for our testing condition. Chapter 3. Preliminary Application - Footing Test 24 3.2.3 Soil Preparation and Testing Procedures The initial stress distribution within the model depends largely on the seepage gradi-ents. In order to keep these gradients uniform throughout the domain and thus apply a constant equivalent body force, it is necessary to keep the permeability constant in the soil domain. To achieve this, the sand should be placed as uniformly as possible. It was found that the water pluviation technique (e.g., Vaid and Negussey, 1986) used in the preparation of triaxial samples was not efficient here because large amounts of sand were required, and the procedure was time consuming. Therefore, a new sample preparation technique was developed for the present tests. This technique employs upward seepage forces, together with sedimentation and densification processes, to form and then reform soil deposits for and after each test and is described below. During sample preparation, the top cap of the cell was removed and the drainage lines from the circulation chamber were closed. De-aired water was used to fill the cell and all the measurement fines. A fixed amount of oven dried sand, about 3 kg, was weighed in flasks. Water was added to each flask and the sand water mixture was then boiled. The base porous stone was also boiled before being installed. After cooling to room temperature, the boiled sand was transferred to the cell using a water pluviation technique flask by flask. It was found that layers tended to form with each flask of sand deposited. To remove this layering effect, a controlled upward seepage gradient was applied to the sample causing it to form a loose slurry which was then stirred to obtain a homogeneous state. The upward gradient was then turned off and the sand allowed to sediment under its self-weight. Since the sand used was very uniform, no segregation was observed. When the sedimentation process was completed, the top cell cap, the lubricated loading ram, and the footing adaptor were all carefully installed. The sample was then densified to the specified density by tapping the side and base of the cell. The model testing cell was moved into the loading frame and the water supply Chapter 3. Preliminary Application - Footing Test 25 lines connected. The \"gravitational\" process began by applying a controlled hydrauhc gradient. The model footing was lowered onto the sand surface, and the displacement controlled footing test commenced. Continuous readings of vertical load and dis-placement were taken throughout the test. After each test was completed, the sand was loosened by an upward gradient and reformed as discussed above. In this way, a number of tests under different gradients and densities could be quickly carried out. 3.2.4 Sample Uniformity and Test Repeatability The soil sample preparation technique described above involves an upward seepage force to disturb the sample, which is then reformed by sedimentation and densifi-cation. This technique has the advantage that it is very fast to prepare a new soil deposit after each and every test. Great effort has been made to evaluate this technique, and ensure initial sample uniformity and repeatability of test results. Gelatin, as suggested by Emery et al (1973), was used to solidify samples prepared by this technique in order to examine the sample uniformity conditions at the end of sedimentation and densification processes. The horizontal as well as vertical distribution of the void ratio determined from slices of the gelatin sample are shown in Tables 3.2 and 3.3 for conditions- after sedimentation and densification, respectively. It may be seen that prior to densification, the top layer is significantly looser than the rest of the sample. After densification, the soil sample is uniform in both horizontal and vertical directions. Through several trials, it was found that the most uniform densification was achieved by tapping the side and base of the triaxial cell. The foregoing sample preparation procedure has also been evaluated by comparing the results of drained compression triaxial tests on samples prepared by the conven-tional water pluviation technique and by the present method, called the 'quick sand' technique. Results are shown in Figure 3.4 to 3.8, where it may be seen that both Chapter 3. Preliminary Application - Footing Test 26 Table 3.2: Sample Uniformity after Sedimentation, Void Ratio 'e' at Different Loca-tions Top Layer Middle Layer Bottom Layer Depth Profile T l 0.9313 M l 1.7161 B l 0.8954 D l 0.9339 T 2 0.9252 M2 0.8971 B2 0.8884 D2 0.9014 T3 0.9306 M3 0.8853 B3 0.8944 D3 0.8900 T4 0.9397 M4 0.8932 B4 0.8892 D4 0.8935 T5 0.9320 M5 0.8966 B5 0.8957 D5 0.8924 Table 3.3: Sample Uniformity after Densification, Void Ratio 'e' at Different Locations Top Layer Middle Layer Bottom Layer Depth Profile T l 0.6472 M l 0.6250 B l 0.6123 D l 0.6073 T2 0.5931 M2 0.6148 B2 0.6091 D2 0.6199 T3 0.6076 M3 0.6350 B3 0.6186 D3 0.6213 T4 0.5978 M4 0.6312 B4 0.6123 D4 0.6220 T5 0.5879 M5 0.6226 B5 0.6172 D5 0.6111 consolidation behaviour and stress-strain response produced by these two different sample preparation methods are very similar. The 'quick sand' model soil preparation technique produced test results which were highly repeatable. In the testing program, each test was performed 2 to 3 times under the same condition to assess the repeatability of the test results. As shown in Figures 3.9 and 3.10, good repeatability for each test condition was obtained for both loose and dense sands. 3.2.5 Experimental Program Tests were performed on both loose and dense sands with different footing dimensions. The experimental program is summarized in Table 3.4. Chapter 3. Prehminary Application - Footing Test 27 1 \\ i - J in o ft 1 | n meth' \u2022 \\ I c o cn l a \\ \u2022 \\ 1 c a. w 4) a \\ I i i i i i i i I i 1 i i I i , o o o o o o o o o o o c o o o c o o o o (VdH) SS3H1S NOIlVmiOSNOD DldOHlOSI \u00b0D Figure 3.4: Comparison of Consolidation behaviour from Two Sample Preparation Methods Chapter 3. Preliminary Application - Footing Test 28 Figure 3.5: Comparison of Stress-strain behaviour at Loose Sand from Two Sample Preparation Methods, DT = 33% 0 - ! 