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Suggested Citation:"Chapter 7 - Development of Simplified Model." National Academies of Sciences, Engineering, and Medicine. 2011. Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils. Washington, DC: The National Academies Press. doi: 10.17226/14574.
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Suggested Citation:"Chapter 7 - Development of Simplified Model." National Academies of Sciences, Engineering, and Medicine. 2011. Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils. Washington, DC: The National Academies Press. doi: 10.17226/14574.
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Suggested Citation:"Chapter 7 - Development of Simplified Model." National Academies of Sciences, Engineering, and Medicine. 2011. Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils. Washington, DC: The National Academies Press. doi: 10.17226/14574.
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Suggested Citation:"Chapter 7 - Development of Simplified Model." National Academies of Sciences, Engineering, and Medicine. 2011. Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils. Washington, DC: The National Academies Press. doi: 10.17226/14574.
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Suggested Citation:"Chapter 7 - Development of Simplified Model." National Academies of Sciences, Engineering, and Medicine. 2011. Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils. Washington, DC: The National Academies Press. doi: 10.17226/14574.
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Suggested Citation:"Chapter 7 - Development of Simplified Model." National Academies of Sciences, Engineering, and Medicine. 2011. Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils. Washington, DC: The National Academies Press. doi: 10.17226/14574.
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Suggested Citation:"Chapter 7 - Development of Simplified Model." National Academies of Sciences, Engineering, and Medicine. 2011. Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils. Washington, DC: The National Academies Press. doi: 10.17226/14574.
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Suggested Citation:"Chapter 7 - Development of Simplified Model." National Academies of Sciences, Engineering, and Medicine. 2011. Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils. Washington, DC: The National Academies Press. doi: 10.17226/14574.
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Suggested Citation:"Chapter 7 - Development of Simplified Model." National Academies of Sciences, Engineering, and Medicine. 2011. Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils. Washington, DC: The National Academies Press. doi: 10.17226/14574.
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Suggested Citation:"Chapter 7 - Development of Simplified Model." National Academies of Sciences, Engineering, and Medicine. 2011. Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils. Washington, DC: The National Academies Press. doi: 10.17226/14574.
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Suggested Citation:"Chapter 7 - Development of Simplified Model." National Academies of Sciences, Engineering, and Medicine. 2011. Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils. Washington, DC: The National Academies Press. doi: 10.17226/14574.
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Suggested Citation:"Chapter 7 - Development of Simplified Model." National Academies of Sciences, Engineering, and Medicine. 2011. Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils. Washington, DC: The National Academies Press. doi: 10.17226/14574.
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Suggested Citation:"Chapter 7 - Development of Simplified Model." National Academies of Sciences, Engineering, and Medicine. 2011. Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils. Washington, DC: The National Academies Press. doi: 10.17226/14574.
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Suggested Citation:"Chapter 7 - Development of Simplified Model." National Academies of Sciences, Engineering, and Medicine. 2011. Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils. Washington, DC: The National Academies Press. doi: 10.17226/14574.
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Suggested Citation:"Chapter 7 - Development of Simplified Model." National Academies of Sciences, Engineering, and Medicine. 2011. Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils. Washington, DC: The National Academies Press. doi: 10.17226/14574.
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Suggested Citation:"Chapter 7 - Development of Simplified Model." National Academies of Sciences, Engineering, and Medicine. 2011. Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils. Washington, DC: The National Academies Press. doi: 10.17226/14574.
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Suggested Citation:"Chapter 7 - Development of Simplified Model." National Academies of Sciences, Engineering, and Medicine. 2011. Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils. Washington, DC: The National Academies Press. doi: 10.17226/14574.
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Suggested Citation:"Chapter 7 - Development of Simplified Model." National Academies of Sciences, Engineering, and Medicine. 2011. Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils. Washington, DC: The National Academies Press. doi: 10.17226/14574.
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Suggested Citation:"Chapter 7 - Development of Simplified Model." National Academies of Sciences, Engineering, and Medicine. 2011. Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils. Washington, DC: The National Academies Press. doi: 10.17226/14574.
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Suggested Citation:"Chapter 7 - Development of Simplified Model." National Academies of Sciences, Engineering, and Medicine. 2011. Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils. Washington, DC: The National Academies Press. doi: 10.17226/14574.
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76 The purpose of the work included herein is to provide the practicing engineer a simplified approach to estimate the per- formance of a pile group exposed to lateral loading consid- ering various ground improvement techniques. A simple approach for design purposes is needed because FE modeling is somewhat cost-prohibitive for routine projects. Addition- ally, because of the complex nature of numerical modeling in general, the use of FE analytical techniques can be misleading, counter-productive, and possibly unconservative without a substantial effort by well-qualified individuals who must per- form the analyses. 7.1 Calibration GROUP Analysis Model A soil model was developed for application with relatively simple (as compared to sophisticated FE techniques) pile- foundation analysis software packages. Such packages are commercially available and widely used. This study employed GROUP (Reese, Wang, Arrellaga et al., 2004b), produced by Ensoft, Inc. The GROUP model was generated by matching the software output to the observed test behavior. Initially, Test 2 (virgin soil, cap not embedded) was used to develop and cali- brate the model. Test 2 was selected such that the unknown passive resistance generated by an embedded pile cap was not included. The subsurface profile used in the analyses is shown in Table 7-1, with 0 depth corresponding to the ground surface. Groundwater was at a depth of 24 in. beneath the ground sur- face. The existing p-y curve formulations available in GROUP were used. Layer 1 used the stiff clay model without free water. Layers 2 and 3 used the soft clay model with K values of 30 pounds per cubic inch (pci) and 100pci, respectively. The axial resistance of the piles is an important parameter affecting the observed rotation of the pile cap. Because the piles are embedded in soft to stiff clay, the nominal axial resistance of the piles used in the GROUP model was estimated using an alpha coefficient of 0.85 for unit side resistance and a bearing coefficient of 9 for unit base resistance. The pile-group effects were modeled using user-specified p-multipliers as suggested by Rollins et al. (2005). Based on the soil type, pile diameter, and pile spacing, the p-multipliers used in the GROUP model were taken as 0.85, 0.70, and 0.50 for the leading row, middle row, and trailing row of piles, respectively. These values are generally higher than those that would be computed internally from the default values used in the soft- ware. The default p-multipliers provided by the software, on 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. The 3 × 3 pile groups shown in Figure 3-14 protrude a little more than 41 ft beneath the bottom of the pile cap. The piles are closed-ended pipe piles filled with reinforced concrete (non-reinforced concrete in the bottom 33.5 ft). The pipes are 12.75-in. diameter with 0.375-in. wall thickness and were impact driven with a hydraulic hammer. The embedment of the pile heads into the cap along with reported details of the connection suggest modeling the group with “fixed condi- tions” is appropriate. The center row of piles contained strain gages mounted exter- nally. An angle iron was attached to protect the instrumentation. Therefore, the EI of the piles in the center row is 1.41 × 107 k-in2. The EI of the outer row piles is 1.23 × 107 k-in2. 7.2 Comparison with Results from Tests in Virgin Soil Using the GROUP model presented above, the observed behavior during full-scale testing and predicted behavior using GROUP was evaluated. Several iterations were required in which cu, 50, and α were varied until an acceptable fit of both deflection and cap rotation was obtained for Test 2. Note the various model inputs that provided the best fit are in good agreement with typically used values and are consistent with C H A P T E R 7 Development of Simplified Model

