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76 CHAPTER 7 Development of Simplified Model The purpose of the work included herein is to provide the alpha coefficient of 0.85 for unit side resistance and a bearing practicing engineer a simplified approach to estimate the per- coefficient of 9 for unit base resistance. formance of a pile group exposed to lateral loading consid- The pile-group effects were modeled using user-specified ering various ground improvement techniques. A simple p-multipliers as suggested by Rollins et al. (2005). Based on the approach for design purposes is needed because FE modeling soil type, pile diameter, and pile spacing, the p-multipliers used is somewhat cost-prohibitive for routine projects. Addition- in the GROUP model were taken as 0.85, 0.70, and 0.50 for the ally, because of the complex nature of numerical modeling in leading row, middle row, and trailing row of piles, respectively. general, the use of FE analytical techniques can be misleading, These values are generally higher than those that would be counter-productive, and possibly unconservative without a computed internally from the default values used in the soft- substantial effort by well-qualified individuals who must per- ware. The default p-multipliers provided by the software, on form the analyses. average (3-D model), for the group tested in this research are 0.81, 0.51, and 0.50 for the leading row, middle row, and trail- ing row of piles, respectively. 7.1 Calibration GROUP The 3 × 3 pile groups shown in Figure 3-14 protrude a little Analysis Model more than 41 ft beneath the bottom of the pile cap. The piles A soil model was developed for application with relatively are closed-ended pipe piles filled with reinforced concrete simple (as compared to sophisticated FE techniques) pile- (non-reinforced concrete in the bottom 33.5 ft). The pipes foundation analysis software packages. Such packages are are 12.75-in. diameter with 0.375-in. wall thickness and were commercially available and widely used. This study employed impact driven with a hydraulic hammer. The embedment of GROUP (Reese, Wang, Arrellaga et al., 2004b), produced by the pile heads into the cap along with reported details of the Ensoft, Inc. The GROUP model was generated by matching the connection suggest modeling the group with "fixed condi- software output to the observed test behavior. Initially, Test 2 tions" is appropriate. (virgin soil, cap not embedded) was used to develop and cali- The center row of piles contained strain gages mounted exter- brate the model. Test 2 was selected such that the unknown nally. An angle iron was attached to protect the instrumentation. passive resistance generated by an embedded pile cap was not Therefore, the EI of the piles in the center row is 1.41 × 107 k-in2. included. The EI of the outer row piles is 1.23 × 107 k-in2. The subsurface profile used in the analyses is shown in Table 7-1, with 0 depth corresponding to the ground surface. 7.2 Comparison with Results Groundwater was at a depth of 24 in. beneath the ground sur- from Tests in Virgin Soil face. The existing p-y curve formulations available in GROUP were used. Layer 1 used the stiff clay model without free water. Using the GROUP model presented above, the observed Layers 2 and 3 used the soft clay model with K values of behavior during full-scale testing and predicted behavior using 30 pounds per cubic inch (pci) and 100pci, respectively. GROUP was evaluated. Several iterations were required in The axial resistance of the piles is an important parameter which cu, 50, and were varied until an acceptable fit of both affecting the observed rotation of the pile cap. Because the piles deflection and cap rotation was obtained for Test 2. Note the are embedded in soft to stiff clay, the nominal axial resistance various model inputs that provided the best fit are in good of the piles used in the GROUP model was estimated using an agreement with typically used values and are consistent with

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77 Table 7-1. Summary of soil properties used in GROUP analysis. Depth (in) Undrained Shear Strength (psi) 50 (%) Total Unit Layer Top Bottom Top Bottom Top Bottom Weight (pcf) 1 0 30 11.0 5.5 0.005 0.01 117.5 2 30 66 5.5 3.3 0.01 0.015 109 3 66 600 3.3 8.0 0.015 0.005 118 data obtained during the subsurface investigation. The final horizontal test conducted without passive resistance of the pile values obtained are those shown in Table 7-1. caps (e.g., soil adjacent to the pile cap was excavated prior to Using the soil model described previously, adequate agree- the test so the cap was not embedded). Figure 7-2 compares ment between the observed behavior during full-scale testing the observed versus modeled pile cap rotation for Test 2. and predicted behavior using GROUP is obtained as can be The lower magnitude horizontal loads were not investi- seen in Figures 7-1 and 7-2. Figure 7-1 compares the observed gated because Test 2 was conducted in the opposite direc- versus modeled pile head deflection for Test 2. Test 2 was the tion of Test 1, and because Test 1 was performed first. It is 300 275 Measured Full-Scale 250 GROUP Model 225 Horizontal Load (kips) 200 175 150 125 100 75 50 25 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 Pile Deflection at Bottom of Cap (in) Figure 7-1. Comparison of measured and computed load-deflection for Test 2 (virgin soil, pile caps not embedded). 300 275 250 225 Horizontal Load (kips) 200 175 150 Measured Full-Scale 125 GROUP Model 100 75 50 25 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Pile Cap Rotation (degrees) Figure 7-2. Comparison of measured and computed load-rotation curves for Test 2 (virgin soil, pile caps not embedded).

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78 300 275 250 225 Horizontal Load (kips) 200 175 150 Measured Full-Scale 125 GROUP Model 100 75 50 25 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 Pile Deflection at Bottom of Cap (in) Figure 7-3. Comparison of measured and computed load-deflection curves for Test 1 (virgin soil, pile caps embedded). believed that performing Test 1 prior to Test 2, but in the passive resistance provided by the pile cap at various deflections opposite direction, may have impacted the lower magnitude is computed as the difference between the actual applied hori- results. zontal force in the field load test and the applied horizontal After matching the Test 2 deflection and rotation via an force in the calibrated model. iterative approach, the model was used to evaluate Test 1 (vir- The pile cap rotation predicted by the GROUP model gin soil, pile cap embedded) to evaluate the effect of the also was compared to the measured rotation, as shown in embedded cap on the total lateral resistance of the group. For Figure 7-4. Although not perfect, the agreement between these analyses, the magnitude of the applied horizontal force the two curves is reasonable and provides further validation was reduced until the field-measured deflection and GROUP of the GROUP model. model deflection were nearly equal, as shown in Figure 7-3. The passive resistance is equal to the difference between the This procedure was performed for each loading increment. The load applied during the test and the load applied in GROUP 300 275 250 225 Horizontal Load (kips) 200 175 150 125 Measured Full-Scale 100 GROUP Model 75 50 25 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Pile Cap Rotation (degrees) Figure 7-4. Comparison of measured and computed load-rotation curves for Test 1 (virgin soil, pile caps embedded).