1 1 1 1 1 1 1 1 1 1 1 1 1 0 2 4 6 0 10 12 14 AXIAL STRAIN (%) Figure 3.6: Comparison of Volumetric behaviour at Loose Sand from Two Sample Preparation Methods, DT = 33% Chapter 3. Preliminary Application - Footing Test 29 Figure 3.7: Comparison of Stress-strain behaviour at Dense Sand from Two Sample Preparation Methods, DT \u2014 75% Figure 3.8: Comparison of Volumetric behaviour at Dense Sand from Two Sample Preparation Methods, D , = 75% Chapter 3. Preliminary Application - Footing Test 30 Figure 3.9: Typical Example of Repeatability for Loose Sand at N=40, Bm = 1.5cm Chapter 3. Preliminary Application - Footing Test 31 Figure 3.10: Typical Example of Repeatability for Dense Sand at N=60, Bm = 1.5cm Chapter 3. Preliminary Application - Footing Test 32 Table 3.4: A Summary of Model Footing Tests H . G . S . F - N 1 10 20 30 40 50 60 80 100 Z?m=1.5cm loose dense loose dense loose dense loose dense loose dense loose dense loose dense loose dense loose dense 5 m =2 .0cm dense B m =2 .5cm dense Note: Loose Sand - DT = 33%; Dense Sand - DT = 75%. 3.3 Results and Discussion 3.3.1 Load-Settlement Curves The observed load-settlement curves for loose and dense sands under a range of hy-drauhc gradient scale factors are shown in Figures 3.11 and 3.12, respectively. A small correction to the measured applied footing pressure was made to account for the hy-drauhc head loss in the porous plate at the base of the footing. This correction is discussed in Appendix B. The footing diameter, BM was 1.5 cm for all the tests shown on these figures. It may be seen that the response is greatly affected by the hydrauhc gradient applied, N , becoming much stiffer as N increases with seepage gradient. For the loose sand condition, DR = 33%, the load-settlement response for any one scale factor is essentially linear except in the early stage when it curves gently downward, but there is no break in the curve corresponding to a limit bearing pressure. For the dense sand condition, the initial portion of the curve is essentially linear, followed by a sharp break corresponding to a hmit pressure, and followed by a gradual increase in pressure with settlement. The increase in pressure beyond the hmit pressure is thought to be due to penetration of the footing into the soil resulting in a surcharge or embedment effect. Chapter 3. Preliminary Application - Footing Test 33 3 . 0 o o o o o N = 1 \u2022 \u2022 \u2022 \u2022 \u2022 N = 1 0 0 0 0 0 0 N = 4 0 \u00bb i i i i N = 6 0 \u2022 \u2022 \u2022 \u2022 \u2022 N = 8 0 N = 1 0 0 - 1 . 0 \u2014 1 c a> E CD (V CO CT1 C 8 \" 5 0 - 9 . 0 i\u2014i\u2014i\u2014i\u2014i\u2014i\u2014i\u2014i\u2014r ~i i i i i i i\u2014 i\u2014r \" i \u2014 i \u2014 i \u2014 r 0 . 0 4 0 . 0 8 0 . 0 F o o t i n g P r e s s u r e ( k p a ) \"i\u2014i\u2014i\u2014i\u2014i 1 2 0 . 0 Figure 3.11: Observed Settlement Curves for Loose Sand Under Different N (5 m =1.5cm, IL=33%) Chapter 3. Preliminary Application - Footing Test 34 3 . 0 - 1 ~ O O O O O N= 1 | - \u2022\u2022\u2022\u2022\u2022 N=10 - a & A f l A N = 2 0 ' _ i i i i i N = 4 0 I N = 60 I \" \u00bb\u00bb\u2022\u2022\u2022 N=80 | \" N= 100, I \u2014 9.0 | i i i i i i i i i I i i i i i i i i i I i i i i i i i i i I i i i i i i i i i | 0.0 100.0 200.0 300.0 400.0 Footing Pressure (kpa) Figure 3.12: Observed Settlement Curves for Dense Sand Under Different N (B m =1.5cm, DT=75%) Chapter 3. Preliminary Application - Footing Test 35 The test results of Figures 3.11 and 3.12 are similar to those observed by Ovesen (1975), in centrifuge tests as shown in Figure 3.13. 3.3.2 Ultimate Bearing Pressure The ultimate bearing pressure, Puit, for dense sands can be estimated from the ob-served load-settlement curves and compared with the Terzaghi bearing capacity equa-tion. Such a comparison allows the trend of the data to be checked against a well-established bearing capacity equation. The Puit values can also be checked against centrifuge test results and triaxial test data. The ultimate pressure from the footing tests on dense sand were determined by the tangent method proposed by Vesic (1975) and illustrated in Figure 3.14. The values obtained for a relative density of 75%, a footing diameter of 1.5 cm and for a range of hydrauhc gradient scale factor, N, are shown in the first row of Table 3.5. The ultimate bearing pressure from the Terzaghi theory is as follows: Puit = ^ 7 7 m B m \/ Y , or (3.1) Puit = ^N-y'BmNy or (3.2) log(P u < ( ) = \\og(^7' BmN^ + \\og(N) (3.3) in which \u00a3 7 = a shape factor = 0.60 for a circular footing; jm = the effective unit weight of the model soil = N7'; 7' = the submerged unit weight of the soil; N = the hydrauhc gradient scale factor = ^ ; Bm = the diameter of the model footing; Chapter 3. Prehminary Application - Footing Test 36 Figure 3.13: Settlement Curves observed from Centrifuge Tests (after Ovesen, 1975) Chapter 3. Preliminary Application - Footing Test 37 10.Qj \u2014 1 0.0 200.0 Footing Pressure (kpa) Figure 3.14: Illustration for Determination of Ultimate Pressure for Dense Sand Chapter 3. Preliminary Application - Footing Test 38 Table 3.5: Bearing Capacity for Dense Sand from H . G . Tests N 1 10 20 30 40 50 60 80 100 Puh 3.8 34.6 41.8 64.2 72.4 99.2 105.3 140.3 165.2 TV 83.4 76.8 46.5 47.6 40.2 44.1 39.0 39.0 36.7 4>' (deg.) 40.5 39.8 37.0 37.0 36.0 36.5 36.0 36.0 35.5 PuH in kPa iV 7 = the bearing capacity factor associated with the unit weight of the soil and is a function of the friction angle only. For a given footing diameter and soil density, Eq . (3.3) indicates that Putt should increase linearly with the scale factor, N , at a 45\u00b0 slope on a log-log scale. The observed trend is shown in Figure 3.15 and indicates essentially a linear relationship with a 45\u00b0 slope for N larger than 20. For N values in the range of 1 to 20, the observed values he above the line. Centrifuge data reported by Ovesen (1975) was found to follow a similar trend and is shown in Figure 3.16. The reason for the nonlinearity at low hydraulic gradient or low stress levels is likely due to the increased tendency for dilation at low stress levels leading to a higher mobihzed friction angle. The friction angle mobihzed in the model tests can be computed as follows: 1. iV 7 values from the model tests can be computed from E q . (3.1) and are listed in Table 3.5. 2. The mobihzed and N1 and are hsted in row 3 of Table 3.5. This relationship is recommended by the Canadian Foundation Engineering Manual (1985). It may be seen that the mobihzed (f> values computed from the model tests are essentially constant and equal to 36\u00b0 to 37\u00b0 for scale factor, N , of 20 or greater. Below Chapter 3. Preliminary Application - Footing Test 39 HYDRAULIC GRADIENT SCALE FACTOR - N Figure 3.15: Observed Ultimate Pressure vs. Scale Factor - N Chapter 3. Preliminary Application - Footing Test 40 Figure 3.16: Bearing Capacity vs. Acceleration Field in Centrifuge Tests (after Ovesen, 1975) Chapter 3. Preliminary Application - Footing Test 41 N = 20, higher (j) values are mobilized. For N = 1 which corresponds to a zero seepage force condition, or a conventional modelling condition, the mobilized friction angle is 4 0 . 