of the re l a t i o n s h i p formulated by Murphy et a l gave values of shear modulus increasing with depth. For the Brighouse p r o f i l e , values of shear modulus were also calculated using the Harden and Black formulation for t i l l , and for layers of clay and sand interbedded between t i l l layers. The modulus predicted for the i n t e r g l a c i a l clay and t i l l was about 80% of that predicted for t i l l by Murphy's method. The modulus of the i n t e r - g l a c i a l sand was less than 50% of the value for t i l l predicted by Murphy's method, because of the lack of any cohesion or over-consolidation e f f e c t . -64- For the computer analysis, the Harden and Black mean curves were used i n the sediments above the t i l l because they gave values of the modulus i n a l l s o i l layers. The data available was not s u f f i c i e n t to permit accurate use of the Seed and Idriss formula i n deep s i l t layers. The Ohsaki and Iwasaki method could not be used i n s i l t because i t was not designed for that, and could not be used i n clay because of lack of data. The modulus predicted by Murphy et a l was used i n t i l l layers. The maximum damping r a t i o i s an important input parameter for the dynamic analysis. Seed and Idriss (1970) show plots of damping r a t i o versus s t r a i n for sands and clays from a large number of tests by various researchers. They show the maximum damping r a t i o i n sands to be from 21% to 28%, and that of clay from 26% to 32%. Hardin and Drnevich (1972) developed relationships from experiments on various s o i l types. They •found that for saturated sands: DMax = 2 8 " 1 , 5 ( l o g n ) For saturated s i l t s : D., = 26 - 4 f * + .If* - 1.5 (log n) Max o ^ and for clays: D„ = 31 - (3 + .03f)v"'^ + L S f 3 * - 1.5 (log n) Max o Here T Q ' i s the mean e f f e c t i v e p r i n c i p a l stress i n kg/cc, f . i s the frequency i n cycles/second and n i s the number of cycles. A v a r i a t i o n within a reasonable range of n and f does not have a large e f f e c t on values of maximum damping r a t i o . These two parameters form part of the equation because the laboratory -65- samples which were tested to form the relat i o n s h i p were subject to cycles of complete stress reversal at a c e r t a i n frequency. The s t r e s s - s t r a i n c h a r a c t e r i s t i c s could be determined for any par t i c u l a r cycle. For th i s computer analysis, values for n and f must be selected which are representative of the ir r e g u l a r motion of the s i g n i f i c a n t part of the earthquake. Seed,Idriss and Kiefer (1969) present a relat i o n s h i p which correlates the earthquake magnitude with the distance from the source of energy release and the predominant period. For the nearby earthquakes analyzed i n th i s study a frequency of 3.3 cycles per second was chosen using t h e i r r e l a t i o n s h i p . The true value w i l l vary with the earthquake used for the object motion and the s o i l layer considered. Methods have been developed (Seed, Idriss,MaRdisi and Banerjee (1975) whereby an i r r e g u l a r stress- s t r a i n history can be represented by a uniform stress series, however because the input to the computer program consists of the average damping over several s o i l layers experiencing a range of of earthquake motions, this analysis would not be of benefit, so a mean value of 15 was selected. The maximum damping r a t i o s computed using these relationships are shown for the three p r o f i l e s i n figures 3-2-8, 3-2-9, and 3-2-10. The .damping r a t i o for the t i l l s o i l s was taken from the average o f those presented by Murphy et a l . I n s u f f i c i e n t data .was available to attempt to characterize a change i n damping r a t i o with depth i n the t i l l . The damping r a t i o anticipated i n layers of sand, clay and s i l t which might be present as i n t e r g l a c i a l deposits between t i l l layers i s shown i n the Brighouse p r o f i l e . The i n t e r g l a c i a l sand and clay would have higher damping rat i o s than the t i l l , while the i n t e r g l a c i a l s i l t would have lower damping. The damping c h a r a c t e r i s t i c s of the rock were obtained from average values presented by Schnabel, Lysmer and Seed (1972) , Both the shear modulus and damping r a t i o vary with the st r a i n amplitude. Seed and Idr i s s (1970) present damping reduction curves for clay and sand, "however,. they indicate only a range of values with an average for each s o i l type. Hardin and Drnevich (1972) present a method of ca l c u l a t i n g the relationship between the maximum shear modulus, and the shear modulus at any given s t r a i n l e v e l . I t has the following formulation: G = 1 where = y 1 + a exp (- frb) G 1 + X. ttr Xr Max h Here: X = s t r a i n l e v e l G =the shear modulus at s t r a i n l e v e l G w =the maximum shear modulus Max a =a cycle factor which depends on the s o i l type b =a s o i l c o e f f i c i e n t y =the reference s t r a i n The reference s t r a i n can be thought of the s t r a i n that the s o i l would experience i f i t had a constant shear modulus of G M a x a ^ d was strained to f a i l u r e . I t can be computed from G M a x and a Mohr plo t of the s o i l stress state. -67- The modulus reduction curves were computed by th i s method for the sands, s i l t s , clays and the t i l l layers i n the p r o f i l e s . The reduction curves for a l l the s i l t and clay layers were v i r t u a l l y i d e n t i c a l , as were a l l the curves of the sand layers and of the t i l l layers. The mean of each curve set i s plotted i n figure 3-2-11 along with the r e l a t i o n for rock obtained from Schnabel et a l (19 72) . . i.n3. uiy th - and another curve for t i l l from Murphy et a l (1978). This additional t i l l curve was obtained by r e p l o t t i n g the laboratory data developed by Murphy et a l without a r b i t r a r i l y forcing the curve to go through an end-point that was determined by geophysical methods. This additional curve predicted a greater reduction i n modulus at a p a r t i c u l a r s t r a i n l e v e l than did the Hardin and Drnevich curves. Hardin and Drnevich also proposed the following r e l a t i o n - ship describing the dependence of the damping r a t i o on the s t r a i n l e v e l : D_ = 1 -_G D„ G Max Max Here D i s the damping r a t i o at s t r a i n l e v e l 2f , and D M a x i s the maximum damping r a t i o . This r e l a t i o n , applied to the curves i n figure 3-2-11 yiel d s the re l a t i o n s h i p for sands, clays and s i l t s and t i l l shown i n figure 3-2-12. The damping reduction curve for rock was obtained from Schnabel et 'al (1972) . For the computer analysis the Hardin and Drnevich damping reduction curves were used for the sands, s i l t s , clays and . . t i l l s , and the Schnabel et a l curves were used for rock. The Seed and -68- Id r i s s reduction curves for s o i l were too general and the Murphy et al. curve did not follow the pattern set by the Hardin and Drnevich curves. Anderson (1976) found that the Hardin and Drnevich curves were more representative of sample behaviour than the Seed and Idriss curves. Arango et a l (19 78) present data which also indicates that the Hardin and Drnevich equations are superior to those of Seed and I d r i s s . 3-3 Pender Island Earthquake Correlation Ground surface acceleration records were obtained for the 1976 Pender Island earthquake, from the P a c i f i c Geoscience Centre in V i c t o r i a . The object was to compare the surface motions recorded at the three s i t e s at which p r o f i l e s had been developed, with the surface records obtained by dynamic analysis, using the SHAKE program and the motions recorded on rock for the same earthquake at the Lake Cowichan S a t e l l i t e Station as the base input motion. The s o i l properties developed i n Section 3-2 were used i n the analysis. Variations were made i n these properties and p r o f i l e s to.determine the extent to which inaccurate data would e f f e c t the analysis r e s u l t s . The question as to whether scaling of the input earthquake motion (Lake Cowichan record) would be necessary was examined. This scaling could be necessary because of a difference i n the distance from the earthquake source to the Lake Cowichan s i t e and the Fraser Delta s i t e s , or a difference i n the rock type through which the seismic waves passed. Scaling could also be necessary because the motions recorded at the -69- surface rock outcrop would be d i f f e r e n t than those experienced by a buried rock surface, even i f both s i t e s were close together. In examining these problems i t was necessary to keep i n mind the accuracy of our knowledge of the dynamic s o i l properties at the s i t e s and the potential magnitude of errors that could be induced by an i n v a l i d assumption regarding the scaling required. The epicentral distance of the Lake Cowichan s i t e i s 54km, while the epicentre distance of the Fraser Delta s i t e s ranges from 37 km to 52km. Figures presented by Schnabel and Seed (1972) give a re l a t i o n s h i p between the maximum acceleration, the magnitude of the earthquake, and the distance from the source of energy release. This r e l a t i o n s h i p compares well with other similar relationships, as shown by Trifunac and Brady (1975), who found that for distances greater than 30km the acceleration amplitude varied inversely with the square of the distance to the source. For a small earthquake, such as the Pender