data obtained during the subsurface investigation. The final values obtained are those shown in Table 7-1. Using the soil model described previously, adequate agree- ment between the observed behavior during full-scale testing and predicted behavior using GROUP is obtained as can be seen in Figures 7-1 and 7-2. Figure 7-1 compares the observed versus modeled pile head deflection for Test 2. Test 2 was the horizontal test conducted without passive resistance of the pile caps (e.g., soil adjacent to the pile cap was excavated prior to the test so the cap was not embedded). Figure 7-2 compares the observed versus modeled pile cap rotation for Test 2. The lower magnitude horizontal loads were not investi- gated because Test 2 was conducted in the opposite direc- tion of Test 1, and because Test 1 was performed first. It is 77 Depth (in) Undrained Shear Strength (psi) 50 (%) Layer Top Bottom Top Bottom Top Bottom Total Unit 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 Table 7-1. Summary of soil properties used in GROUP analysis. 0 25 50 75 100 125 150 175 200 225 250 275 300 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 H or iz on ta l L oa d (ki ps ) Pile Deflection at Bottom of Cap (in) Measured Full-Scale GROUP Model Figure 7-1. Comparison of measured and computed load-deflection for Test 2 (virgin soil, pile caps not embedded). 0 25 50 75 100 125 150 175 200 225 250 275 300 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 H o riz o n ta l L o ad (k ips ) Pile Cap Rotation (degrees) Measured Full-Scale GROUP Model Figure 7-2. Comparison of measured and computed load-rotation curves for Test 2 (virgin soil, pile caps not embedded).

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

to displace the cap the same distance. A comparison between the passive resistance reported and that computed by the GROUP model is shown in Figure 7-5. The good agreement appears to further validate the GROUP model. 7.3 Comparison with Results from Tests Involving Mass Mixing The calibrated model and the procedure for estimating the contribution of the pile cap to lateral resistance described above provides a means of directly evaluating the benefit of using mass mix soil improvement adjacent to a pile cap. Mass mix soil improvement was performed adjacent to Pile Cap 1. In plan view, the treatment was 4 ft parallel to, and 11 ft per- pendicular to, the direction of loading. The treatment depth was 10 ft, which resulted in improved soil adjacent to and 7.5 ft beneath the bottom of the pile cap. Details of the mass mix procedure are provided in Section 3.8 and Herbst (2008, Appendix 3). The unconfined compressive strength of the mass mix material was reportedly on the order of about 130 psi and was therefore substantially stronger than the in-situ fine-grained soil. Similar to the approach used for Test 1 (virgin soil, pile cap embedded), the magnitude of the applied horizontal load was reduced in the GROUP model until the field-measured deflection and GROUP model deflection were nearly equal, as shown in Figure 7-6. This procedure was performed for each loading increment. The passive resistance provided by the pile cap plus mass mix at various deflections was computed as the difference between the actual applied horizontal force in the field load test and the applied horizontal force in the cali- brated model. The pile cap rotation predicted by the GROUP model was then compared to that which was measured, as shown in Fig- ure 7-7. Although not perfect, adequate agreement between the two exists. These results again seem to confirm the applicabil- ity of the GROUP model. The additional resistance provided by the mass mix is equal to the difference between the load applied during the test and the load applied in GROUP to displace the cap the same distance. A comparison between the virgin soil (passive) resis- tance and that observed during the mass mix test (computed by the GROUP model) is shown in Figure 7-8. The magnitude of additional resistance provided by the mass mix is consid- ered to be a combination of passive resistance acting on a por- tion of the leading edge of the mass mix block and adhesion along the sides of the block. 7.4 Development of Simplified Method The simplified method proposed for design is based on estimating the contribution of the treated ground around the pile group using a limit equilibrium analysis of the treated soil mass. This analysis includes passive resistance acting against the face of the treated soil mass and adhesion acting on the sides of the treated soil mass as lateral displacement mobilizes the passive soil resistance. To model the effect of ground treatment using generally available computer software, the contribution of the treated 79 Figure 7-5. Computed passive resistance acting on pile cap in virgin soil. 0 5 10 15 20 25 30 35 40 45 50 55 60 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 Pa ss iv e R e s is ta nc e (k) Pile Cap Deflection (in) GROUP Model Herbst (2008)