5 \u00b0 . The computed friction angles shown in Table 3.5 are compared with the peak friction angles obtained from triaxial tests in Figure 3.17. It should be noted that the friction angles computed from model tests represent some \"average\" values mobilized along the whole failure surfaces in the model tests. It may be seen that while the computed mobilized friction angle is about 3\u00b0 lower than the peak value obtained from the triaxial test, the trend of decreasing friction angle with stress level for the same relative density is in agreement with the triaxial test results. The effects of hydrauhc gradient or stress level on the bearing capacity can also be examined by considering the model footing to have a prototype dimension which increases with the scale factor, N . The calculated bearing capacity coefficient, i V 7 , in Table 3.5 can be related to the corresponding prototype footing width, Bp, using the scaling relation, Bp = N \u2022 Bm. The results are shown in Figure 3.18. It may be seen in the figure that iV 7 decreases linearly with footing size on the log-log scale. This reduction with footing size is expected because larger footings have higher stress levels in their failure zone, and this results in a lower mobilized friction angle, , and hence a lower Ny value. This observation is in accordance with other model test results by De Beer (1970) and centrifuge test results by Kimura et al (1985). In addition, the experimental observation from hydrauhc gradient tests shown in Figure 3.18 tends to support the theoretical studies by Graham and Hovan (1986) in which a log-hnear decrement of N7 value against footing size is predicted using a critical state model for sand. From this study, it is demonstrated that the hydrauhc gradient modelling test has a very attractive feature that it provides a simple and inexpensive method of loading soil or foundation at stress conditions corresponding to field conditions. This allows Chapter 3. Prehminary Application - Footing Test 42 -1 t QQQQO P e a k F r i c t i o n A n g l p f r o m T r i a x i a l T e s t s \u2022J3QDX3 A v e r a g e F r i c t i o n A n g l e f r o m M o d e l T e s t s ~i 1 1 1 1 \u2014 i \u2014 i \u2014 r n 1 1 1 1\u2014i\u2014i\u2014r 10 Stress Levels ( s i g 3 \/ P a ) 10 Figure 3.17: Variation of Friction Angles with Confining Stress Levels Chapter 3. Preliminary Apphcation - Footing Test 43 Figure 3.18: Prototype Footing Size Effect on iV 7 Coefficient Chapter 3. Preliminary Application - Footing Test 44 characteristic behaviour to be examined at these stress levels as well as providing a data base from which method of analysis can be compared. 3.3.3 Evaluation of Scaling Law - Modelling of Models Model footing tests were carried out on dense sand using a range of model footing diameters as well as hydrauhc gradients. This allowed a given prototype condition to be modelled in more than one way and hence allowed a check on the scaling laws implied by the hydrauhc gradient tests. Ovesen (1975) has referred to this experimental method of checking the scaling laws as the method of \"modelling of models\". This method has been frequently used in centrifuge tests to evaluate the centrifugal scaling laws. By using this technique, some technical limitation on the modelling tests can also be identified, such as boundary effects of model container. Two sets of model tests with each set representing the same prototype are shown in Table 3.6. Set 1 involves model footings having Bm \u2014 1.5 and 2.5 cm and subjected to hydrauhc gradient scale factor, N=100 and 60 respectively. Each test represents a prototype footing with Bp = 150 cm. The prototype responses from these two tests are shown in Figure 3.19 where it may be seen that they are very similar. The corresponding bearing capacities are shown in Table 3.6 and are in good agreement. Set 2 involves model footings having Bm = 1.5 and 2.0 cm subjected to scale factor, N = 80 and 60 respectively. Each test represents a prototype footing with Bp = 120 cm as shown on Table 3.6. The prototype responses from these tests are shown in Figure 3.20 and are again very similar. The ultimate bearing capacities are shown in Table 3.6 and the values are again in good agreement. These results verify that the experimental data follow the expected scaling laws as discussed in Chapter 2, and also show that the possible scale effects caused by the distortion of soil permeability during the loading process are very small. It is noted that in Figure 3.19 the load-settlement curve for Bm = 2.5 cm becomes Chapter 3. Preliminary Application - Footing Test 45 Table 3.6: Comparison of Bearing Capacity at the Same Prototype Scale, Dense Sand Set Model Footing Bm Prototype Bearing at Different N Dimension Capacity (kPa) 1 Bm = 1.5 cm, N = 100 150 165.2 Bm = 2.5 cm, N = 60 150 157.2 2 Bm = 1.5 cm, N = 80 120 140.3 Bm = 2.0 cm, N = 60 120 135.2 stiffer than the curve for Bm = 1.5 cm at footing pressure of about 250 kPa. This may be due to the boundary effect of the model container for this large footing diameter. The model container used in these tests is 127 mm in diameter. By comparing results in Figures 3.19 and 3.20, it may be seen that the soil container boundary only comes into effect when the diameter ratio between the soil container and the footing becomes less than 6. This is in agreement with the centrifuge result reported by Cheney (1985), who indicated that boundary effect becomes important when the diameter ratio between the soil container and the footing is less than 5. 3.4 Summary and Conclusion The response of a soil-structure system to load is highly dependent on the stress level involved. This is so because the stress-strain response of soil depends on stress level. Consequently, tests on small scale conventional models are unlikely to capture the response of large prototype structures. It is possible to overcome this problem with centrifuge tests in which the prototype stress level can be duplicated in a small model by applying very high centripetal accelerations, thus inducing large body forces. However, this is a very expensive testing procedure. High stress can also be induced in small models by using very high hydrauhc gradients to increase the body force. In this chapter, this technique was applied to a series of model footing tests. The testing apparatus and procedure were discussed, and Chapter 3. Preliminary Application - Footing Test 46 200.0 - i B\u201e= 1.5cm N=100 o o a e o B m = 2.5cm N=60 Both producing a prototype footing width of B.