S. Iai, T. Tobita & M.N. Hussien
Disaster Prevention Research Institute, Kyoto University, Uji, Kyoto, Japan
K.M. Rollins
Brigham Young University, Provo, Utah, USA
O. Ozutsumi
Meisosha Co., Tokyo, Japan
ABSTRACT: The paper reviews (1) soil-pile interaction in horizontal plane, (2) a simplified approach for idealizing the soil-pile interaction in terms of a non-linear spring, and (3) effect of soil-pile separation. The review is based on the experimental (laboratory and full scale in-situ tests) and numerical studies performed by the authors over recent years.
1 INTRODUCTION
Performance of laterally loaded pile group has been under study for more than four decades. The results of these extensive studies have formed the basis for the current design practice of pile group under lat-eral loads. However, there are certain categories of mechanisms that are not fully studied in research and consequently not fully considered in design practice.
Soil-pile interaction in horizontal plane and effect of soil-pile separation belong to those categories among others. This paper reviews these issues based on experimental and numerical studied performed by the authors over recent years.
2 SOIL-PILE INTERACTION IN HORIZONTAL PLANE
In order to study the local soil displacement field in the vicinity of the piles associated with a global displacement of soil around the pile foundation, two dimensional model tests were performed on a hor-izontal cross section of a soil-pile system in a pile foundation (Iai et al, 2006). Two dimensional effective stress analyses in horizontal plane were also performed to generalize the findings from the model tests. An effective stress model based on multiple shear mecha-nisms is used through a computer code FLIP (Iai et al, 1992).
Actual soil deformation is three dimensional and does not always follow the assumption made in this study that primary soil movement around the pile is in plane. This aspect of the problem is partially solved by incorporating the horizontal 2D behavior as soil-pile interaction spring in the vertical 2D analysis domain as discussed in Chapter 4.
Figure 1. Apparatus for model tests for soil-pile interaction in horizontal plane.
In an aluminum container (inner dimensions:
800 mm long, 500 mm wide, 40 mm high), a cylin-drical pile model made of Teflon, 40 mm high with a diameter of 50 mm, was embedded in a sand deposit formed in the container as shown in Figure 1. The sand deposit was formed by air pluviation for dry con-dition, and by pouring a slurry mixture of sand and viscous fluid (120cSt) for saturated condition. Silica No.7 sand was used. Relative densities of the sand deposits were about 70% for dry condition and about
−150% (negative relative density) for saturated con-dition. After the sand deposit was formed, an acrylic plate was placed on the surface on the sand deposit.
Displacement was induced to the pile model by pulling a wire attached to the mid portion of the pile model at the rate of 7.2 mm/min. Although the pile model was moved in the model tests, the primary interest of the model tests was to measure the displacement field of soil relative to the movement of the pile. Thus, the results of the model tests are readily applicable to the conditions when the global soil movement is induced around the pile foundation.
The local displacement field monitored through a video-camera was plotted in terms of displacement
Figure 2. Measured displacement field (pile displacement 11mm, load= 20 N) (Case-1: dry).
Figure 3. Measured displacement field (pile displacement 21mm, load= 6N) (Case-3: saturated).
Figure 4. Displacement distributions in the vicinity of soil-pile interface for dry and saturated sand deposits (Cases-1 and 3).
vectors at nodes of the grid formed by colored sand markers. Under dry condition (Case-1), the displace-ment vectors were directed away from the front of the pile in a pattern of a fan as shown in Figure 2. The dis-placement vectors at pile side rapidly decreased with an increasing distance from soil-pile interface. A void was formed behind the pile following the movement of the pile. Under saturated condition (Case-3), vor-tices were formed at pile side as shown in Figure 3.
Void formation was not observed behind the pile under saturated condition. Displacement distribution in the vicinity of soil-pile interface was obtained as shown in Figure 4.
Figure 5. Two dimensional analysis of a soil-pile system in horizontal plane.