Island earthquake with a magnitude i n the order of 5 to 5.5, these relationships show that the difference i n maximum accelerations for these s i t e s would be small. The earthquake was not scaled on the basis of distance from the source since other factors which could not be accounted for, such as bedrock topography, would have a greater e f f e c t on the maximum accelerations. The bedrock underlying the three Fraser Delta s i t e s consists of r e l a t i v e l y low shear wave v e l o c i t y sandstone, conglomerate, and shale, overlying higher v e l o c i t y g r a n i t i c rocks. Since the low ve l o c i t y rocks are present i n thicker strata at the Fraser Delta s i t e s than at the Lake Cowichan s i t e , i t i s possible that seismic waves travelling, to. the delta s i t e s would experience more damping than those t r a v e l l i n g to the Lake Cowichan s i t e . Because of the d i f f i c u l t y i n assessing the magnitude of these e f f e c t s no attempt was made to compensate for them by scaling. This e f f e c t may compensate to'some degree for the difference from the epicentre to the Lake Cowichan and Fraser Delta s i t e s . The theory of shear wave propagation i n a one-dimensional system i s described by Schnabel, Lysmer, and Seed (1972). They point out that the horizontal displacements at any layer i n the system are caused by two components of the shear wave. One component i s due to the incident wave t r a v e l l i n g upwards towards the surface and the other i s caused by the r e f l e c t e d wave t r a v e l l i n g back into the earth. At the free surface, the magnitude of the incident and r e f l e c t e d waves are the same. It i s reasonable to assume that the incident waves at the rock outcrop w i l l be of the same amplitude as the incident waves at a nearby buried rock layer, since the incident waves are not effected by the overlying s o i l s . However, while the r e f l e c t e d wave at the rock outcrop i s equal to the incident wave, the relected wave amplitude at the buried rock surface w i l l be less than the incident wave amplitude because of the damping q u a l i t i e s of the overlying s o i l layers. From t h i s i t can be seen that the amplitude of the buried base rock motion w i l l be between 50% and 100% of the amplitude of the rock outcrop motion. I t would be 50% i f the wave propagating up from the buried rock surface and r e f l e c t e d back had been -71- completely absorbed before i t reached the rock surface again. It would be 100% i f the wave had not changed i n character on i t s return to the buried rock l a y e r . The actual r a t i o of amplitudes would depend on the damping i n the deposit, the impedence r a t i o between the deposit and the rock, and the frequency d i s t r i b u t i o n of the wave energy i n the rock r e l a t i v e to the resonant frequency of the deposit (Schnabel, Lysmer, Seed, 1972). This means that the difference i n the response spectra for a p r o f i l e which had been computed using the true motion on the buried rock layer and the response spectra for the same p r o f i l e which had been computed using a nearby measured rock outcrop motion would be greatest at the periods where the largest amplification had taken place between the rock motion and the surface motion. Lysmer, Seed, and Schnabel (1971) performed a series of analyses on p r o f i l e s consisting of up to 90 meters of sand and clay over rock, and found that the maximum acceleration i n the buried rock layers was between 85% and 92% of the maximum acceleration oh nearby rock outcrops, for rock having a shear wave v e l o c i t y of 1800 m/s, and between 80% and 85% of the maximum acceleration for rocks having a shear wave v e l o c i t y of 1200 m/s. The three s i t e s i n the Fraser Delta were analyzed using a base rock modulus of 16,000 MPa, which corresponds to a shear wave v e l o c i t y of less than 2400 m/s. Lysmer et a l (1971) also found that the response spectra for the surface motions were e s s e n t i a l l y the same i n shape whether computed using the rock outcrop motion or the actual motion on - 7 2 - the buried rock as the object motion. Because there was l i t t l e difference i n the response spectra, and the difference i n the rock outcrop motion and buried motion was dependant on the properties of the overlying s o i l and not e a s i l y scaled, i t was decided to perform the analysis using the unsealed records obtained from the Lake Cowichan s i t e rock outcrop, which we are assuming would have simi l a r motion to a rock outcrop i n the Fraser Delta, i f such an outcrop existed. The res u l t s of the analysis could be examined i n the l i g h t of the known e f f e c t s that t h i s v a r i a t i o n from r e a l i t y would produce. Comparison of the computed motions and recorded motions for the three s i t e s was made using acceleration response spectra. This was done because the ground surface accelerations are related to the maximum forces experienced by structures at the s i t e , and because the spectra presents the acceleration that would be experienced by structures of varying fundamental periods. The acceleration response spectra were produced for single degree of freedom structures having 5% of c r i t i c a l damping. This corresponds to the amount of damping that would be present i n most buildings when the structure had reached y i e l d , where most of the energy of the earthquake would be absorbed. Response spectra were produced for the layers that marked the d i v i s i o n between s o i l s of d i f f e r e n t types to permit an assessment of the r e l a t i v e e f f e cts of each s o i l , type on the. ground motion. The response spectrum that was used for comparison with the actual recorded surface spectrum was one which was computed at a 1.5 meter depth below the s o i l surface. This was done to try to account for the fact that the accelerographs were on r i g i d concrete f l o o r slabs i n buildings, which added a normal load. In the case of the Brighouse recording, the accelerograph was in a basement. 3-4 Seismicity and the Design Earthquake The Fraser River Delta l i e s i n one of the most seismically active zones i n Canada. A network of accelerographs has been set up by the Earth Physics Branch of the Department of Energy, Mines and Resources, to monitor earthquake a c t i v i t y i n t h i s area. Through information obtained from these recorders and from others i n the United States, an understanding of the magnitude and frequency of the earthquakes i n this area, and the causitive mechanism as related to plate tectonics, has emerged. The records magnify the ground motions to give plots of the earthquake motions in three coordinate d i r e c t i o n s . By examining the phases of the records produced by the a r r i v a l of body and surface waves, i t i s possible to estimate the distance and asimuth to the epicentre and the depth to the focus. A l l accelerograph records that show the p a r t i c u l a r event can be used to locate the epicentre. Inaccuracies i n the location can r e s u l t from inaccurate acceleration records, or a poor knowledge of the time at each of the recording stations. The v e l o c i t y c h a r a c t e r i s t i c s of the earth's crust must also be modelled, so the solution cannot be expected to be exact. The accuracy of location w i l l vary with the size of the earthquake and the location of the recording stations, so that -74- both scattering and systematic errors are introduced. Earth- quakes of small magnitude, or those at a large distance from recording centres may not be detected. A r e l a t i v e l y unbiased map of epicentres can be produced by eliminating the low magnitude earthquakes, which are detected only i n areas where there are nearby seismographs. Bias due to the locations of the recording stations i s a p a r t i c u l a r problem with h i s t o r i c a l l y old earthquakes, which may have occurred at a time when there were very few recording stations. They would be detected only i f they were large and near an inhabited area and could not be so accurately located. Figure 3-4-1 from Milne et a l (1978) shows d i s t r i b u t i o n of earthquakes greater than magnitude 2 i n the Puget Sound - S t r a i t of Georgia area. The earthquakes which are of a magnitude which i s subject to regional bias because of the d i s t r i b u t i o n of accelerographs are marked with an"X", while others are graded by magnitude. On a regional scale, the boundaries between the major l i t h o s p e r i c plates (Figure 3-4-2) correspond to areas of high seismic a c t i v i t y . Milne et al.