= 150cm -800.0 0.0 i i i | i i i i i i i 100.0 00.0 I I I I I I I I I I I I I I I 300.0 400.0 Footing P ressu ie (kpa) Figure 3.19: Evaluation of Scaling Law for Hydraulic Gradient Footing Tests on Dense Sand at Bp = 150cm \u2014700.0 I i i i i i i i i i | i i i i i i i i i | i i i i i i i i i | i i i i i i i i i | 0.0 100.0 200.0 300.0 400.0 Footing Pressure (kpa) Evaluation of Scaling Law for Hydraulic Gradient Footing Tests on Dense = 120cm Figure 3.20: Sand at Bp Chapter 3. Preliminary Apphcation - Footing Test 47 a new method of soil sample preparation technique was developed and evaluated for the hydraulic gradient modelling tests which enabled a fast preparation of soil sample after each and every test. The model testing results were presented and compared with centrifuge and triaxial test results. The observed load-settlement curves were found to have very similar characteristics to those observed in centrifuge tests. The footing tests on dense sands displayed a marked limit pressure effect while those on the loose sand did not. The limit pressure showed the influence of stress level in reducing the mobihzed friction angle at high stress levels. This is in agreement with both centrifuge and triaxial testing. The consistency of the model tests data was checked by comparing the results of two different model tests which simulated the same prototype. The results were found to be in very good agreement and verified that the hydraulic gradient tests followed the expected scaling laws as in the centrifuge tests. This also confirms that the distortion of soil permeability during the loading process has little effect on the test results. In addition, the \"modelling of model\" tests shows that the soil container boundary may only come into effect when the diameter ratio between the container and the footing becomes less than 6. It is demonstrated from this study that the hydrauhc gradient similitude method can be used to examine characteristic response of soil structure systems and existing knowledge under prototype stress levels, so as to obtain a better understanding of the importance of stress level. It is also shown that the hydrauhc gradient modelling test has the following ad-vantages as compared to the centrifuge tests: 1. The model test equipment involved is much cheaper. 2. The skills required by the experimenter are less demanding. 3. Tests can be performed much more quickly. Chapter 3. Preliminary Application - Footing Test 48 4. The tests could be readily carried out in most conventional soil laboratory. Based upon this experience, a more general testing device of larger size was built for the hydraulic gradient modelling tests with emphasis on foundation testing, which will be described in Chapter 4. Further applications of this modelling technique using the new testing device will be discussed in Chapters 5 and 7. Chapter 4 Hydraulic Gradient Similitude Testing Device 4.1 Introduction In this chapter, the newly developed hydrauhc gradient similitude test device at the University of British Columbia ( U B C - H G S T ) is described in detail. Its supplemen-tary equipment and associated techniques developed for different applications will be described in later chapters along with each application. The preliminary design and fabrication of this device started in December, 1987 and the first calibration test was operated in about one year later. Since then, the device is under continuous modification and improvement to incorporate different applications. The design of the U B C - H G S T apparatus was directed towards achieving an optimum combination of the following considerations: 1. simplicity in design, construction and operation; 2. versatility in application, and 3. reliabihty in measurements. Since the testing device of this kind is the first one in North America, full use was made in the design of the experience gained at U B C through the development of laboratory soil element testing devices and insitu testing devices, along with the experience gained from the previous preliminary application - footing tests described in Chapter 3. 49 Chapter 4. Hydraulic Gradient Similitude Testing Device 50 4.2 General Description In its present configuration, the U B C - H G S T device is mainly designed to perform the force controlled lateral loading tests on vertical piles. However, provision has been made to allow for performing displacement controlled test, and axial loading tests on piles or other types of foundations resting on level ground. The device can also be used to perform dynamic or seismic studies of piles or other foundations with due consideration of boundary effect. A schematic layout of the U B C - H G S T device is shown in Figure 4.1, and the photograph of the device is shown in Figure 4.2. The main body of the U B C - H G S T device consists of five major components, namely; 1. sand container and air pressure chamber; 2. water supply and circulation system; 3. air pressure supply system; 4. pile loading system, and 5. data acquisition and control system. During a test, the water is continuously supplied by a high power centrifugal water pump. The hydrauhc gradient across the soil deposit is obtained by applying an air pressure in the air chamber with water pressure venting to a low pressure at the base of soil container. The water level is maintained about 1 in. above the sand surface by balancing the air pressure and water flow for a given hydrauhc gradient. Three pore pressure transducers are used to measure the pore pressure distribution within the sand deposit. The average hydrauhc gradient within the sand deposit is obtained from the pore pressure measurements and sample height as followed: Chapter 4. Hydraulic Gradient Similitude Testing Device 51 bending strains air regulator pile loading system load deflection two way cyclic HZ] air pressure supply system air pressure chamber data acquisition system V 1 : i sand sample 12 3 water regulator ;\u2022 water supply system \\ model! pile ! 9. 9.