Two dimensional analysis of a horizontal cross section of the soil-pile system was performed under pseudo-static conditions. An effective stress model based on multiple shear mechanism was used through a computer code FLIP (Iai et al, 1992). In this analysis, a single row of equally spaced piles deployed perpendic-ular to the direction of load (Figure 5(a)) was idealized into an analysis domain defined by the boundaries that run parallel to the load direction and go through the centers of the pile spacing. These boundaries were peri-odic, sharing the same displacements at the boundary nodes with the same x-coordinate through the multiple constraint conditions (MPC) applied, where x-axis is directed towards right on the figure. At the right and left side boundaries on the figure, x-displacements were fixed.
Finite element mesh used for the analysis of a sin-gle row of piles with a spacing of L= 10D and a pile diameter D= 5 cm is shown in Figure 6 for the area ranging from L= −5D to +5D. In the analysis, whole soil-pile system was initially consolidated with a con-fining pressure of 0.28 kPa for simulating the concon-fining condition at the mid-depth of the model sand deposit (i.e. 2 cm from the surface). The cylindrical pile sec-tion was idealized using linear solid elements. This pile section was replaced by the soil elements in the initial phase of analysis for consolidation in order to avoid artificial stress concentration. Following this ini-tial phase, the pile was loaded with a monotonically increasing load. Soil deformation around the cylindri-cal cross section of the pile was computed in drained and undrained conditions. Parameters for sand used for the analysis were determined referring to the results of laboratory tests on Silica sand No.7 as shown in Table 1.
Computed displacement field for the dry and satu-rated condition are shown in Figures 7 and 8. In the dry condition, the displacement vectors are directed away from the front of the pile in a pattern of a fan. The dis-placement vectors at the pile side rapidly decreases with an increasing distance from the soil-pile interface. For the saturated condition, displacement vectors beside the pile shows vortices as shown in Figure 8. These displacement fields are basically con-sistent with those measured in the laboratory and shown in Figures 2 and 3. Only difference is noted with respect to the formation of voids behind the pile in the model tests. No void was formed in the analysis
Figure 6. Finite element mesh used for the analysis.
Table 1. Parameters for silica sand No.7.
ρt Gma ν σma φf Hmax
(g/cm3) (kPa) (kPa) (deg)
2.0 3760 0.33 0.28 35 0.24
ρt: density; Gma: initial shear modulus at a confining pressure of σma ; σma : reference confining pressure; φf: internal friction angle; ν: Poisson’s ratio; Hmax; limiting value of hysteretic damping factor (φp: phase transformation angle and w1, p1, p2, c1, s1: parameters for dilatancy were not used.)
Figure 7. Computed displacement field around pile (drained) (Case-2).
Figure 8. Computed displacement field around pile (undrained) (Case-4).
probably because the confining stress in the analysis was more uniform than the one in the model tests where the stress field became 3-D when the void began to form.
In order to clearly show the displacement distribu-tion between the piles, horizontal components of the
Figure 9. Computed displacement distributions between the piles: (left) dry (Case-2), (right) saturated (Case-4).
displacements are plotted in Figure 9. These results are basically consistent with those measured and shown in Figure 4. Only difference noted is with respect to the manner in which the displacements are decaying from the center of the pile: the model tests with large friction (not shown in this paper) shows much slower rate of decay at the soil-pile interface than the analy-sis. A further study may be needed to follow up this issue.
In Figures 4 and 9, the soil farthest from the pile moves in the opposite direction of pile movement. This phenomenon may be due to the fact that displacement of the total mass of soil is fixed so that soil has to move in order to maintain the overall mass balance.
Primary findings from this study are as follows:
(1) In dry condition, displacement vectors are directed away from pile front, and displacement at pile side rapidly decreases with an increasing dis-tance from soil-pile interface. In saturated con-dition, displacement field shows vortices at pile side associated with push-out/pull-in pattern of displacements in front of and behind the pile.
(2) Distribution of local soil displacement between piles deployed perpendicular to direction of global displacement of soil shows high strain concentra-tion (i.e. discontinuity in displacement) at soil-pile interface.
Generalization of the results of this experiment is obviously affected by various conditions such as pile-spacing, stress levels, sand grain size, soil angularities, relative densities and strain-softening/hardening soils.
This aspect of the study remains as a homework in future.