80 0 50 100 150 200 250 300 350 400 450 500 0 0.25 0.5 0.75 1 1.25 1.5 H or iz on ta l L oa d (ki ps ) Pile Deflection at Bottom of Cap (in) Measured Full-Scale GROUP Model Figure 7-6. Comparison of load-deflection curves for pile group test involving mass mixing. Figure 7-7. Comparison of measured and computed load-rotation curves for test involving mass mixing. 0 50 100 150 200 250 300 350 400 450 500 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 H or iz o n ta l L oa d (ki ps ) Pile Cap Rotation (degrees) Measured Full-Scale (low) Measured Full Scale (high) GROUP Model soil to the lateral resistance of the foundation is modeled by reducing the magnitude of horizontal load applied to the foundation by the estimated amount of passive and adhesive resistance provided by the improved (treated) area. The limit equilibrium analysis is used to estimate the magnitude of pas- sive resistance acting on the leading face of the treated block and the amount of adhesive resistance acting on the sides and the base of the block. The geometry of the treated soil mass is subject to limitations on the projected area and the depth of the treated area relative to the width of the group. Passive Resistance Acting on the Face of the Treated Soil Mass Based upon the computed magnitude of passive resistance acting against the leading face of the pile cap (50 kips at 1-in.

deflection), and the dimensions of the embedded cap (8.75 ft by 2.5 ft), a unit value for passive resistance acting against the cap in virgin soil can be computed as follows: Because of observed desiccation of the crust and associated cracks in the soil matrix, it is considered likely that the effective shear strength contributing to passive lateral resistance in the upper 1 ft of the soil mass would be slightly less than the strength measured using the relatively small cone penetrometer or lab- oratory tests on relatively small samples. With the computed unit passive resistance determined above, Rankine earth pressure theory can be used to determine the undrained shear strength profile over the depth of the pile cap. Note that the details of the strength profile within this depth range do not change the calibrated GROUP model dis- cussed previously because the piles are embedded beneath this zone and are not affected by the shear strength surround- ing the pile cap (cap not embedded in the GROUP model). The following expression for Rankine passive resistance was used to correlate the relationship between the undrained shear strength of the soil and the lateral soil resistance acting against the cap: Below the top 1 ft of soil, this relationship was used with the shear strength profile used in the GROUP model. In the upper 1 ft of soil, the shear strength profile was back-calculated using p cp u v= + ′2 10σ ( ) p k ft ft ksfp = ×( ) =50 2 5 8 75 2 29 9. . . ( ) this relationship so as to provide a total lateral resistance against the cap equal to that determined from the previous compar- isons of measured contribution of the pile cap. Since pp has been determined to provide an average value of 2.29 ksf and σ′v can be estimated from the unit weight of the soil, cu can be determined in the upper foot. The undrained shear strength profile used to estimate passive and adhesive resistance is shown in Figure 7-9, along with the effective vertical stress and unit passive resistance (Rankine 2-D) profiles. Adhesion Acting on the Sides and Base of the Treated Soil Mass The parametric study using finite element analyses provided an evaluation of the effect of treatment depth on the lateral resistance contributed by the treatment. One of these analyses considered treatment only to the bottom of the cap (depth of 2.5 ft) and adjacent to the leading face of the cap. The zone of treatment in the model was 4 ft in the direction of loading and 9 ft perpendicular to the direction of loading, slightly smaller than actually tested due to limitations in the geometry of the model. The results indicate that 45k of additional resistance resulted from creating this treated block above the magnitude of the resistance provided by virgin soil. This additional resis- tance is likely to have been developed by adhesion along the two sides and the base of the treatment block, assuming the unit passive resistance acting on the leading face of the block is equal to that of the pile cap with identical dimensions. Because the dimensions of the treated block are known and the magnitude of additional resistance provided by adhesion 81 Figure 7-8. Additional lateral resistance provided by mass mixing estimated by the GROUP model. 0 50 100 150 200 250 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Pa ss iv e + Ad he s io n (ki ps ) Pile Cap Deflection (in) Mass Mix (GROUP Model) Virgin Soil (GROUP Model)