-1 water disperser soil container \/ filter Shaking Table Note: 1,2,3 - pore water pressure transducer #PWP1 ,#PWP2,#PWP3 4 - lateral soil stress transducer LATP Soil Container Dimension: 445x230x420mm Figure 4.1: Schematic of U B C - H G S T Device Chapter 4. Hydraulic Gradient Similitude Testing Device 52 Figure 4.2: Photograph of U B C - H G S T Device Chapter 4. Hydraulic Gradient Similitude Testing Device 53 \u2022 when the bottom drainage valve is closed, and there is no water flow; i = 0 (4.1) \u2022 when the bottom drainage valve is open, and water flows under its own gravity; i = JJT * 1 (4-2) \u2022 when the bottom drainage valve is open, and the controlled air pressure is applied in the air chamber; 8 \\W\u00b1X 8 where Pi and P3 are the water pressures measured at the top and base, respec-tively, of the soil sample. Hs is the sample height, and Hw is the water table elevation relative to the sample base. A stress transducer latp is flush mounted on a side wall of soil container to measure the total lateral stress in the soil during a test. This transducer is installed at the same height as the pore pressure transducer pwp#2, so that the lateral effective stress in the soil at this point can be obtained by subtracting the measurements from these two transducers, as K ) i a t p = Mlatp ~ (u)p\u00ab\u00bbP#2 (4.4) where a'h is the horizontal effective stress at latp, ah is the lateral total stress measured by latp transducer, and (T i ) p T O p #2 is the water pressure measured by the water pressure transducer pwp#2. Calibration of the lateral stress transducer and discussion of stress gradient effect on the measurement are given in Appendix C . 4.3 Sand Container and Air Pressure Chamber The sand container is a rectangular box with inside cross section dimension of 405 x 190mm 2 and a depth of 350 mm. The box is comprised of 19.05 mm thick welded Chapter 4. Hydraulic Gradient Similitude Testing Device 54 aluminum plates. The whole box and aluminum platform are all anodized with hard coatings to prevent water corrosion. The size of the sand box is chosen based on consideration of minimum boundary effect and flexible pile condition under lateral pile load tests. Nonlinear finite element studies (Yan, 1986) have shown that under plane strain condition and hyperbohc soil stress-strain relation the outside boundary larger than 25 pile diameter have httle effect on pile response under lateral loading. In the real situation, this constraint may be more relaxed due to three dimensional displacement effect. In addition, the boundary condition in the direction perpendic-ular to the loading direction has much less effect. Thus, a rectangular cross section is designed to reduce the box cross section area, and the flow quantity. This reduces the requirement for water pump capacity and hydrauhc piping size for a given hydrauhc gradient. A comparison of the soil container size with some centrifuge boxes is given in Table 4.1. The maximum hydrauhc gradient is designed to increase the soil body force by 100 times. The maximum pressure expected for the maximum designed hydrauhc gradient will be about 350 kPa within the enclosed system. At the bottom of sand container, a filter is designed to retain the sand deposit. The filter is supported on a grid of perforated aluminum strips about 50 mm high, and cellular chambers are provided to allow water to freely flow before draining out of the soil tank. Table 4.1: A Comparison of Box Size with Some Centrifuge Boxes Test Reference long x wide x deep R D L D Scott; 1977 529 x 172 x 254 65D 50D Centrifuge Prevost, 1981 335.6 x 335.6 x 241.3 33D 40D Barton, 1982 860 x 860 x 380 27D 20D H . G . S . T . Zehkson, 1978 300 x 300 x 450 10D U B C 404 x 190 x 375 20 - 32D 34 - 50D Note: R - Outer Boundary of Container; D - Pile Diameter; Unit in mm. Chapter 4. Hydraulic Gradient Similitude Testing Device 55 The filter consists of a 6.35 mm thick perforated aluminum plate overlain by a series of stainless steel sieves including #10, #140, and #200 mesh sieves. As the sand used has been re-sieved and only the portion retained in sieve #140 is to be used in the test, the soil will be retained in this filter with little water pressure head loss across it. The filter and its support strips are designed as a grid system under a uniform distributed load (Timoshenko and Woinowsky-Krieger, 1959). The spacing of the cellular support is chosen so that the vertical deflection of the filter at each cell center would be less than 0.1mm. The soil container lid is made of a 19.05 mm thick aluminum plate which is bolted down on the container wall by 14 Hex Head cap stainless steel screws. A rubber gasket is used to seal the water pressure between the hd and container wall. The side view and plan view of the container hd are shown in Figure 4.3. The hd has a 127 mm open hole at its center to allow for sticking out of the model pile in the pile tests as well as the instrumentation wires. A n annular aluminum block of 63.5 mm high is bolted on the hd permanently to provide a vertical space for mounting pile loading and deflection measurement units for lateral pile head loading tests. A '0 ' ring is used between the annular block and the hd to seal the air pressure. A plexiglass cylinder rests on the annular block and is sealed by ' O ' rings at its two ends. The air pressure is supphed from an entry at the cap on the plexiglass cylinder. Several special pressure tight electrical plugs are installed on the cap to collect the instrumentation wires leading to the data acquisition unit. The plexiglass cylinder forms an air pressure chamber, and also allows for a visual observation of the test. This gives an additional advantage over the centrifuge test where remote monitoring on the test is necessary (video camera is often used for this purpose). The water is constantly supphed by the pump through a 25.4 mm I.D. entry hole at one side of the hd. Beneath the entry hole, a 25.4 mm thick dispersive material er 4. Hydraulic Gradient Similitude Testing Device (a). Plan View of Soil Container Lid double acting air piston eye link air chamber dispersive material model pile (b). Side View of Soil Container Lid Figure 4.3: Side and Plan Views of Soil Container Lid Chapter 4. Hydraulic Gradient Similitude Testing Device 57 is attached to disperse the water flow and prevent sand surface erosion. During the tests, the water table is kept about 25.4 mm above the sand surface but below the lid level so that the pile head loading and deflection measuring units are all above the water level. 4.4 Water Supply and Circulation System Figure 4.4 shows the water flow chart in U B C - H G S T device. The water pump is a centrifugal type with a capacity of 24 US G P M at a total pressure head of 30.48 m, manufactured by Monarch industries Ldt.. It has a 1.5 horse power built-in motor and requires 31.75 mm and 25.4 mm I.D. suction and discharge pipes, respectively. Plastic hoses are used to connect the pump with H G S T device. Before raining the sand into the container, the box and all the hoses connected to the pump and circulation tank are all saturated with the water. As shown in Figure 4.4, during the test, a downward water flow is created by opening valve #1 and #3. Then, after each test, an upward water flow is created by opening valve #2 while closing valve #1 and #3. De-air water is used in the whole system to ensure full saturation in the sand sample and alleviate possible nonuniform stress distribution due to nonsaturation of soil sample as discussed in Chapter 2. Although there is an air-water interface above the sand surface, considering the short duration and dynamic nature of the test, the possible effect of air diffusion can be neglected. 