(1978) have described t h i s r e l a t i o n s h i p . The Queen Charlotte-Fairweather f a u l t , the northern equivalent of the San Andreas f a u l t , marks a d i v i s i o n between the P a c i f i c and America plates. These plates have a r e l a t i v e motion of about 5 cm/year. South of 51 degrees la t i t u d e , the ridge fracture . zone between the Juan de Fuca and Explorer plates marks the area of i n t e r a c t i o n between these two small plates and the P a c i f i c plate. In the continental area the Explorer and Juan de Fuca plates are subducting under -75- the /America plate at a rate of 2^ cm/year. Mile e t a l (1978) found that the seismic records indicate that the int e r a c t i o n between the two oceanic plates and the America plate i s i n the form of a s t r i k e s l i p fault.rather than the thrust f a u l t normally expected i n areas of subduction. This i s due to the oblique convergence of the plates. Rogers and Hasegawa (1978) point out that the majority of larger earthquakes i n thi s continental region occur at depth, within the continental crust. The tectonic forces causing these earthquakes probably r e s u l t from the motion of the upper plates i n the subduction zone. An assessment of the maximum probable earthquake motion to occur i n the Fraser Delta can be made on the basis of several c r i t e r i a , which must consider both the magnitude of the earthquake, and i t s horizontal distance and depth from the s i t e , since the earthquake c h a r a c t e r i s t i c s change as the waves propogate through the lithosphere. These c r i t e r i a are the s t r a i n release versus time r e l a t i o n s , magnitude versus time r e l a t i o n s and the anticipated mechanism. Strain release i s a measure of the t o t a l energy released by an earthquake, and i s related to i t s magnitude. By p l o t t i n g s t r a i n release against time and assuming a constant rate of potential s t r a i n accumulation, estimates can be made of the maximum expected earthquake on a p a r t i c u l a r f a u l t system. In figure 3-4-3 Milne et aL (1978) show the p o s s i b i l i t y of a s i g n i f i c a n t earthquake,, greater than magnitude 7, i n the Georgia S t r a i t - Puget Sound area. Various methods of examination of accelerograph records are used to determine the magnitude of an earthquake. These -76- methods may give results which vary by one unit. I t i s possible to f i n d empirical relationships between earthquake magnitude and return period for a p a r t i c u l a r area. These relationships are d i f f i c u l t to determine accurately because of the bias i n magnitude estimates. At low magnitudes, events may go undetected, and at high magnitudes events may be quite rare. Milne et a l (1978) have analyzed the data for the Georgia S t r a i t - Puget Sound area and have formed a relat i o n s h i p which can be represented as shown i n figure 3-4-4. This r e l a t i o n predicts that a one-hundred-year earthquake i n the Fraser Delta area would have a magnitude of about 7.4 The maximum magnitude of an event i s li m i t e d by the mechanism and by the extent of the f a u l t i n g . Milne et a l (1978) estimate that the maximum magnitude earthquake i n the Puget Sound - Georgia S t r a i t area would be greater than 8 for thrust f a u l t i n g , which i s the most common f a u l t type found i n subduetion zones. However, the earthquakes i n thi s area appear to exhibit s t r i k e s l i p or normal f a u l t i n g mechanisms so the maximum magnitude i s l i k e l y to be less than 8. The distance from the Fraser Delta si t e s to the source of energy release i s an important factor i n assessing the earthquake motion since i t e f f e c t s the predominant period and the accelerations experienced. Large magnitude events, due to the tectonic forces developed i n the subduetion process, are l i k e l y to occur at depths of up to 60km within the continental lithosphere (personal communication G. Rogers). These events would probably not cause surface rupture, so they would not necessarily be -77- associated with the presence of surface f a u l t s . Such earth- quakes could reasonably be expected to have a source of energy release 20 or 30km within the earth's crust. An earthquake with a hypocentre closer to the earth surface has a greater l i k e l i h o o d of being related to an e x i s t i n g f a u l t with surface expression. Rogers and Hasegawa (1978) point out that the magnitude 7.2 B r i t i s h Columbia Earthquake of 1946 may have resulted from rupture along the projection of an e x i s t i n g f a u l t . Some geological interpretations have inferred that there i s a f a u l t e x i s t i n g i n the S t r a i t of Georgia. Muller (1977) shows this interpretation, while others, (Jackson and Seraphin (19 76)), do not indicate the presence of a f a u l t . The existance or otherwise of a f a u l t . i n the S t r a i t of Georgia, where surface rock exposures cannot be mapped, i s d i f f i c u l t to v e r i f y and would be open to the interpretation of i n d i v i d u a l geologists, based on an understanding of the regional geology and seismic patterns. Because the presence of a f a u l t i s not generally, accepted, the assumption i s made i n th i s study that i f such a f a u l t exists i n the S t r a i t of Georgia, and i f i t could undergo move- ments due to an earthquake, that the source of energy released would be no closer to the Fraser Delta s i t e s than the 20 or 30km expected from the deep earthquake. For the purposes of th i s work earthquakes of several magnitudes were studied. On the basis of the information just outlined, an earthquake of magnitude 7.4 at a distance of 30km was selected as the maximum probably earthquake. In order to assess the e f f e c t of earthquake i n t e n s i t y on the s o i l s , earthquake -78- of magnitude 8.0, possible i f there was f a u l t i n g i n a thrust mechanism, and of magnitude 6.5 were also selected for analysis. Several design earthquakes were used i n an attempt to observe the effects of earthquakes i n general, since i t i s unlikely that the actual earthquake occurring at the s i t e would resemble completely any p a r t i c u l a r design earthquake. Ideally, the design earthquakes should have the same c h a r a c t e r i s t i c s as the potential earthquake. They should be caused by the same mechanism, have the same magnitude, and have the same distance to the hypocentre through similar geologic formations. Because of the form of the analysis used,the input must be an earth- quake recorded on rock. The Western Washington earthquake of 1949 and the Puget Sound Earthquake would be the id e a l design earthquakes i f recordings had been obtained on rock, since they s a t i s f y the above c r i t e r i a . I t would be possible to perform an analysis similar to that now being undertaken, to obtain a base rock motion at the recording s i t e s of these two earthquakes using the surface record, i f the s o i l s deposits at the s i t e were well known. This was not done, because the data were not r e a d i l y available and such an.analysis would introduce additional errors into the Fraser Delta analysis. Recordings made on rock outcrops of earthquakes of similar magnitude and distance from source to s i t e were used i n the computer analysis. This eliminated the need to scale the period, which as can be seen from Figure 3-4-5 i s not a well defined or accurate procedure. The earthquakes chosen were the N21E component of the magnitude 7.6 Kern County earthquake of 19 52 - 7 9 - as recorded 56km from the source at Taft, the S69E component of magnitude 6.6 San Fernando earthquake as recorded 26km from the source at Lake Hughes Station #4, and the N21E component of the magnitude 6.6 San Fernando earthquake as recorded 21km from the source at Lake Hughes station #12. The Kern County earthquake i s of a larger magnitude but with a source at greater distance than the p r i n c i p l e design earthquake for the Fraser Delta s i t e s , while the two San Fernando earthquakes are of a smaller magnitude but a shorter distance. Figure 3-4-5 shows that i t is l i k e l y that a l l three recordings would have a predominant period s i m i l a r to the anticipated earthquake. The San Fernando earthquake exhibits predominately l a t e r a l s l i p motion, which i s the type of motion most l i k e l y to occur i n the Fraser Delta area. The analysis used i n the SHAKE program i s based on the assumption, that the earthquake record input as the exc i t a t i o n motion repeats i t s e l f to produce a continuous record. The records used i n the analysis were the f i r s t 16 seconds of recorded motions of the selected earthquakes. This time-period contains the major part of the strong motions. The three design earthquakes were scaled according to the r e l a t i o n developed by Schnabel and Seed (1972) and reproduced i n figure 3-4-6. This r e l a t i o n s h i p was developed from earth- quakes which occurred i n C a l i f o r n i a , but N u t t l i (1973) stated that"there i s no evidence for a marked contrast i n attenuation properties of the earth as observed i n C a l i f o r n i a and i n Western North America". At a distance of 30km from the source, of energy release t h i s r e l a t i o n gives the maximum acceleration due to magnitude -80- 8.0, 7^4, and 6.5 earthquakes as 0.33g, 0.25g, and 0.16g respectively. The earthquake recordings were not scaled i n any other way, to f a c i l i t a t e comparison of the re s u l t s on the basis of only one changing parameter. -81- CHAPTER 4 RESULTS 4-1 Pender Island Earthquake Correlation The r e s u l t s of the dynamic analysis using the p r o f i l e s developed i n Section 3 and the Lake Cowichan earthquake as object motion, are presented i n the form of acceleration response spectra. They are compared to the spectra of the actual surface motion as recorded at the three s i t e s . The degree of correspondence between the recorded.and computed curves i s examined and the significance of.the curve shape as a function of varying s o i l properties i s investigated. The acceleration response spectra for a single-degree-of freedom structure with 5% of c r i t i c a l damping produced when the Lake Cowichan record of the Pender Island Earthquake was used as the object motion on the profilesdeveloped.in Section 3, are shown with the spectre of the actual surface record for the same earthquake i n figure 4-4-1, 4-1-2 and 4-4-3. The spectra of the