on the block is known, an adhesion factor (αpass) can be deter- mined based on a comparison of the adhesion acting on the block with the undrained shear strength of the soil. This adhesion factor represents the ratio of the adhesion to the undrained shear strength, a parameter that is similar but not identical to the alpha factor (α) used for the axial resistance of the driven piles (which was 0.85). Of course, considering the different construction methods and materials, there is no rea- son to assume that the adhesion on the treated block would be the same as the adhesion on a driven steel pile. From Fig- ure 7-9, the average undrained shear strength acting along the depth of the pile cap (0 to 2.5 ft) is 1.07 ksf; the undrained shear strength adjacent to the bottom of the pile cap is 0.79 ksf. The adhesion factor (αpass) can then be estimated as follows: Accordingly, a simplified approach to estimate the addi- tional lateral resistance provided by a block of improved soil adjacent to the pile cap in the direction of loading has been developed. This simplified approach has been calibrated to the parametric studies conducted using an FE model and is presented in Chapter 6. The parametric studies, which utilized a model calibrated to the full-scale load test results, investigated the relative improvement of lateral resistance gleaned by vary- ing both the width and depth of treatment. The results of these studies are shown in Figures 7-10 and 7-11. 45 2 2 5 4 1 07 1 k sides ft ft ksf base pass= × × × ×( ) + × . . α 9 4 0 79 0 9 11 ft ft ksf pass pass × × ×( ) = . . ( ) α α Limitations Related to the Geometry of the Treated Soil Mass The parametric FE studies generally indicate a linear increase in lateral resistance when the improvement dimension paral- lel to the direction of loading increases. Intuitively, this linear increase should continue to an upper bound that is defined by the entire soil layer around the pile cap and having the prop- erties of the treated soil. Alternatively, the relative amount of improvement with increasing depth of treatment is observed to decrease. Beyond a depth of about three times the pile cap embedment depth (equal to 7.5 ft for this study), relatively little increase in lat- eral resistance is observed. The small amount that is observed is likely a result of the treatment affecting the lateral behavior of the piles as opposed to only providing additional resistance to the cap. The simplified design approach presented herein conservatively neglects the slight additional resistance that may exist beneath a depth of three times the pile cap embed- ment depth. Iterative analyses indicate the geometry of the constructed block (treated soil) is not identical to the constructed dimen- sions with regard to surface area available for passive and adhe- sive resistance. For this purpose, a “projected area” is proposed. The projected area is defined by a line projecting at a 52° angle from the heel of the leading edge of the pile cap through the treated block. All surface area above this projected line is available for either passive resistance or adhesion. This pro- jected area is shown relative to the FE parametric study in Fig- ures 7-12 and 7-13. 82 Figure 7-9. Variation of undrained strength, effective vertical stress and Rankine unit passive resistance vs depth at the virgin soil profile. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 D ep th b el ow G ro u n d Su rf ac e (ft ) ksf Undrained Shear Strength Effective Vertical Stress Rankine Unit Passive Resistance Bottom of Pile Cap

83 Figure 7-10. Results from FE parametric depth study for soil mixing. Figure 7-11. Results from FE parametric length study for mass mixing.

84 Figure 7-12. Projected area available for passive and adhesive resistance (1 of 2). Figure 7-13. Projected area available for passive and adhesive resistance (2 of 2). -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 52° Passive Resistance Adhesion (2 Sides) Pile Cap Pile Mass Mix Treatment Projected Area Contributing to Additional Lateral Resistance (Typical) 52° Passive Resistance Adhesion (2 Sides) Pile Cap Pile Mass Mix Treatment Projected Area Contributing to Additional Lateral Resistance (Typical) Adhesion - Base (where applicable) -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 The 52° angle defining the projected area was determined to provide a best fit with respect to a comparison between the results of the parametric study and the simplified method. For design purposes, the projected area can conservatively be defined using a 45° angle, which is recommended. Further- more, based on results of the FE parametric study as well as the investigated treatment geometries using a projected area defined by a 52° angle, the benefit of treatment and applica- bility of this simplified approach should be truncated at a depth equal to 3 times the pile cap embedment depth assum- ing the depth dimension of the treatment controls. Note that the sides of the contributing treatment block defined by the projected area are trapezoidal in shape. Accord- ingly, a three-dimensional weighted average is necessary for

estimating the undrained shear strength acting along the sides (assuming the shear strength profile varies with depth). If the treatment block projected area contains a horizontal base, the adhesion acting on the base of the block also should be included. If the treatment depth is deeper, a tension crack is expected to develop behind the trapezoidal block beneath the bottom of the pile cap, thereby nullifying any base adhesion. Incorporation of the Lateral Resistance from the Treated Soil Mass into the Analysis of the Pile Group The proposed method decouples the limit equilibrium analysis of the treated soil mass from the analysis of the pile group. The magnitude of lateral resistance provided by the projected area is computed in accordance with the methodol- ogy outlined previously. In order to incorporate this contri- bution into the analysis of the foundation response using available software (such as GROUP or similar), the magnitude of the applied horizontal force acting on the pile group is reduced by the contribution of the treated soil mass. To illustrate the applicability of this simplified approach, Figures 7-14 and 7-15 have been developed for comparison purposes. The plots in Figure 7-14 provide a comparison of results including the FE parametric studies involving changes in the treatment dimension parallel to the direction of loading. The FE results and projected area dimensions were presented in Figures 7-10 and 7-12, respectively. For all cases, the simpli- fied approach is within 15% of the FE model. Less agreement is apparent for increasing dimensions of treatment, so extrap- olation beyond the results investigated herein is not recom- mended. With any simplified approach, some discrepancy is anticipated, and 15% would appear to be within the realm of sufficient accuracy and precision for general design purposes. The graph in Figure 7-15 provides a comparison of results including the FE parametric studies involving changes in the treatment depth. The FE results and projected area dimensions were presented in Figures 7-11 and 7-13, respectively. For all cases, excellent agreement is obtained and further substanti- ates truncating the projected area depth at three times the embedded pile cap depth. 7.5 Evaluation for Jet Grouting Cases Similar to the mass mix tests, jet grout ground improvement techniques were performed in or around the pile groups and tested to evaluate the benefit on performance of the group under lateral loading. Jet grout ground improvement was con- structed adjacent to Pile Cap 1 and the leading row of piles in the group, as shown in Figure 7-16. It also was constructed beneath Pile Cap 2 around the piles in the group. The plan dimensions provided in Figure 7-16 indicate a treatment area of 10 ft perpendicular to the direction of load- ing and 15 ft parallel to the loading. The profile dimensions indicate ground improvement from the bottom of the pile cap to a depth of 12.5 ft below ground surface. All dimensions defining jet grout ground improvement must be considered as estimates only. Neat lines do not exist considering the nature of the jet grout process. 85 Figure 7-14. Simplified and FE results with varying treatment width. 0 25 50 75 100 125 150 175 200 225 250 275 0 1 2 3 4 5 6 7 8 Pa ss iv e + Ad he s io n (ki ps ) Mass Mix Treatment Dimension in Direction of Loading (ft) Simplified (Rankine + Adhesion) Modeled (FE & GROUP) Modeled + 15% Modeled -15%

86 Figure 7-15. Simplified and FE results with varying treatment depth. 0 20 40 60 80 100 120 140 160 180 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Pa ss iv e + Ad he si on (ki ps ) Mass Mix Treatment Depth (ft) Simplified (Rankine + Adhesion) Modeled (FE & GROUP) Figure 7-16. Layout of test for pile group with jet grout treatment. Schematic plan view of Test 4.