4.5 Pile Head Loading and Measuring System Pile Loading System For lateral pile head loading tests, a double acting air piston is mounted on the soil container hd with which a one-way or two-way force controlled cyclic load can be applied through a loading bushing to the pile head inside the air chamber. The Chapter 4. Hydraulic Gradient Similitude Testing Device 58 Figure 4.4: Water Flow System in U B C - H G S T Device Chapter 4. Hydraulic Gradient Similitude Testing Device 59 applied load is measured by a low capacity load cell mounted between the piston rod and the loading ram. Since in a model test, the load applied to the model pile for a given deflection would be expected to be small, the friction in a loading system becomes important if the pile response is to be measured accurately. Mostly the friction in a loading system comes from the bushing through which the loading ram apphes the force to the loaded object. In the conventional triaxial cell, relatively large friction exists in the loading bushing mostly due to the ' 0 ' ring seals. Correction for the friction has been used, however, the procedure is complex and is function of loading rate and cell pressure, especially for stress control tests. To avoid friction problem due to the loading bushing, load measurement inside the pressure cell have been suggested by some people. However, this option would greatly complicate the experimental set-up and sample preparation with no sure guarantee of better result (Chan, 1975). Based on these considerations, a decision was made to use a low friction system with no ' 0 ' ring seal. Chan (1975) and Mustapha (1982) have used a very low friction bushing system in the triaxial cell for testing soft soil at low stress confinement. A modified version of that system is used in current H G S T device, and is shown in Figure 4.5. In such a system, the axial guidance of the loading ram is provided by two stainless steel Thompson linear ball bearings. In the test, the water table is maintained below the hd of soil container. Thus a certain amount of air leaks out constantly around the loading ram. There are three components to seal. One is the fixed ring of brass which is press fitted against the housing with large clearance for the rod. The second is the closer-fitting Teflon floating seal that is spring loaded against the brass ring. The diametric clearance between the rod and Teflon seal is 0.0254 mm. The third is the spring that keeps the flat surfaces together and yet allows lateral movement of the floating seal. With this system, very small friction force (approximate 10 grm Chapter 4. Hydraulic Gradient Similitude Testing Device reaction bar Thompson linear bearing \\ brass seal plexiglass cyliner annular aluminum block \u2014 T l o \/ n n ^ o l \/ V V .. . \"O\" ring -^y fibre washer \"O\" ring w A>l oi'niiVnn\/T-) fibre washer Teflon seal V loading ram .www \/ ^ \" s p ' r i n g \" ^ \" \" \" \" \" ^ * ^ ^ s P r i n 9 Teflon seal *>J!0\" ring rubber gasket container wall soil container lid Figure 4.5: A Low Friction Bushing System for Lateral Loading Ram Chapter 4. Hydraulic Gradient Similitude Testing Device 61 force) may develop only at the contact between the loading ram and the linear bearing balls. Since the volume of the air leaking out is very small, there is no problem in maintaining the pressure inside the pressure chamber. Pile Head Connection Different pile head connections are made to study their effects on pile response. Free head connection is made by connecting the loading ram and model piles with rod end connector, as shown in Figure 4.6. A spherical bearing in the rod end connector allows for free rotation of piles in any direction. Fixed head connection is made by threading the loading ram into a rigid aluminum block which is capped on the pile head by two thread screws. Different loading adaptors are also made to load model piles at different eccen-tricities above the sand surface. Thus, for given lateral load and pile, the effect of moment to load ratio at ground surface can be studied, as discussed in Chapter 7. Pile Head Deflection Measurement As shown in Figure 4.7, a frictionless air leaking bearing system similar to the loading system is used for L V D T (a hnear variable displacement transformer) cores. This system is used to provide axial guidance to the L V D T cores approaching the model pile. The clearance between the Teflon bearing and the core is 0.0254 mm. Two L V D T s are used to measure pile head deflection at and above the loading points from outside the air chamber. Then, the pile head rotation at the loading point can be calculated from these two deflection measurements and the corresponding distance. The L V D T s are mounted on the soil container hd. They are in alignment with the loading ram but on the opposite side of the model pile. The pile deflection and rotation at the ground surface are then estimated from the following equations Chapter 4. Hydraulic Gradient Similitude Testing Device 62 loading ram ~7|T d \u2022 rod end connector spherical bearing loading adapter for different loading eccentricity loading ram rod end connector free head connection V c model pile loading ram fixed head connection rigid pile cap model pile Figure 4.6: Pile Head Loading Connections Chapter 4. Hydrauhc Gradient SimiHtude Testing Device 63 annular aluminum block \\ I I model pile side view Figure 4.7: Pile Head Deflection Measurement Chapter 4. Hydraulic Gradient Similitude Testing Device 64 based on the elastic beam theory: 09 = 0o- (4.5) yg = yo-Og-e-F-e3 SEPIP (4.6) where F is the applied load; e is the loading eccentricity; EPIP is the pile rigidity; 6D and 6g are the pile rotation at loading point and ground level respectively; and y0 4.6 Instrumentation and Data Acquisition Model Piles Model piles are made of 6061-T6 Aluminum tubing. Three pile diameters 6.35 mm, 12.7 mm, and 9.525 mm O . D . are used in the lateral load testing program to study the pile diameter effect. Of the three piles, only one pile with 6.35 mm O . D . is instrumented with strain gauges to measure the bending moment along the pile. A three point loading test on the model pile has been performed. The yielding and plastic bending moments so determined are 5772 N.mm and 7696 N.mm, respectively. A summary of the physical properties of these three piles is hsted in Table 