ground motions recorded on two mutually perpendicular component axes are shown for both the recorded and the computed motions. It w i l l be noticed that the abscissa axis has been plotted using a variable scale, to show the important d e t a i l at low periods while allowing a f u l l range of periods to be presented. The curves were not smoothed to develop a single curve to represent the c h a r a c t e r i s t i c s of each of the recorded and computed motions. This was done to show the v a r i a b i l i t y between the spectra of two components of the same earthquake, and because producing a smooth curve from such a data base. -82- could be misleading. Figure 4-1-1, shows the spectra of the recorded and computed motions at the Annacis .Island s i t e . The two curve sets compare very favorably. There i s a major peak i n the . spectra at a period of 0.25 seconds to a magnitude of about 0.14g and a minor peak at a period of 0.8 seconds to magnitude of 0.08g. The spectra of the computed motion shows a peak i n the high period range, where none was observed i n the spectra of the recorded motion. This i s probably the r e s u l t of the mechanics of the analysis and w i l l be discussed l a t e r . The spectra developed from the computed and recorded motions at the Brighouse s i t e are shown i n figure 4-1-2. A major peak to an acceleration of O.llg i s present at a period of 0.2 seconds. The curves are similar i n shape, though the spectra developed from the computed motions do exhibit minor peaks i n the high period range, which are not obvious i n the spectra of the recorded motions. The spectra developed for the Roberts Bank motion are shown i n figure 4-1-2. The general shape of the computed and recorded spectra i s the same. The major exc i t a t i o n i s at a period of 0.2 seconds with smaller peaks i n the period range of 0.5 seconds to 0.8 seconds, but the magnitude of the accelerations shown i n the spectra of the computed motions i s larger. As at the other two s i t e s , the spectra developed from the computed motions are less smooth than those developed from the recorded motions and show larger peaks i n the high period range. -83- Generally, the spectra of the recorded and computed motions compared well. The major peaks occurred at the same periods and with the exception of the Roberts Bank s i t e , showed the same acceleration. The chief difference between the spectra was that those developed from the computed motion were less smooth and show small acceleration peaks at high periods where they were less evident i n the spectra developed from the recorded motions. The better agreement between spectra at the Brighouse and Annacis Island s i t e s than.at the Roberts Bank s i t e suggests that the method of analysis used i s appropriate but the parameters used at Roberts Bank were less representative of the actual s i t u a t i o n than those used at the other s i t e s . I t i s unlikely that the dynamic s o i l p r o f i l e developed was less . accurate at the Roberts Bank s i t e because reasonable s o i l data was available i n that area. A more probable explanation i s that the object motion used for the analysis at the Roberts Bank s i t e was not as representative of the true object motion as i t was at the other two s i t e s . This could be due to the e f f e c t of buried bedrock topography on the earthquake waves. I t may also be due to the positions of the s i t e r e l a t i v e to the earth- quake source and the underlying geology. The object motion used was the surface bedrock motion recorded at Lake Cowichan. Seismic waves t r a v e l l i n g from the source at Pender Island to Lake Cowichan would tr a v e l primarily through igneous and metamorphic rock which have a high shear wave v e l o c i t y . To the east of Pender Island the surface rocks are sedementary, with lower shear wave ve l o c i t y and higher damping than the g r a n i t i c rocks. Because the Roberts Bank s i t e i s closer to the epicentre than the Annacis Island -84- s i t e , which has a similar s o i l p r o f i l e , seismic waves reaching the Roberts Bank s i t e may have t r a v e l l e d more through the low shear wave v e l o c i t y upper layer sedementary rocks, and may therefore have been more subject to damping than those waves reaching the Annacis Island s i t e . This could account for the recorded motion being less severe than the computed motion at the Roberts Bank s i t e . The analysis involves the d i v i s i o n of the s o i l p r o f i l e into d i s c r e e t layers which can be represented by s p e c i f i c s o i l properties. The number of layers that may be used i s limited by the cost of additional computing time. Obviously such a model using layers of s o i l with discreet d i v i s i o n s where dynamic properties change i s not completely accurate. Each of these small sublayers used i n the analysis w i l l have a predominant period which can be estimated i n the e l a s t i c range by the equation: T = 4H_ eq'n 4-1-1 n V (2n-l) s Here T i s the natural period, H i s the layer thickness, V i s n s the shear wave v e l o c i t y of that material, and n i s the mode. The r e s u l t of this i s that every sublayer w i l l be excited at s l i g h t l y d i f f e r e n t periods of motion. Although these excitations w i l l be modified by the effects of the other surrounding layers, the response spectrum w i l l mirror these small excitations as small, perturbations. The spectra of the actual recorded motions are smooth because the properties of any s o i l type w i l l change gradually with depth, so the spectra w i l l not be influenced by the resonance of a r t i f i c i a l layers. -85- Where major layers of s o i l with greatly d i f f e r e n t dynamic properties e x i s t i n the same profile,: major peaks i n the response spectra can be observed. Each peak r e f l e c t s the ch a r a c t e r i s t i c s of a p a r t i c u l a r s o i l group. These acceleration peaks are at periods which correspond roughly to the natural period range calculated for the major s o i l group using equation 4-1-1, since at the low l e v e l of exci t a t i o n of the Pender Island earthquake, the s o i l s are near t h e i r e l a s t i c response range. Changing the properties of a p a r t i c u l a r s o i l group (Rock, t i l l , or soft sediment) w i l l have a primary e f f e c t on the peak i n the response spectra caused by the resonance of that p a r t i c u l a r s o i l group and secondary e f f e c t on the general shape of the spectra. The inte r a c t i o n of the various s o i l groups i n the development of the earthquake motions from that causing the ex c i t a t i o n at the base of a s o i l deposit to the res u l t i n g surface motion can be seen i n figure 4-1-4. This figure shows plots of the response spectra of the motion at various lev e l s i n the s o i l deposit for the Annacis Island p r o f i l e , with the Pender Island earthquake recorded at Lake Cowichan as object motion. The object motion i s shown to have a predominant period of 0.2 seconds with very l i t t l e e x c i t a t i o n at high periods. The motion at the top of the t i l l layer shows one peak in acceleration at the same period as seen i n the object motion. It also shows another at a period of 0.8 5 seconds which i s close to the natural period of 0.7 seconds calculated for the t i l l layers using equation 4-1-1.; The response spectrum of the surface motion shows these two peaks i n approximately the same position, along with a new area of increased ex c i t a t i o n at larger periods -86- caused by the soft sediments overlying the g l a c i a l t i l l . The c h a r a c t e r i s t i c s of any response spectrum w i l l be modified s l i g h t l y by minor changes i n the dynamic properties of any s o i l layer and by changes i n the configuration of the s o i l p r o f i l e . In any r e a l s i t u a t i o n , i t i s not possible to select p a r t i c u l a r values for the dynamic properties of the s o i l with complete confidence,, nor i s i t always possible to have complete confidence i n the thickness of the various s o i l layers which make up the p r o f i l e . F i e l d investigation and laboratory analysis y i e l d a range of values that may represent the f i e l d s i t u a t i o n . For the three s i t e s examined, changing the input parameters within their probable range did not greatly e f f e c t the general shape of the response spectra. The peaks i n acceleration occurred at the same periods, but the magnitude of the peak could change by up.to 50%. The most important parameter i n determing the shape of the response spectra i s the depth to bedrock, followed by the thickness of the overlying t i l l layer. This i s what one would expect since the shear modulus and damping d i f f e r by orders of magnitude between the rock, g l a c i a l t i l l and soft sediments. By comparison, the difference i n dynamic properties between sand, s i l t , and clay, and the range i n properties l i k e l y for any given layer are small. Because of the int e r a c t i o n between layers i n the p r o f i l e , seen mathematically as an i n t e r r e l a t i o n s h i p between the .strain dependant damping r a t i o and shear modulus, i t - i s not possible to make meaningful comment on the s p e c i f i c e f f e c t s of changes i n t h e p a r a m e t e r s . I n g e n e r a l , h o w e v e r , c h a n g i n g t h e d a m p i n g a n d m o d u l u s s t r a i n r e l a t i o n s h i p s f o r s o i l l a y e r s h a d ' , a s o n e w o u l d e x p e c t , a p r i m a r y e f f e c t i n t h e p e r i o d r a n g e o f t h e s p e c t r a w h e r e t h o s e l a y e r s p r o d u c e d e x c i t a t i o n a n d a l e s s e r e f f e c t a t o t h e r p e r i o d s . I n c r e a s i n g t h e m o d u l u s t o s t i f f e n a p a r t i c u l a r l a y e r p r o d u c e d l a r g e r a c c e l e r a t i o n s a t g i v e n p e r i o d s , a s w o u l d r e d u c i n g t h e d a m p i n g o f t h e l a y e r . 