The unconfined compressive strength of the jet grout improved soil at the time of the tests is estimated to be greater than 600 psi. Further discussion of the strength is provided in Chapter 4. However, the results of these analyses, as with the FE analyses, are not sensitive to the strength of the jet grout improved soil since it is significantly stronger than the in-situ soil. The first attempt at testing the two groups was not success- ful. Because only one actuator was initially used, the load to produce significant deflection was not available. Accordingly, an additional actuator was used in series with the first to dou- ble the horizontal load applied to Cap 2. However, additional loading capacity was not available for Cap 1. The measured load-displacement curves for Caps 1 and 2 are provided in Figures 3-26 and 3-27, respectively. The maximum loading magnitude applied to Caps 1 is about 450k, slightly more than half the 800k maximum load applied to Cap 2. The 800k maximum load applied to Cap 2 appears to initiate an ulti- mate, or limit state, condition with excessive deflection under constant load. The simplified procedure described previously is compared with the results of the jet grout ground improvement, based on the results measured at Cap 2 (jet grout beneath cap and around piles). Insufficient load versus deflection data exist for Cap 1 to draw definitive conclusions. However, based on the similar load-deflection behavior observed at both caps at rela- tively small displacements, and the applicability of the simpli- fied procedure to mass mix or jet grout improved soils, it is considered reasonable that the simplified procedure is appro- priate for conditions tested at Cap 1. The lateral resistance provided by the jet grout ground improvement is estimated using a limit equilibrium approach, and the contribution of the improved soil incorporated into the analysis by reducing the magnitude of the applied force by the contribution to lateral resistance from the block of improved ground. This reduced force is then used in GROUP (or equivalent) to compute the response of the pile group separately from the contribution of the improved ground. The passive resistance is estimated using Rankine earth pres- sure theory and should be truncated at a depth equal to the width of the group from outside pile edge to outside pile edge perpendicular to the direction of loading. The adhesive resis- tance along the sides of the treatment block, also truncated with depth, is estimated using αpass=0.9 times the undrained shear strength. The undrained shear strength may be com- puted using a weighted average over the surface of the block. The adhesive resistance along the base should also be included in a similar manner to that along the sides. This simplified pro- cedure is shown graphically in Figures 7-17 and 7-18 for the actual and simplified cases, respectively. Considering the jet grout ground improvement geometry beneath Cap 2 and the unit passive resistance and shear strength versus depth data presented in Figure 7-9, the summation of passive and adhesive resistance can be estimated as follows for the truncated depth: • Passive Resistance: 10 ft × 7.5 ft × 1.85ksf = 139k – where 10 ft is the treatment dimension perpendicular to loading, – where 7.5 ft is the truncated depth, and 87 Figure 7-17. Jet grout test as performed (Cap 2). -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Fe et Ground Surface Jet Grout

– where 1.85 ksf is the average unit passive resistance over the truncated depth. • Adhesive Resistance (sides): 2 sides × 5 ft × 15 ft × 0.9 × 0.58ksf = 78k – where 5 ft is the truncated treatment depth beneath the cap (note the sides of the cap are not in contact with the soil), – where 15 ft is the treatment dimension parallel to loading, – where 0.9 is αpass, and – where 0.58 ksf is the average undrained shear strength over this depth. • Adhesive Resistance (base): 10 ft × 15 ft × 0.9 × 0.50ksf = 68k – where 10 ft is the treatment dimension perpendicular to loading, – where 15 ft is the treatment dimension parallel to loading, – where 0.9 is αpass, and – where 0.50 ksf is the undrained shear strength at this depth. • Therefore, reduce the applied load by: 139k + 78k + 68k = 285k. Alternatively, if the depth were not truncated, the summa- tion of passive and adhesive resistance would be estimated as follows for the entire treatment depth: • Passive Resistance: 10 ft × 12.5 ft × 1.84ksf = 230k – where 10 ft is the treatment dimension perpendicular to loading, – where 12.5 ft is the treatment depth, and – where 1.84ksf is the average unit passive resistance over the treatment depth. • Adhesive Resistance (sides): 2 sides × 10 ft × 15 ft × 0.9 × 0.56ksf = 151k – where 10 ft is the truncated treatment depth beneath the cap (note the sides of the cap are not in contact with the soil), – where 15 ft is the treatment dimension parallel to loading, – where 0.9 is αpass, and – where 0.56 ksf is the average undrained shear strength over this depth. • Adhesive Resistance (base): 10ft × 15ft × 0.9 × 0.58ksf = 78k – where 10 ft is the treatment dimension perpendicular to loading, – where 15 ft is the treatment dimension parallel to loading, – where 0.9 is αpass, and – where 0.58 ksf is the undrained shear strength at this depth. • Therefore, reduce the applied load by: 230k + 151k + 78k = 459k. If the magnitude of the applied load is reduced by the amounts listed above (285k for truncated depth and 459k for full treatment depth), and applied considering the appropri- ate effective cap depth (7.5 ft and 12.5 ft beneath ground sur- face, respectively) using the GROUP model discussed above, good agreement with measured performance is obtained. A comparison of the results predicted using the aforementioned simplified procedure versus the measured data is provided in Figure 7-19. 88 Adhesion (2 Sides) Adhesion (Base) Passive Resistance Truncated Depth Reduced Load 18 19 200 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 Fe et Figure 7-18. Forces on pile cap for simplified procedure for jet grout test.