4.2. Pile Instrumentation The 6.35 mm O . D . model pile was instrumented by eight pair of 120fi foil strain gauges at eight positions along the pile length, as illustrated in Figure 4.8. The strain gauges are glued to the outside surface of the model pile on an axis coincident with the direction of loading. Small holes are drilled on the tubing so that all the connection wires come out from inside the tubing. A l l the strain gauges are covered by layers of M-coat which provide moisture protection and smooth the pile surface over the strain gauge areas. and yg are the pile deflection at loading point and ground level respectively. Chapter 4. Hydrauhc Gradient Sirmlitude Testing Device 65 90.8 \/ F T model pile (O.D. 1\/4\") 20.0 15.0 20.0 20.0 30.0 40.0 S.G. #1 S.G. #2 S.G. #3 S.G. #4 S.G. #5 S.G. #6 S.G. #7 sand surface \/\/\/\/\/ \/\/\/\/\/\/ 60.0 S.G. #8 129.2 unit: mm \"~7\\ bottom of sand deposit \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ \/ Figure 4.8: Layout of Strain Gauges in Model Pile Chapter 4. Hydrauhc Gradient Similitude Testing Device 66 Table 4.2: Physical Properties of Model Piles Diam. O . D . (in) I (inst'ed) 3 8 I 2 Wall Thick.(in) 0.032 0.05 0.05 Length (mm) 424.0 423.5 425.0 Wt . (g) 20.3 38.2 53.4 m (g\/mm) 0.0479 0.0902 0.1256 EI (N.mm2) 4.03 x 106 19.56 x 106 52.05 x 106 The first two pairs of strain gauges are located above the sand surface to register the linear portion of the bending moment distribution above the ground. The strain gauge pairs are at spacings of 20, 15, 20, 20, 30, 40, 60 mm down the pile with closer measurements near the soil surface. Each pair of strain gauges is arranged across the pile diameter so that one gauge registered compression and the other tension strain. This arrangement will reduce the adverse effects of temperature, and cancel any axial strain effects at that level. Each pair of strain gauges in the model pile become the two active resistors in the Wheatstone bridge circuit. Normally, the half bridge circuit formed by each pair of gauges is completed to make up a full bridge by another two dummy resistors, as shown in Figure 4.9(a). Thus, a total of 16 dummy resistors and 32 wires are required for the present pile instrumentation scheme. This will lead to a great complication in the circuitry wiring and testing set-up. Complicated wiring may also create potential problems such as noisy signals. In the present design, a simpler circuit has been adopted. As the strain gauges all have the same resistance (120Q), they can be configured to share the same pair of dummy resistors, as shown in Figure 4.9(b). In addition, all the strain gauges can be excited by the same power supply. Their signal outputs can be in common at one end while different at the other, giving single ended signals. In this configuration, only two dummy resistors are required, and only 11 wires are needed to complete the Chapter 4. Hydraulic Gradient Similitude Testing Device 67 pile instrumentation. This greatly simplifies the wiring connection and experimental set-up, and also reduces potential problems in signal noise. With this strain gauge configuration, a Wheatstone bridge completion board using only two dummy precision resistors has been installed underneath the air chamber cap to complete all the strain gauge signals in a full bridge before they go out the air chamber. The calibration of the instrumented model pile was carried out by fastening the pile at one end as a cantilever, and applying dead weights at the other end. By knowing the distance to strain gauges from the dead weight, the strain gauge output signals can be calibrated against the known bending moment. As expected, a hnear calibration was obtained. By measuring the deflection at the dead weight loading point, the equivalent rigidities, EI, of the model piles were also obtained, and were shown in Table 4.2. Data Acquisition System A micro-computer based data acquisition system was used in this research. This system consists of three components: a multi-channel signal amplifier, a multi-channel analog\/digital converter DT2801A card, and a I B M - P C micro computer. A l l the transducers were excited by a common power supply which was set at 6.00 volts. In the lateral load testing on piles, a total of 15 channels were monitored, and 12 of them were recorded on each scan. The first channel carried time reference. Transducer readings were contained in the subsequent 11 channels (8 strain gauges, 2 L V D T s , and 1 load cell). The transducer signals except the 2 L V D T ' s were all amplified at a gain of 1000 by the amplifier before they reached A \/ D converter through a ribbon cable. The DT2801A A \/ D converter has 12 bits in its accuracy, which gives a = 4.88mv in accuracy for a \u00b1 1 0 V bipolar configuration. The noise level has been mon-itored for each channel, and was found to be in the order of \u00b1 5 m v at the prescribed Chapter 4. Hydraulic Gradient Similitude Testing Device 68 8 sets of bridges (need 16 S.G.; 16 dummy resistors; 32 wire leads) Figure 4.9(a) Normal Wheatstone Bridge Connection v 8 single ended output signals (need only 16 S.G.; 2 dummy resistors; 11 wire leads) strain gauge (S.G.) - V \\ A A - dummy resistor Figure 4.9(b) Simpler Wheatstone Bridge Connection Chapter 4. Hydraulic Gradient Similitude Testing Device 69 scanning frequency in the tests. This corresponds to an accuracy of \u00b1 0 . 2 kPa for the pore water pressure, \u00b1 0 . 0 2 mm for the displacement, and \u00b1 0 . 0 1 4 kg for the load. During the gravitational process, a monitoring program written in QuickBasic was used to monitor all transducer readings, especially for the three pore pressure readings, in engineering units. This permitted a control on the gravitational process. However, during the actual lateral load tests on piles, a commercial software LabtechNotebook was employed to scan and record all the readings in the disk at a prescribed rate. The data acquired were in voltage changes, and were processed at the end of each test to the desired level using other data processing programs written in F O R T R A N that will be discussed in Chapter 7. Chapter 5 A Simulation of Downhole and Crosshole Seismic Tests in HGST Device 5.1 Introduction In soil dynamics and geotechnical earthquake engineering, the shear modulus of soils at small strain level ( < 10 _ 4 % ), often called Gmax, is one of the important param-eters to be determined. It is often used to directly evaluate dynamic soil structure interaction response at small strain that occurs in machine foundation problems, or is used as an initial reference value for large strain problems that arise due to earthquake