4 - 2 A n a l y s i s U s i n g t h e D e s i g n E a r t h q u a k e T h e c l o s e c o r r e l a t i o n b e t w e e n t h e r e s p o n s e s p e c t r a o f t h e o b s e r v e d m o t i o n c a u s e d b y t h e P e n d e r I s l a n d E a r t h q u a k e , a n d t h e r e s p o n s e s p e c t r a o f t h e c o m p u t e d m o t i o n u s i n g t h e L a k e C o w i c h a n r e c o r d a s o b j e c t m o t i o n a t t h e B r i g h o u s e a n d A n n a c i s I s l a n d s i t e s c o n f i r m s t h e s u i t a b i l i t y o f t h e s o i l p r o f i l e s a n d t h e a n a l y s i s m e t h o d . U s i n g t h e s a m e s o i l p r o f i l e s , a n d t h e o b j e c t m o t i o n s f o r l a r g e r e a r t h q u a k e s a s d e s c r i b e d i n s e c t i o n 3 - 4 , . t h e s a m e d y n a m i c a n a l y s i s w a s p e r f o r m e d . T h e s u r f a c e r e s p o n s e a t e a c h o f t h e t w o s i t e s w a s c o m p u t e d u s i n g t h e S H A K E p r o g r a m w i t h e a c h o f t h e t h r e e c h o s e n o b j e c t m o t i o n s s c a l e d t o g i v e t h r e e d i f f e r e n t a c c e l e r a t i o n s a t b e d r o c k . T h i s p r o d u c e d n i n e r e s p o n s e s p e c t r a a t e a c h s i t e . T h e s e r e s p o n s e s p e c t r a w e r e c o m p a r e d w i t h e a c h o t h e r a n d w i t h g e n e r a l r e l a t i o n s h i p s d e v e l o p e d b y o t h e r s , t o d e t e r m i n e t h e s i g n i f i c a n c e o f t h e r e s u l t s t o t h i s a r e a . T h e r e s p o n s e s p e c t r a o f t h e t h r e e d e s i g n e a r t h q u a k e s , u s e d a s t h e o b j e c t m o t i o n s , s c a l e d t o 0 . 2 5 g m a x i m u m a c c e l e r a t i o n , , a r e s h o w n i n f i g u r e 4 - 2 - 1 . F i g u r e 4 - 2 - 2 s h o w s t h e r e s p o n s e -88- spectra developed from the three sets of surface motion at the Annacis Island s i t e , that were computed from these three input earthquakes scaled to a maximum acceleration of 0.16g. These three curves exhibit the same general, c h a r a c t e r i s t i c s , with a peak i n the surface acceleration for periods of about one second. The response spectra developed from surface motions due to an object motion scaled to 0.25g and 0.33g are shown i n figures 4-2-3 and 4-2-4 respectively. The same series of curves for the Brighouse s i t e are presented i n figures 4-2-5, 4-2-6, 4-2-7. The spectra produced at a given s i t e using the three d i f f e r e n t object motions, scaled to the same value of maximum acceleration, are sim i l a r i n form and i n magnitude i n every case. For ease i n comparison, the three response spectra curves shown on each of the aforementioned figures have been f i t t e d with a smooth curve so that the spectra developed at three d i f f e r e n t acceleration le v e l s may be summarized for each s i t e on one page. The response spectra of the surface motion caused by a base layer e x c i t a t i o n by earthquakes of three d i f f e r e n t magnitudes are shown for the Brighouse s i t e i n figure - 4-2-8, and for the Annacis Island s i t e i n figure 4-2-9. The most s t r i k i n g c h a r a c t e r i s t i c of these curves i s that changing the maximum acceleration on bedrock by over 100% produces very l i t t l e difference i n the spectra of the surface motions. For these three r e l a t i v e l y large magnitude earthquakes, increasing the acceleration of the object motion results i n a .very small increase i n the acceleration at the ground surface. When considering -89- the potential -damage to buildings i t i s important to remember that the accelerations experienced are only one of the factors involved. The duration of these strong accelerations i s also important, since the capacity of a structure to absorb the energy of the earthquake i s f i n i t e . Larger magnitude earthquakes would be of longer duration. The predominant period of the surface motion, as shown by the peak i n the surface acceleration response spectra, i s also important because buildings which have a predominant period similar to that of the earthquake w i l l experience much larger accelerations than those which do not. The period of peak acceleration for the three design earth- quakes has changed dramatically from the predominant periods for the rock motion and the low magnitude Pender Island earthquake surface motion. However, differences i n the predominant period of the surface acceleration caused by a single object motion scaled to the three d i f f e r e n t large accelerations cannot be s i g n i f i c a n t l y observed with the data- base used. The t i l l layers have a shear modulus which i s substantially greater than that of the overlying so f t sediments, but i s s t i l l s i g n i f i c a n t l y less than that of the underlying bedrock. If an analysis which applied an object motion to the g l a c i a l t i l l surface would y i e l d s i m i l a r r e s u l t s to an analysis which applied the same motion to the bedrock surface, modelling the s i t e for dynamic analysis would be s i m p l i f i e d , because data on t i l l properties and the depth to bedrock would not be required. Figure 4-2-10 and 4-2-11 show the response spectra for the three design earthquakes scaled to .25g and applied as object motions - 9 0 - t o t h e t o p o f t h e t i l l l a y e r a t t h e B r i g h o u s e a n d A n n a c i s I s l a n d s i t e s . C o m p a r i s o n w i t h f i g u r e s 4-2-6 a n d 4-2-3, w h i c h show t h e s p e c t r a f o r t h e same a n a l y s i s p e r f o r m e d w i t h t h e o b j e c t m o t i o n a p p l i e d t o b e d r o c k , d e m o n s t r a t e s t h a t t h e t h i c k t i l l l a y e r h a s a s i g n i f i c a n t e f f e c t o n t h e s h a p e o f t h e s p e c t r a a n d t h e m a g n i t u d e o f t h e a c c e l e r a t i o n . I f t h e r e s u l t s o f a n a n a l y s i s a r e t o be m e a n i n g f u l , t h e o b j e c t m o t i o n m u s t be a p p l i e d t o t h e s u r f a c e o f t h e b e d r o c k a n d t h e d y n a m i c e f f e c t s o f t h e t i l l a c c o u n t e d f o r i n t h e a n a l y s i s . When c o m p a r i n g t h e s p e c t r a f o r t h e t w o s i t e s i t c a n b e s e e n t h a t a t t h e A n n a c i s I s l a n d s i t e b o t h t h e maximum s u r f a c e a c c e l e r a t i o n a n d t h e a c c e l e r a t i o n p e a k o n t h e s p e c t r a a r e l a r g e r t h a n a t t h e B r i g h o u s e s i t e . T h i s may be b e c a u s e t h e A n n a c i s I s l a n d p r o f i l e h a s l e s s t h i c k n e s s o f s o f t s e d i m e n t s a b o v e t h e b e d r o c k , so t h e d a m p i n g i s l e s s . The p e r i o d a t w h i c h t h e p e a k a c c e l e r a t i o n o c c u r s i s l a r g e r f o r t h e A n n a c i s I s l a n d s i t e t h a n f o r t h e B r i g h o u s e s i t e . I n t e r m s o f p h y s i c a l r e s u l t s , t h i s means t h a t f o r t h e d e s i g n e a r t h q u a k e s u s e d , s t r u c t u r e s w i t h p e r i o d s o f a b o u t 0 . 8 s e c o n d s w o u l d b e m o s t s u s c e p t i b l e t o l a r g e m o t i o n s a n d t h e r e s u l t i n g damage a t t h e B r i g h o u s e s i t e , a n d s t r u c t u r e s w i t h p e r i o d s o f a b o u t 1 .0 s e c o n d s w o u l d be m o s t s u s c e p t i b l e a t t h e A n n a c i s I s l a n d s i t e . G e n e r a l l y , g round- a c c e l e r a t i o n s a n d t h e a c c e l e r a t i o n o f b u i l d i n g s , a s r e p r e s e n t e d b y t h e r e s p o n s e s p e c t r a , a t t h e B r i g h o u s e s i t e w e r e l e s s t h a n t h e a c c e l e r a t i o n s a t t h e A n n a c i s I s l a n d s i t e . C o m p a r i s o n o f t h e s p e c t r a d e v e l o p e d f r o m t h e o b j e c t m o t i o n a n d t h o s e d e v e l o p e d f r o m t h e c o m p u t e d s u r f a c e m o t i o n s shows t h e s h i f t i n predominant period of the motion from about 0.25 seconds for the earthquakes recorded on rock and used as object motion, to 0.8 seconds or 1.0 seconds for the earthquake motions computed at the surface of the deep s o i l deposits. This general observation of an increase i n the predominant period of the earthquake motion recorded at the surface of deep s o i l deposits over that recorded on rock i s i n accordance with the trends observed by others, (Seed, Ugas, Lysmer 1976). Figure 4-2-12 i s a p l o t of the mean response spectra of the object motions scaled to 0.25g, with a p l o t of the r e s u l t i n g surface motions at the Annacis Island s i t e . The r e l a t i o n s h i p between the curves i s t y p i c a l of what was found at both s i t e s using the three large magnitude earthquakes. These reponse spectra can be thought of as plots of the acceleration that a single degree of freedom structure with 5% of c r i t i c a l damping would experience, as i t s period was changed. Figure 4-2-12 shows that the r e l a t i o n between the peak i n acceleration and the building period i s more important than the ground acceleration i n determining the behaviour of the structure