Note that the simplified procedure as presented requires adjustment at lower magnitude loading because full passive resistance is not mobilized at small deflections. To compute the contribution of the treated block at less than full pas- sive resistance, the method requires that the passive resis- tance be reduced to the mobilized resistance as a function of deflection. This condition would require an iterative approach using estimates of the mobilized passive resistance versus deflection. A comparison of the measured and modeled (simplified procedure in conjunction with GROUP) behavior of the cap and center pile in the leading row is provided in Table 7-2. The proposed simple design procedure appears to provide reason- able agreement with full-scale test measurements, sufficient for general design purposes. The results shown in Figure 7-19 indicate that the proposed procedure for truncating the depth of treated soil for design purposes produces a design that is slightly conservative. This slight conservatism seems appropriate for design, particularly when a simplified method is employed. Furthermore, the reduced benefit of treatment with depth is indicated by param- etric analyses conducted using an FE model. The results from the parametric FE model study are shown in Figure 7-20. Note that the ground improvement dimensions evaluated in the FE parametric study are slightly different to those constructed and tested in-situ. The effect of increasing the depth of treatment on lateral resistance is shown in Figure 7-20 where depth is relative to the ground surface. As indicated in Figure 7-20, the relative magnitude of the improvement in lat- eral resistance does not increase linearly in proportion to the depth of treatment. These results suggest that the proposed use of a truncated depth is a suitable simplification. Recall that the simplified procedure truncates the treated soil block at a depth equal to the outside-to-outside dimension of the piles in the group perpendicular to the direction of loading. 7.6 Design Recommendations Pile Group Improved with Cemented Soils or Flowable Fill Assuming that the treated soil has a compressive strength of at least 75 psi, the following simplified design approach is rec- ommended for the purpose of estimating the additional lateral resistance provided by the ground improvement: 1. Based on the proposed geometry of the treatment area, compute the magnitude of passive resistance acting on 89 Table 7-2. Comparison of results from full-scale test and simplified procedure. Figure 7-19. Comparison of simplified procedure to measured results. 0 100 200 300 400 500 600 700 800 0 0.5 1 1.5 2 2.5 3 H or iz on ta l L oa d (ki ps ) Pile Cap Deflection (in) Measured Full-Scale Simplified (Load minus Rankine & Adhesion to D=12.5ft) Simplified (Load minus Rankine & Adhesion to D=7.5ft) Measured Simplified Pile Cap Rotation 0.76° 0.96° Pile Deflection at a Depth of 7.5 ft beneath Ground Surface 1.14in 1.22in Maximum Bending Moment in Leading Row, Center Pile 100 to 160 k-ft 195 k-ft Depth to Maximum Moment beneath Ground Surface 15.5ft 13.5ft

the leading face of the block using Rankine earth pressure theory with the following constraints: – The surface area of the leading face for passive resis- tance calculations should be the projected area defined by a 45° angle projecting from the pile cap (in all directions) if ground improvement is adjacent to the pile cap. – The depth dimension of the projected area should be truncated at a depth below ground surface equal to the outside-to-outside dimension of the piles in the group perpendicular to the direction of loading. 2. Compute the magnitude of adhesion acting along the sides of the treatment block using αpass = 0.9. The sides of the contributing treatment block (defined by a 45° angle from the pile cap) are trapezoidal in shape and limited to the geometric constraints noted in Step 1. A three- dimensional weighted average is used to estimate the undrained shear strength acting along the sides (assuming the shear strength profile varies with depth). If the treat- ment block projected area contains a horizontal base, the adhesion acting on the base of the block also should be included. If the treatment depth is deeper and/or the base is not horizontal, a tension crack is expected to develop behind the trapezoidal block beneath the bottom of the pile cap, thereby nullifying any base adhesion. 3. Compute the total lateral resistance contributed by the treated block as the sum of the passive resistance and adhe- sion acting on the projected area of the treatment block. Reduce the external horizontal loading force magnitude applied to the pile cap by the lateral resistance contributed by the treated block. 4. Use the reduced horizontal forces described in Step 3 in GROUP (or a similar software package) to estimate the contribution of the pile group to the total foundation per- formance (e.g., deflection, moment, shear, etc.). 5. The total foundation resistance to force effects is the sum of the lateral resistance provided by the treated soil block and the lateral resistance provided by the pile group, (i.e., the unreduced foundation forces from Step 4). 6. If force-deflection calculations are necessary, the side shear can be assumed to develop with a displacement of approx- imately 0.25 in. and the passive force-displacement curve can be computed using a hyperbolic curve as described by Duncan and Mokwa (2001). Example 1—Soil Cement Wall Adjacent to Pile Group Consider a typical existing foundation for a bridge pier that includes a 3 × 4 group of 1-ft diameter piles spaced at 90 Figure 7-20. Summary of results from FEM parametric study of jet grout treatment.