loading. In the laboratory, the dynamic shear modulus is usually obtained from a resonant column test in which a cylindrical soil sample is subjected to torsional vibration with a resonant frequency proportional to Gmax. For practical applications, the relevance of the measurement by this technique depends upon the extent to which the sample represents the actual field condition, which is usually difficult to duplicate especially for granular material such as sands. The resonant column test has been more fre-quently used to study the various factors affecting Gmax, such as the ambient stress state and soil void ratio. From these studies, various empirical formulae have now been developed to describe these effects. More recently, the interrelationships be-tween Gmax and stress state under different stress paths have been studied by Stokoe et al (1985) using a large true triaxial cell. In the field, Gmax, can be derived from measurement of shear wave velocity, Vs, 70 Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 71 using the equation: Gma*=PVl2 (5.1) where p is the bulk density of soil mass. Crosshole and downhole tests including seismic C P T (cone penetration tests) are now commonly used to determine the insitu shear wave velocity (Stokoe and Woods, 1972, Stokoe and Hoar, 1978, Woods, 1978 and Robertson et al, 1984). These methods employ procedures for generating a po-larized shear wave in one borehole, or at the surface, and measuring the time for the shear wave to travel a known distance to a sensor in another or the same borehole. However, large differences have been reported between the shear wave velocity ob-tained from laboratory resonant column tests and insitu downhole and crosshole tests (Stokoe and Richart, 1973, Anderson and Woods, 1975, Woods, 1978 and Arango, et al 1978). The shear wave velocities from insitu measurements are commonly twice the values from laboratory tests. Soil disturbance, aging and differences in bound-ary conditions have been suggested as factors to account for this large discrepancy between field and laboratory test results. Therefore, it is desirable to perform insitu downhole and crosshole shear wave tests under more controlled conditions, so that the interrelationships between the stress state and shear wave velocity developed from the conventional laboratory techniques can be compared with field conditions. In this chapter, a method of simulating downhole and crosshole tests on sand in a laboratory model scale is presented. The downhole and crosshole shear waves are generated and received by piezoceramic bender elements, while the insitu stress conditions (Ka condition) are simulated by using the Hydrauhc Gradient Similitude method. With this technique, the soil state and field stress conditions including Ka values can be controlled and measured. The primary objectives of the testing program are as follows: Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 72 \u2022 to develop a technique of using piezoceramic bender element to measure Gmax in the model soils that will be used later in the pile tests presented in Chapter 8; \u2022 to examine the validity of existing empirical equations for Gmax in terms of field stress condition; \u2022 to compare the downhole and crosshole shear wave velocities to evaluate the soil structure anisotropy; \u2022 to examine the possibility of using shear wave velocity to determine horizontal stress (or K0 values) in the field. In addition, an application of this kind itself, although in its infancy, will illustrate the usefulness of the hydrauhc gradient similitude method in studying certain soil dynamics problems. 5.2 Review of Existing Empirical Equations 5.2.1 Stress Level Effects Various forms of empirical relationships for Gmax of sand based on the results of laboratory tests have been proposed by a number of researchers. These equations generally include factors to account for grain shape, void ratio or density, and stress state or level. Based upon early resonant column test data, Hardin (1978) proposed the following equation: Gmax=A.F(e).Pa-(^)m (5.2) where A is a factor related to particle size and shape, F(e) is a function of void ratio, Pa is the atmospheric pressure, m is the stress exponent, and crm is the mean effective normal stress, i.e. crm \u2014 c r ' + c ^ + 0 ' 3 . Values of A , F(e), and exponent m as proposed Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 73 by various researchers are presented in Table 5.1. As Eq.(5.2) suggests that Gmax is a function of mean normal stress level, this formula is called the mean normal stress method. A modified version of Hardin's equation proposed by Yu and Richart (1984) called the average stress method suggests that the shear modulus is dependent upon the average stress within the plane of wave travel, i.e. Gmax = A \u2022 F(e) \u2022 Pa \u2022 (5-3) where aav = A A + \u00b0 T ; rra is the stress component in the wave propagation direction, and crp is the stress component in the particle motion direction. In Eq.(5.3), A and F(e) have the same values as in Eq.(5.2). A n alternative equation called the individual stress method was first proposed by Roesler (1979) based on his tests on a cubic sample upon which three principal stresses were applied independently. His results also suggested that it is not the mean normal stress, but the individual stress components in the plane of wave travel, which have the major influence on the shear modulus. His relation is expressed as follows: Gmax = A \u2022 F(e) \u2022 p^-ma-mP) . ama . ^ (54) From a dimensional analysis, it can be shown that ma + mp = m, which is also Table 5.1: Suggested Values and Equations for A and F(e) Sands A F(e) m References Clean Rounded 700 (2.17-e)2 0.5 Yu and Richart (1984) Clean Angular 326 (2.97-e)2 \u00b0 r (0.3+0.7e2) 0.5 Yu and Richart (1984) Clean Sand 320 (2.97-e)2 (1+e) 0.5 Hardin and Drnevich (1972) Clean Sand 625 1 (0.3+0.7e2) 0.5 Hardin (1978) Clean Sand 900 (2.17-e)2 (1+e) 0.38 Iwasaki and Tatsuoka (1977) Chapter 5. A Simulation of Downhole and Crosshole Seismic Tests 74 supported by test results (Roesler, 1979). Shear wave velocity measurement by Stokoe et al (1985) in large triaxial device supports Roesler's equation, but with ma \u2014 mp = m\/2 . Interpretation of some resonant column test results in terms of Roesler's equation (Yu and Richart, 1984, and Stokoe et al, 1985) also suggests that ma = mp = m\/2 . In fact, as the shear wave propagates through a soil element, it imposes a set of complementary dynamic shear stress both on a a and a p planes in the directions as shown in Figure 5.1. Since the same amount of shear stress is applied on both a a and