during an earth- quake . Using the approximation that the period of a structure i s equal to 0.1 times the number of s t o r i e s , the Figure 4-2-12 shows that a building of 2 or 3 s t o r i e s with a predominant period of about 0.25 sec. would experience very large accelerations i f b u i l t on bedrock, while an i d e n t i c a l building i n the Fraser Delta would experience much smaller accelerations. A 10 storey building, with a period i n the order of 1.0 sec. would -92- experience greater accelerations i n the delta area than i t would i f constructed on bedrock. These observations apply for the large magnitude earthquakes analyzed. The analysis of the Pender Island Earthquake indicated that the maximum building acceleration due to smaller magnitude earthquakes occurred at small periods whether the structure was on rock or a deep s o i l deposit. The r e l a t i o n between the maximum acceleration recorded on rock and the maximum acceleration recorded at the ground surface, i s shown i n figure 4-2-13. The data developed i n thi s analysis are shown with the average curves produced from recorded data by Seed, Murarka, Lysmer and Idr i s s (1976). The general shape of the curve developed from the data produced i n this study i s similar to the curve for other deep s o i l deposits developed by Seed et a l (1976). Low magnitude earthquakes produce larger accelerations on the surface of deep s o i l deposits than they do on rock, while larger magnitude earthquakes produce smaller accelerations on the surface of deep s o i l deposits than they do on rock. Low magnitude earthquakes excite the s o i l deposits and cause them to s t r a i n only s l i g h t l y so the s o i l s remain close to the i r e l a s t i c stress s t r a i n range, and damping i s small even though the s o i l i s being displaced by the earth- quake. Large magnitude earthquakes cause larger movement of the s o i l p a r t i c l e s , which s t r a i n greatly and follow t h e i r h y s t e r i t i c stress s t r a i n path to produce large amounts of damping, which reduce the acceleration of the s o i l . The c o r r e l a t i o n between the data developed i n t h i s analysis and the average curve shown i n figure 4-2-13 i s good. The curve shape i s s i m i l a r , though the curve developed for the Fraser Delta s o i l deposits predicts smaller surface accelera- tions for the same rock acceleration than do the average curves of Seed et a l (1976) . The data from t h i s analysis should not be expected to f a l l close to the Seed et a l (1976) curve because t h e i r curve shows the average r e s u l t s from many d i f f e r e n t s i t e s , none of which w i l l be i d e n t i c a l to the s i t e s analyzed i n t h i s study. The curve developed from the data i n t h i s study indicates that as the magnitude of the earthquake increases, the surface acceleration of a deep s o i l deposit becomes an increasingly smaller percentage of the rock acceleration. This i s i n keeping with the findings of T r i f u n i c and Brady (19 75), who noted that the maximum accelerations were reached by earthquakes of magnitude 6.5 to 7.0, which for the area and configuration that we are dealing with, corresponds to a maximum acceleration of about 0.2g. Larger magnitude earthquakes do not produce a noticeable increase i n maximum acceleration, though the duration w i l l be larger. The curves from Seed et a l (1976) exhi b i t t h i s trend, but not as markedly as the curve for the data developed i n t h i s study. This may be i n part because the Seed et a l curves have been extrapolated beyond.the 0.3g acceleration. The s p e c i f i c r e s u l t s of t h i s analysis can be compared with the recommendations of the National Building Code. The National Building Code recommends that design i n ttie Fraser Delta area incorporate the effects of acceleration due to an earthquake of 0.08g on firm ground and 0.12g on soft sediments. The results of thi s work are somewhat.different. Based on the study of the seismicity of t h i s area, a design earthquake of magnitude 7.4 i s expected, which could r e s u l t i n an acceleration of 0.25g on rock. The dynamic analysis has predicted that the maximum acceleration on the surface of the deep s o i l deposits due to such an earthquake would be i n the order of 0.16g. The maximum accelerations predicted by this analysis are more severe than those predicted by the National Building Code, though Byrne (1977) has pointed out that the d u c t i l i t y of most buildings i s such that i f designed according to the National Building Code c r i t e r i a , they could a c t u a l l y r e s i s t greater accelerations than the code would predict. Design should also incorporate the ef f e c t s of the s h i f t of predominant period of the earthquake that i s observed where large magnitude earthquakes occur i n areas of deep s o i l deposits. The s h i f t i n predominant period r e s u l t s i n buildings on deep s o i l deposits experiencing greatly d i f f e r e n t accelera- tions from buildings on bedrock, quite apart from what the ground accelerations might be. CHAPTER 5 COMMENT ON THE LIQUEFACTION.POTENTIAL OF THE FRASER.DELTA A detailed description of the mechanics of l i q u e f a c t i o n and a study of the factors involved and t h e i r r e l a t i o n to the s i t e s being investigated i s beyond the scope of t h i s work. Empirical methods of estimating l i q u e f a c t i o n potential have been developed through f i e l d investigation of many s i t e s . These methods were applied to the Fraser Delta s i t e s using the s o i l s data presented i n Chapter 2 to provide a simple measure of the l i q u e f a c t i o n potential at these s i t e s . Refinements on the r e s u l t s presented here could be made using the more com- pl i c a t e d a n a l y t i c a l procedures that are i n existence. Areas of saturated s o i l subjected to c y c l i c shear stresses such as those caused by an earthquake, may experience increased pore pressures. If these pore pressures increase u n t i l they are equal to the overburden pressure, the e f f e c t i v e stress i n the s o i l w i l l become zero. S o i l i n t h i s state i s said to have l i q u e f i e d , since i t cannot r e s i s t shear stresses and i t s behavior resembles that of a dense f l u i d . A l i q u e f i e d s o i l can pose a threat to man i n several ways. Liquefied s o i l cannot r e s i s t shear stresses, so horizontal forces applied to the s o i l cannot be r e s i s t e d , and.large deflections r e s u l t . The other major problem i s that l i q u e f i e d s o i l behaves l i k e a f l u i d , so structures i n or on the s o i l w i l l change elevation u n t i l t h e i r buoyant force i s equal to the weight of the displaced f l u i d . Buildings could sink into the s o i l and - 9 6 - buried structures such as storage tanks or sewers could r i s e to the surface. The factors influencing the earthquake induced l i q u e f a c t i o n potential of a s i t e are related both to the c h a r a c t e r i s t i c s of the s o i l and the c h a r a c t e r i s t i c s of the earthquake motion. These factors have been investigated i n the laboratory under well known conditions, and i n the f i e l d where generally the liq u e f a c t i o n potential has been correlated to Standard Penetration Test data. The data developed from the laboratory analysis i s extensive enough that the process of l i q u e f a c t i o n can be modelled-analytically (Finn, Byrne and Martin 1 9 7 6 ) . However, there may be d i f f i c u l t y i n applying the re s u l t s of these analyses to f i e l d situations because the c o r r e l a t i o n between the laboratory and f i e l d s o i l properties must be done using Standard Penetration Test r e s u l t s i f i t i s to be done on a wide basis using e x i s t i n g data. The problems involved i n obtaining a representative c o r r e l a t i o n between the re s u l t s of the Standard Penetration test and other s o i l properties have been outlined in. Chapter 2. The f i e l d data was developed using the Standard Penetration Test values d i r e c t l y , so the problem of choosing a suitable c o r r e l a t i o n i s eliminated. However, the re s u l t s of these empirical r e l a t i o n s are not s p e c i f i c since the s o i l properties have been considered through a single parameter only. These empirical r elations do provide a simple method of estimating the liq u e f a c t i o n potential of a s i t e . Oshaki ( 1 9 7 0 ) proposed the c r i t e r i a that i f the blow count at some depth from the standard penetration tests i s - 9 7 - e q u a l t o t w o t i m e s t h e d e p t h i n m e t e r s , l i q u e f a c t i o n w i l l n o t o c c u r . K i s h i d a ( 1 9 6 9 ) p r o p o s e d a r e l a t i o n s h i p a l s o b a s e d o n t h e b l o w c o u n t o f t h e S t a n d a r d P e n e t r a t i o n T e s t . T h e s e t w o m e t h o d s c o n s i d e r t h e p r o p e r t i e s o f t h e s o i l b u t . n o t t h e p r o p e r t i e s o f t h e e a r t h q u a k e . C h r i s t i a n a n d S w i g e r ( 1 9 7 5 ) a t t e m p t t o c o n s i d e r t h e e f f e c t s o f t h e e a r t h q u a k e b y r e l a t i n g t h e s t r e s s r a t i o t o t h e r e l a t i v e d e n s i t y d e t e r m i n e d f r o m t h e G i b b s a n d H o l t z c r i t e r i a a t f i e l d s i t e s . F o r a p a r t i c u l a r s i t e , t h i s r e l a t i o n c a n b e e x p r e s s e d as a r e l a t i o n s h i p b e t w e e n t h e b l o w c o u n t a n d d e p t h as shown i n a p p e n d i x 3 . S e e d , M u r a r k i , L y s m e r , a n d I d r i s s ( 1 9 7 6 ) h a v e d e v e l o p e d a m e t h o d w h i c h r e l a t e s t h e s t r e s s r a t i o t o a n o r m a l i z e d b l o w c o u n t . T h i s c a n a l s o be e x p r e s s e d as a r e l a t i o n b e t w e e n b l o w c o u n t a n d d e p t h , a s shown i n a p p e n d i x 3 . T h e s e f o u r r e l a t i o n s w h i c h s e p a r a t e s o i l s t h a t h a v e b e e n known t o l i q u e f y f r o m t h o s e t h a t h a v e n o t , a r e shown i n f i g u r e 5 - 1 f o r a m a g n i t u d e 7 . 