a 3-ft center-to-center spacing in both directions as shown in Figure 7-21. The piles are structurally fixed (full moment connection) to a 3-ft-thick reinforced concrete pile cap. The top of the pile cap is at the ground surface. The direc- tion of horizontal loading induced by the structure is as shown. The soil is soft to medium clay with a uniform undrained shear strength of 500 lb/ft2. The total unit weight of the soil is 110 lb/ft3 and the water table is at a depth of 10 ft beneath the ground surface. Due to an anticipated increase in structural demand applied to the foundation, the lateral resistance (geotechnical) pro- vided by the existing foundation requires enhancement. There- fore, ground improvement is being considered as shown in Figure 7-22. The ground improvement involves introducing and mixing Portland cement into the virgin soil such that a mass of treated soil is created that substantially exceeds the in-situ strength of the virgin soil. To model the geotechnical benefit provided by the ground improvement, the simplified method described herein is used to compute the additional resistance provided by the ground improvement. This additional resistance is then sub- tracted from the lateral demand imposed on the foundation. Upon determining the reduced lateral demand, the problem can be modeled as one would typically do using commercially available software such as GROUP, or similar. Note that when using GROUP, the option for considering an “embedded pile cap” should not be activated. Analysis Procedure 1. Compute the magnitude of passive resistance acting on the projected area at the leading face of the ground 91 Figure 7-21. Existing foundation prior to ground improvement. Figure 7-22. Existing foundation after ground improvement. 12ft 7ft9ft (a) Plan View 12ft 3ft (b) Elevation View 5ft 20ft (a) Plan View 8ft 5ft (b) Elevation View

improvement block. The projected area is defined by 45° angles projecting from the pile cap edges (in all directions) and is truncated a depth below ground surface equal to the outside-to-outside pile spacing perpendicular to the direc- tion of loading as follows (see Figure 7-23): a. Projected Area of Leading Face, ALF: b. Average Effective Vertical Stress at Leading Face of Projected Area, σv′: c. Passive Pressure Acting on Leading Face of Projected Area, pp: d. Passive Force Acting on Leading Face of Projected Area, Fp: 2. Compute the magnitude of adhesion acting along the sides and horizontal base (if applicable) of the projected area of the treatment block using an adhesion factor, αpass, equal to 0.9. a. Projected Area of Sides, AS: A sides ft ft ft ft ft fts = × ×( ) + ×( )+ × ×( )[2 5 3 1 4 4 41 2 ] = 54 2ft F A p ft lb ftp LF p= × = × =133 1 3852 2, 184k p c lb ft lb ft lb ftp u v= + ′ = ×( ) + =2 2 500 385 1 3852 2 2σ , ′ = × =σv lb ft ft lb ft110 3 5 3853 2. A ft ft ftLF = × =19 7 133 2 b. Adhesion along Sides, Fαs: c. Projected Area of Horizontal Base, Ab: d. Adhesion along Base, Fαb: e. Cumulative Adhesion along Sides and Base, Fa: 3. Compute the total lateral resistance contributed by the treated block, F, as the sum of the passive resistance, Fp, and cumulative adhesion, Fα, acting on the projected area of the treatment block: 4. Compute the reduced horizontal load to be used in foun- dation analyses, Preduced, by subtracting the total lateral resistance contributed by the treated block, F, from the external horizontal loading force magnitude applied to the foundation, P: 5. Use Preduced to analyze the foundation using commercially available software such as LPILE, GROUP, FBPier, etc. P P Freduced = − = −P 217k F F F k kp a= + = + =184 33 217k F F F k ks bα α α= + = + =24 9 33k F A c ft lb ft kb b pass uα α= × × = × × =19 0 9 500 92 2. A ft ft ftb = × =19 1 19 2 F A c ft lb ft ks s pass uα α= × × = × × =54 0 9 500 242 2. 92 Figure 7-23. Existing foundation after ground improvement with projected areas. 19ft (a) Plan View 1ft 7ft (b) Elevation View

Example 2—Soil Cement Wall Around a Pile Group Consider the same pile group foundation and soil profile described in Example 1. Due to an anticipated increase in structural demand applied to the foundation, the lat- eral resistance (geotechnical) provided by the existing foundation requires enhancement. The ground improve- ment involves introducing and mixing Portland cement into the virgin soil beneath the cap and around the piles as shown in Figure 7-24 such that a mass of treated soil is cre- ated that substantially exceeds the in-situ strength of the virgin soil. To model the geotechnical benefit provided by the ground improvement, the simplified method described herein is used to compute the additional resistance pro- vided by the ground improvement (see Figure 7-25). This additional resistance is then subtracted from the lateral demand imposed on the foundation. Upon determining the reduced lateral demand, the problem can be modeled as one would typically do using commercially available soft- ware such as GROUP, or similar. Note that when using GROUP, the option for considering an embedded pile cap should not be activated. Analysis Procedure 1. Compute the magnitude of passive resistance acting on the projected area at the leading face of the ground improve- ment block. The projected area is defined by 45° angles pro- jecting from the outer edges of the piles and is truncated at a depth below ground surface equal to the outside-to- outside pile spacing perpendicular to the direction of load- ing as shown in: a. Projected Area of Leading Face, ALF: A ft ft ftLF = × =11 7 77 2 b. Average Effective Vertical Stress at Leading Face of Projected Area, σv′: c. Passive Pressure Acting on Leading Face of Projected Area, pp: p c lb ft lb ft lb ftp u v= + ′ = ×( ) + =2 2 500 715 1 7152 2 2σ , ′ = × + ÷( )[ ] =σv lb ft ft ft lb ft110 3 5 7 2 7153 2. 93 Figure 7-24. Existing foundation after ground improvement. Figure 7-25. Existing foundation after ground improvement with projected areas. 14ft 11ft (a) Plan View 14ft 10ft (b) Elevation View 11ft (a) Plan View 7ft (b) Elevation View

d. Passive Force Acting on Leading Face of Projected Area, Fp: 2. Compute the magnitude of adhesion acting along the sides and base of the projected area of the treatment block using an adhesion factor, αpass, equal to 0.9. a. Projected Area of Sides, AS: b. Adhesion along Sides, Fαs: c. Projected Area of Base, Ab: d. Adhesion along Base, Fαb: e. Cumulative Adhesion along Sides and Base, Fa: 3. Compute the total lateral resistance contributed by the treated block, F, as the sum of the passive resistance, Fp, and cumulative adhesion, Fα, acting on the projected area of the treatment block: 4. Compute the reduced horizontal load to be used in foun- dation analyses, Preduced, by subtracting the total lateral resistance contributed by the treated block, F, from the external horizontal loading force magnitude applied to the foundation, P: 5. Use Preduced to analyze the foundation using commercially available software such as LPILE, GROUP, FBPier, etc. Adaptation for Pile Groups with Bent Caps Some states use pile bents where piles extend from the ground to a support beam under the deck without including a pile cap in the ground. The piles then extend down below the bent cap, often through water, and into the ground without having a cap that comes in contact with the ground. The results of the field tests conducted during this study indicate that even though a pile cap is not present, the piles and cemented soil still function as a composite block, which increases the lateral P P Freduced = − = −P 289k F F F k kp a= + = + =132 157 289k F F F k ks bα α α= + = + =88 69 157k F A c ft lb ft kb b pass uα α= × × = × × =154 0 9 500 692 2. A ft ft ftb = × =11 14 154 2 F A c ft lb ft ks s pass uα α= × × = × × =196 0 9 500 882 2. A sides ft ft fts = × ×( ) =2 14 7 196 2 F A p ft lb ftp LF p= × = × =77 1 7152 2, 132k resistance of the group. To apply the simplified method to this case, we recommend that an equivalent “pile cap” geometry be constructed to the outside edges of the pile group as illus- trated in Figure 7-26. In this case, the base of the equivalent pile cap would be the top of the cemented soil zone. Using this equivalent pile cap geometry, the resistance can be estimated using the same approach as that described for the case with the piles in Examples 1 and 2. Construction Considerations For new construction, ground improvement can be performed most economically and efficiently if it is performed prior to foundation construction. Clearly, if piles or drilled shafts are not in place, then a wider variety of treatment methods can be employed to create a soilcrete block. For example, in the absence of piles, the soil could be treated to a depth of 5 meters using mass soil mixing. For high-moisture-content soils, the dry method could be used while the wet method could be used for other soils. Wet or dry mixing by column methods could be performed to much deeper depths, if necessary. Piles could be driven through the treated soil if driving was performed within a day or two after treatment, otherwise, pre-drilling might be required. If new piles were driven prior to soil treatment, soil mixing techniques could still be used to treat the soil around the periphery of the pile group prior to construction of the cap so that the treated soil would be in direct contact with the exterior piles. However, jet grouting would be required to treat the soil between the piles to create intimate contact between the interior piles and the treated soil. Because jet grouting is more expensive than other treatment methods and the piles would restrict access, the cost of treatment would be high. 94 Figure 7-26. Equivalent pile cap geometry for use with piles with a bent cap.

For retrofit of existing structures where piles and pile caps are already in place, soil mixing methods could be used to cre- ate a soilcrete wall adjacent to the pile cap, but contact would not be achieved between the underlying piles and the treated soil. Jet grouting would allow the creation of a soilcrete zone around the periphery of the pile group that would also be in contact with the piles below the cap to improve lateral resis- tance. Core drilling through the pile cap would be required to allow jet grouting to be performed below the pile cap that would again increase the cost of treatment. Pile Group Improved by Excavating Clay and Replacing with Compacted Granular Fill Based on available test results and limited numerical results, the compacted granular zone should extend at least 6 pile diameters below the ground surface and 10 pile diam- eters beyond the edge of the pile face in the direction of load- ing. The lateral resistance can then be analyzed using the properties of the compacted fill with a computer program such as GROUP. Pile Group Improved by Compacting Narrow Dense Granular Soil Adjacent to the Pile Cap in Loose Sand The dense compacted granular zone should have a mini- mum width of 3 ft and extend 2 ft below the base of the pile cap or abutment back wall. In addition, the granular zone should be compacted to a minimum of 95% of the modified Proctor maximum unit weight. The passive resistance for the pile cap can then be computed using the following procedure: 1. Compute the ultimate passive force per width (Ep) for the dense granular zone using the pile cap or abutment back- wall height (H) and unit weight (γ) of the dense granular soil using the equation: Use the log-spiral method to compute the Kp value with the friction angle of the dense granular zone and a wall friction (δ) equal to 0.7 times the friction angle of the soil. 2. Compute the passive force ratio (PFR) for geometry and frictional properties of the dense and loose granular soils using Equation 1. 3. Multiply the passive force computed in Step 1 by the PFR to obtain the horizontal passive force per length for the combined geometry. 4. For long abutments, multiply the passive force per length by the actual length of the abutment wall to obtain the total horizontal passive force on the wall. For pile caps, multiply the passive force per length by the effective width of the cap, which is equal to the actual width of the cap multiplied by the R3D factor to account for 3D end shear effects. E H Kp p= 0 5 122. cos ( )γ δ 95

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Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils Get This Book
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TRB’s National Cooperative Highway Research Program (NCHRP) Report 697: Design Guidelines for Increasing the Lateral Resistance of Highway-Bridge Pile Foundations by Improving Weak Soils examines guidance for strengthening of soils to resist lateral forces on bridge pile foundations.

The report presents computational methods for assessing soil-strengthening options using finite-element analysis of single piles and pile groups and a simplified approach employing commercially available software.

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