4 e a r t h q u a k e . a t 30 k m . T h e s e r e l a t i o n s d e f i n e a b a n d o f b l o w c o u n t v a l u e s w h e r e l i q u e f a c t i o n may o c c u r . The Seed e t a l r e l a t i o n s h i p , w h i c h i s m o r e f i n e l y d e v e l o p e d t h a n t h e o t h e r s , o c c u p i e s a mean p o s i t i o n w i t h i n t h e g r o u p o f c u r v e s . C u r v e s o b t a i n e d u s i n g t h e Seed e t a l r e l a t i o n s h i p w i t h t h e t h r e e d e s i g n e a r t h q u a k e s u n d e r c o n s i d e r a - t i o n i n t h i s s t u d y a r e shown i n f i g u r e 5 - 2 . The a c c e l e r a t i o n s u s e d i n t h e a n a l y s i s a r e O . l g f o r t h e m a g n i t u d e 6 . 5 e a r t h q u a k e , 0 . 1 6 g a s a n u p p e r l i m i t f o r t h e m a g n i t u d e 7 . 4 e a r t h q u a k e , a n d 0 . 1 8 g f o r e a r t h q u a k e s o f m a g n i t u d e g r e a t e r t h a n 8 , as shown i n F i g u r e 4 - 2 - 1 3 . T h e s e c u r v e s a r e shown s u p e r i m p o s e d o n t h e c u r v e s -98- presenting the relations between blow count and depth for various areas in the Fraser Delta. An examination of this figure indicates that when sand s o i l s e x i s t above the 6 meter depth, l i q u e f a c t i o n i s l i k e l y to occur i n most areas of the delta when subjected to a magnitude 7.9 earthquake at 30km, while below the 6 meter depth, most sand areas are unlikely to li q u e f y when subjected.to the same earthquake. Under the influence of a larger earthquake, of magnitude greater than 8, li q u e f a c t i o n i s l i k e l y at depths less than 9 meters, while for a magnitude 6.5 earthquake, l i q u e f a c t i o n i s u n l i k e l y at any depth. Examination of these figures also reveals that there are p r o f i l e s that do not conform to this generalization, and more importantly that the application of d i f f e r e n t c r i t e r i a give d i f f e r e n t r e s u l t s for the same s i t e . These empirical methods give a general idea of the li q u e - faction potention 6f the Fraser Delta. For more s p e c i f i c results at a p a r t i c u l a r s i t e , more rigorous analysis i s needed. To make this analysis useful, close c o r r e l a t i o n i s needed between f i e l d and laboratory conditions. -99- CHAPTER 6 CONCLUSIONS AND SUGGESTIONS FOR FUTURE RESEARCH 6-1 Conclusions 1) The co r r e l a t i o n developed between the blow count recorded 0 to 12 inches penetration and that recorded for 6 to 18 inches penetration i n the Standard Penetration Test gives meaningful r e s u l t s , and allows data recorded i n both manners to be used together. 2) The relat i o n s h i p between r e l a t i v e density and the blow count of the Standard Penetration Test developed by Schultze and Menzenbach best t y p i f i e s the behavior of the sands found i n the Fraser Delta. 3) The co r r e l a t i o n between the f r i c t i o n angle of sands and the blow count of the Standard Penetration Test developed by de Mello gives reasonable results i n the Fraser Delta s o i l s . 4) The dynamic analysis used i n the SHAKE computer program gives e f f e c t i v e representation of the surface motions r e s u l t i n g from an object motion acting at the base of a s o i l p r o f i l e , the dynamic properties of which have been determined from more re a d i l y available s o i l information. 5) In the dynamic analysis, the most c r i t i c a l parameters of the s o i l p r o f i l e are the depth to bedrock and the thickness of the g l a c i a l t i l l e x i s t i n g above the bedrock. The difference i n dynamic properties between clay, s i l t and sand layers i s not as s i g n i f i c a n t . (100) 6) A suitable design earthquake for dynamic analysis i n the Fraser Delta i s one of magnitude of 7.4 at a distance of 30km, which produces a bedrock acceleration of about 0.25g. However, the p o s s i b i l i t y of larger earthquakes of magnitude greater than 8 should not be ruled out. 7) Use of the dynamic analysis with design earthquakes of magnitudes 6.5, 7.4 and 8.0 at two s i t e s i n the delta yielded surface motions with a predominant period of 0.8 to 1.0 seconds, and a maximum ground acceleration of about 0.16g. For the large magnitude earthquakes used, an increase i n the magnitude of the object motion did not greatly a f f e c t the predominant period or the maximum acceleration at the ground surface. The maximum ground acceleration at these magnitudes was much less than the bedrock acceleration. The predominant period of the surface motion under the large magnitude earth- quakes had increased greatly from the predominant period of both the bedrock motion under large magnitude earthquakes, and the surface motion under small magnitude earthquakes. 8) The dynamic e f f e c t s of the t i l l layer are important and must be modelled with the other s o i l layers. 9) The l i q u e f a c t i o n potential estimated from empiracal relationships suggests that for an earthquake of magnitude 7.4 l i q u e f a c t i o n i s l i k e l y i n the upper 6 meters of sand sediments, but less l i k e l y below the 6 meter depth. Under a severe earthquake of magnitude greater than 8, l i q u e f a c t i o n i s unlikely to occur i n sands below the 9 meter depth. (101) 6-2 Suggestions 1 for- Further Research 1) For laboratory data to be applied to f i e l d situations a r e l i a b l e method i s needed to determine the f i e l d r e l a t i v e density. Research which develops accurate f i e l d technique for determining the r e l a t i v e density and r e l a t i n g i t to the Standard Penetration Tests would be valuable. 2) The l i q u e f a c t i o n potential of the Fraser Delta could be investigated using rigorous a n a l y t i c a l methods as well as the empirical methods used i n th i s study. 3) The Fraser Delta contains a large proportion of s i l t s o i l s . Because of the problems involved i n sampling and testing these s o i l s where permeability i s i n a mid range between that of clay and sand, l i t t l e f i e l d or laboratory investigation of dynamic properties has been done. An investigation into the dynamic properties of s i l t , and a method of defining i t s properties by simple f i e l d tests would be valuable. 4) The Western Washington Earthquake of 1949 and the Puget Sound Earthquake of 19 65 are large-magnitude earthquakes which would probably resemble the type of earthquakes that would e f f e c t the Fraser Delta area. An analysis s i m i l a r to the one performed i n this study could be undertaken to produce the bedrock motion of these earthquakes from the motion recorded at ground surface. These bedrock motions could then be used as the object motions for analysis i n the Fraser Delta area. (102) Suggestions for Further Research cont'd 5) The analysis performed i n t h i s study has ignored the effects that a building would have on the underlying s o i l s . 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Af/9X/t^f(//-l 1 I V - I — — I . 5 ./ .a 'PSCAV r-oc<4' /j) *ft<i/ Sorter's Curve ef,cvC/oy>ce/ ?*Ar * *Acjoftj A <9rjA ® e/oAa f eft***  -189- P/& 5-2 : L/Q U/FA CT/O/V Po r£AJ T//)i\ OJC T/VJf pMAS£/Z /Oz/.rs> -190- REFERENCES Anderson, A.M., Espana, C , McLamore, V.R., 1978, Estimating In-Situ Shear Moduli at Competent Site s " , Earthquake Engineering and S o i l Dynamics Specialty Conference, Pasadena, 181-197. Arango, I., Moriwaki, Y., Brown, F., 1978, "In S i t u and Laboratory Shear Veloci t y and Modulus." Earthquake Engineering and S o i l Dynamics Specialty Conference, Pasadena, pp. 198-212. Armstrong, J.E., 1956, " S u r f i c i a l Geology of Vancouver Area, B.C." G.S.C. Paper 5 5-4 0. Armstrong, J.E., 1957, " S u r f i c i a l Geology of New Westminster Map Area, B.C." G.S.C. Paper 5 7-5. Armstrong, J.E., 1960, " S u r f i c i a l Geology of Sumas, New Westminster, B.C." G.S.C. Map 44-1959. 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Of S o i l Mechanics and Foundation Div. A.S.C.E. Vol. 10 3 pp. 565-588. Mathews, W.H., Fyles, J.G., Nasmith, H.W., 1970, "Postglacial Crustal Movements i n Southwestern B.C. and Adjacent Washington State." Cdn. Jour. Earth Sciences Vol. 7, pp. 690-702. Mathews, W.H., Shepard, F.P., 1962, "Sedimentation of the Fraser Delta, B.C." Bui. of the Am. Assoc. of Petroleum Geologists, Vol. 46, pp. 1416-1438. McTaggart, K.C., Dolmage, V., 1977 "Vancouver Geology-Field Excursion #11 Guide Book." G.S.C. Milne, W.G., Rogers, G.C., Riddihou, R.P., McMechan, G.A., Hyndman, P.D., 19 78, "Seismicity of Western Canada." Cdn. Jour, of Earth Sciences Vol. 15, pp. 1170-1193. Muller, J.E., 1977, "Evolution of the P a c i f i c Margin, Vancouver Island and Adjacent Regions." Cdn. Jour. Earth Sciences, Vol. 14, pp. 2062-2085. Murphy, D.J., Koutsoftas, D., Covey, J.N., Fischer, J.A., 1978, "Dynamic Properties of Hard G l a c i a l T i l l . " Earthquake Engineering and S o i l Dynamics Specialty Conference, Pasadena. N u t t l i , O.W., 1973, "Seismic Wave Attenuations and Magnitude Relations for Eastern North America." S.Geophys. Res. Vol. 78, pp. 876-885. Ohsaki, Y., 1970, "Effects of Sand Compaction on Liquefaction during the Tokachiaki Earthquake." S o i l s and Foundations, Vol. 10, No. 2 - 1 9 3 - O h s a k i , . Y . , I w a s a k i , R. , 1973, "On D y n a m i c S h e a r M o d u l i a n d P o i s s o n s R a t i o o f S o i l D e p o s i t s . " S o i l M e c h a n i c s a n d F o u n d a t i o n s , V o l . 1 3 , N o . 4 , p p . 6 1 - 7 3 . R a d h a k r i s h n a , H . S . , K l y m , T .W. , 1 9 7 4 , " G e o t e c h n i c a l P r o p e r t i e s o f Dense G l a c i a l T i l l " . C d n . G e o t e c h n i c a l J o u r . V o l . 1 1 , p p . 3 9 6 - 4 0 8 . R o d d i c k , J . A . , 1 9 6 5 , " V a n c o u v e r N o r t h , C o q u i t l a m , a n d P i t t L a k e Map A r e a s , B . C . . " G . S . C . m e m o i r 3 3 5 . R o g e r s , G . C . , H a s e g a w a , 1 9 7 8 , "A S e c o n d L o o k a t t h e B . C . E a r t h q u a k e o f 23 J u n e , 19 4 6 . " B u l l e t i n o f S e i m o l o g i c a l S o c i e t y o f A m e r i c a , V o l . 6 8 , p p . 6 5 3 - 6 7 5 . S a i t o , A . , 19 7 7 , " C h a r a c t e r i s t i c s o f P e n e t r a t i o n R e s i s t a n c e o f a R e c l a i m e d Sandy D e p o s i t a n d t h e i r Change t h r o u g h V i b r a t o r y C o m p a c t i o n . " S o i l s a n d F o u n d a t i o n s V o l . 17 # 4 , p p . 3 1 - 4 3 . S c h m e r t m a n , J . H . , 1 9 7 1 , D i s c u s s i o n o n P a p e r b y V . d e M e l l o , 4 t h Pan A m e r i c a n C o n f e r e n c e o n S o i l M e c h a n i c s a n d F o u n d a t i o n E n g i n e e r i n g , p p . 9 1 - 9 8 . S c h n a b e l , J . , 1 9 7 1 , D i s c u s s i o n o n P a p e r b y V . de M e l l o , 4 t h Pan A m e r i c a n C o n f e r e n c e o n S o i l M e c h a n i c s a n d F o u n d a t i o n E n g i n e e r i n g , p p . 8 9 - 9 8 . S c h n a b e l , P . B . , L y s m e r , J . , S e e d , H . B . , 1 9 7 2 , "SHAKE-A C o m p u t e r P r o g r a m f o r E a r t h q u a k e R e s p o n s e A n a l y s i s o f H o r i z o n t a l l y L a y e r e d S i t e s . " EERC 7 2 - 1 2 E a r t h q u a k e E n g i n e e r i n g R e s e a r c h C e n t r e , U n i v e r s i t y o f C a l i f o r n i a , B e r k e l e y . S c h n a b e l , P . B . , S e e d , H . B . , 1 9 7 2 , " A c c e l e r a t i o n s i n Rock f o r E a r t h q u a k e s i n t h e W e s t e r n U n i t e d S t a t e s . " R e p o r t N o . EERC 7 2 - 2 , E a r t h q u a k e E n g i n e e r i n g R e s e a r c h C e n t r e , U n i v e r s i t y o f C a l i f o r n i a , B e r k e l e y . S c h u l t z e , E . , M e l z e r , K . J . , 1 9 6 5 , " T h e D e t e r m i n a t i o n o f t h e D e n s i t y a n d M o d u l u s o f C o m p r e s s i b i l i t y o f N o n - C o h e s i v e S o i l s b y S o u n d i n g s . " P r o c e e d i n g s 6 t h I n t . C o n f . S o i l M e c h a n i c s a n d F o u n d a t i o n E n g i n e e r i n g , M o n t r e a l , V o l . 1 p p . 5 1 7 - 5 2 1 . S c h u l t z e , E . , M e n z e n b a c h , E . , 1 9 6 1 , " S t a n d a r d P e n e t r a t i o n T e s t a n d C o m p r e s s i b i l i t y o f S o i l . " 5 t h I n t . C o n f . S o i l M e c h a n i c s a n d F o u n d a t i o n E n g i n e e r i n g , V o l . 1 , p p . 5 2 7 - 5 3 1 . S c o t t o n , 1 9 7 7 , " T h e O u t e r B a n k s o f t h e F r a s e r R i v e r D e l t a , " E n g i n e e r i n g P r o p e r t i e s a n d S t a b i l i t y C o n s i d e r a t i o n s . " M . A . S c . t h e s i s , U . B . C . -194- Seed. H.B., Id r i s s , I.M., 1970, " S o i l Moduli and Damping Factors for Dynamic Response Analysis." EERC Report No. 70-10, Earthquake Engineering Research Centre, University of C a l i f o r n i a , Berkeley. Seed, H.B., I d r i s s , I.M, 1971, "Simplified procedure for Evaluating S o i l Liquefaction Potential." Journal of S o i l Mechanics and Foundation Divi s i o n , ASCE, Vol. 97, No. 5 pp. 1249-1273. Seed, H.B., I d r i s s , I.M.,Keifer, F.W., 1969, "Characteristics of Rock Motions During Earthquakes." Jour. S o i l Mechanics and Foundations Div. ASCE, Vol. 95, No. 5, pp.1199-1218. Seed, H.B., I d r i s s , I.M. Makdise, F., Banerjee, N., 1975, "Representation of Irregular Stress Time Hi s t o r i e s by Equivalent Uniform Stress Series i n Liquefaction Analyses." EERC 75-29, Earthquake Engineering Research Centre, University of C a l i f o r n i a , Berkeley. Seed, H.B., Mori, K., Chan, C.K., 1977, "Influence of Seismic History on the Liquefaction of Sands." Jour, of Geotechnical Engineering D i v i s i o n , ASCE, Vol. 103, No. G74, pp. 257-270. Seed, H.B., Murarka, R., Lysmer, J., Id r i s s , I.M., 1976, "Relationships of Maximum Acceleration, Maximum Velocity, Distance from Source, and Local Site Conditions for Moderately Strong Earthquakes." B u l l e t i n of Seismological Society of America, Vol. 66 No. 4, pp. 1323-1342. Seed, H.B., Vgas, C , Lysmer, J., 1976, "Site Dependent Spectra for Earthquake Resistant Design." B u l l e t i n of Seismological Society of America, Vol. 66 No. 4, pp. 221-24 3. Tavenas, F.A.,Ladd, R.S., La Rochelle, P., 1972, "The Accuracy of Relative Density Measurements: Results of a Comparative Test Program." Department de Genie C i v i l , Universite Laval. Trifunac, M.D., Brady, A.G., 1975, "Correlations of Peak Acceleration Velocity and Displacement with Earthquake Magnitude Distance, and Site Conditions. - 1 9 5 - APPENDIX 1 GEOLOGIC TIME SCALE ERA PERIOD APPROXIMATE NUMBER OF YEARS AGO* Quaternary Recent Pleistocene (Ice Age) Last 1 0 , 0 0 0 1 0 , 0 0 0 to 1 , 0 0 0 , 0 0 0 Cenozoic Tertiary Pliocene Miocene Oligocene Eocene Paleocene (Millions) 1 to 13 13 to 25 25 to 36 36 to 58 58 to 6 3 Mesozoic Cretaceous Jurassic T r i a s s i c 63 to 1 3 5 13 5 to 1 8 1 18 1 to 230 Palaeozoic Permian Pennsylvanian and Mississippian Devonian S i l u r i a n Ordovician Cambrian 230 to 280 280 to 3 4 5 345 to 4 0 5 405 to 4 2 5 425 to 500 500 to 600 Proterozoic Keweenawan Huronian 600 to 2,00 0 Archaean Temiskaming Keewatin 2 , 0 0 0 to 4, 8 0 0 •Science, A p r i l 1 4 , 1 9 6 1 , p.1111 -196- APPENDIX 2 USE OF FRICTION CONE S.P.T. FORMULA TO SEPARATE PENETRATION RESISTANCE DUE TO END BEARING AND FRICTION From Schmertmann (1971) we have F = Fe + Fs Fe = Ae* qc Fs = TT (Di + Do) L-fs FR fs/qc where F = to sampler resistance to advance Fe = end bearing component of resistance Fs = f r i c t i o n a l component of resistance Ae = ho r i z o n t a l l y projected end area of SPT sampler" qc = end bearing resistance, at same depth from s t a t i c cone test Di = inside diameter of sampler Do = outside diameter of sampler L = length of sampler imbedded i n s o i l fs = l o c a l f r i c t i o n from s t a t i c cone penetration t e s t FR = F r i c t i o n r a t i o , a function of s o i l type Take the r a t i o of end bearing and f r i c t i o n a l components: Fe Ae • qc = Ae Fs (Di + Do) L .fs (Di + Do)L . FR for Ae — 10.7cm2 Di — 1.375 i n Do - 2 i n FR = 1% (Loose to med. sands, Schmertmann 1971) We get Fe Fs = 39.7 L -197- FOR VARIOUS LENGTHS OF SAMPLER IMBEDMENT THIS GIVES: DEPTH OF SAMPLER IMBEDMENT (in) Fe Fs Resistance From End Bearing % Resistance From F r i c t i o n % 6 2.60 72% 28% 12 1.30 56% 44% 18 0.868 46% 59% 24 0.651 39% 61% -198- APPENDIX 3 LIQUEFACTION POTENTIAL RELATIONSHIPS CHRISTIAN & SWIGER (1975) A = d T where A = stress r a t i o at some depth *S0' \T = overburden pressure at that depth QV = e f f e c t i v e stress at that depth a = maximum ground acceleration for a water table at the surface at the s o i l , as i n the Fraser Delta: cr J» rr ' /\ for design earthquake of 17 = 7.4, F i g . 4-2-12 predicts maximum ground surface acceleration of 0.16g. So: A = 2 (.16) = .32g The r e l a t i o n developed by Ch r i s t i a n & Swiger (19 7 5) and presented by Byrne (1977) predicts that for A = .32g liq u e f a c t i o n i s unl i k e l y to occur i n sands with a Relative Density greater than 71% as determined from the Gibbs and Holtz r e l a t i o n s . The Gibbs and Holtz r e l a t i o n for Nvs. DR = 71% was plotted i n f i g . 5-2. SEED, MURARKI, LYSMER, IDRISS (19 76) A = 0.65 a (To. where A = c y c l i c stress r a t i o of some depth causing l i q u e f a c t i o n a = maximum ground acceleration g = acceleration due to gravity \u» = t o t a l overburden stress CTa =effective overburden stress rd = stress reduction factor -199- for - water table at the surface -totaluunit weight of 122 pcf -d of 0.16g A - .65 ft).16g\ 122 (depth) • rd I g J (122- 62.4) (depth) A = .21rd Seed and Idriss (1971) produced re l a t i o n s between rd and depth so the stress r a t i o can be determined with depth. The stress r a t i o causing l i q u e f a c t i o n can be related empirically to the penetration resistance, so from data presented by Seed, Arango and Chan 19 75, the blow count i n sands un l i k e l y to li q u e f y may be determined for the various stress r a t i o s calculated. The blow count given i s one corrected to a standard overburden pressure so from i t the actual blow count required at each depth may be determined from the r e l a t i o n . CN = 1-1.25 log V~0' where N = Ni CN here CN = correction factor N = true blow count N = blow count normalized to standard pressure. In this way a relationship •.between the blow count required to reduce the p o s s i b i l i t y of l i q u e f a c t i o n under a p a r t i c u l a r earthquake, and depth may be developed. This r e l a t i o n i s plotted i n f i g . 5-1.

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