3 SOIL-PILE INTERACTION SPRING
By using the same mesh and parameters, the displacement relationship of a pile under cyclic load-ing is computed for the horizontal cross section shown in Figure 6 for dry and saturated conditions. The dis-placement is defined as that of the pile relative to that at the periodic side boundary that is located at the pile to pile center. As a comparison, simple shear tests of a single element of soil were simulated using the same parameters for dry and saturated condition. In satu-rated condition, liquefaction front parameter S0was set equal to 0.05, which is equivalent to the states of excess pore water pressure ratio of 0.95. The initial confin-ing pressure used for the computation was 24 kPa for dry sand and 98 kPa for saturated sand. The finite ele-ment mesh used for the simulation was assigned for the diameter of pile equal to D= 1 m. The analyses were performed for the pile spacing of 2.5D, 5D and 10D.
Examples of the computed results for spacing of 5D for dry and saturated conditions are shown in Fig-ure 10. As shown in this figFig-ure, load-displacement curve for dry condition follows a typical shape of the p-y curve specified in the design recommendations whereas the curve for saturated condition follows a hardening-spring type shape similar to the stress strain curve during cyclic mobility of saturated sands. As a comparison, the simple shear test results of a single soil element of a multiple shear mechanism model are shown in Figure 11.
Figure 10. Load-displacement relationship of pile-soil sys-tem in horizontal plane under cyclic loading; (a) dry (σm0 = 24.5 kPa), (b) saturated (S0= 0.05) (σm0= 98 kPa).
Although the mechanisms involved in the load-displacement curve are the results of complicated soil-pile interaction as exemplified by the local dis-placement field shown in Figures 3 through 9, the load-displacement curves shown in Figure 10 have practically the same shapes as those of the single soil element shown in Figure 11.
There might be a several reasons for the similarity between the results of load-displacement relationship of pile-soil system and the shear stress-shear strain relationship of a single soil element. In this review paper, however, it may be sufficient to say that the similarity is confirmed for a wide range of pile spacing and geotechnical conditions. Based on the similarity between the results of load-displacement relationship of pile-soil system and the shear stress-shear strain relationship of a single soil element, the following relationships are derived (Ozutsumi 2003) as follows:
where u denotes relative displacement, D denotes pile diameter, L denotes pile length, αp= 11.5 to 12.6, and βp= 0.5 (dry) to 2.5 (saturated) depending on the pile spacing and dry/saturated conditions. The path dependent function f in Equation (3) is given by using
Figure 11. Shear stress-shear strain relationship of a single soil element under cyclic simple shear; (a) dry (σm0 = 24.5 kPa), (b) saturated (S0= 0.05) (σm0 = 98 kPa).
a fictitious single soil element of a multiple shear mechanism model.
For the analysis of pile-soil interaction during earth-quakes, two dimensional analysis domain is set for a vertical cross section of soil-pile system. In this analysis, the soil–pile interaction in horizontal plane formulated through Equations (1) through (3) is ideal-ized as a soil-pile interaction spring element as shown in Figure 12. While the conventional spring elements used in the analysis of soil-pile interaction is embedded in the same plane of the two dimensional finite ele-ment analysis domain, the soil-pile interaction spring defined in this study is used as a spring that connects a free pile to a two dimensional cross section of soil between the piles. If looked in a plan view, the soil ide-alized through the finite element analysis is in a plane that goes along the periodic boundary line shown in figure 5(b) while the pile analyzed is located a part at a distance of a half pile spacing.
In addition to the pile interaction spring, soil-pile interface effect, including sliding and separation, should be appropriately taken into account in the anal-ysis. In this study, this effect is idealized by inserting a joint element between the corresponding nodes on the pile-soil spring and the pile element. A schematic fig-ure for representing soil-pile separation effect is shown in Figure 13.
Figure 12. Schematic figure of pile-soil interaction spring.
Figure 13. Schematic figure of joint element for represent-ing soil-pile interface effect.
4 FULL SCALE MODEL TESTS & ANALYSIS OF PILE GROUP UNDER LATERAL LOAD The applicability of the multiple shear mechanism model incorporating the soil-pile interaction spring and a joint element for allowing soil-pile separation effect is studied through a two dimensional analysis of a full scale lateral loading tests of a 3× 5 pile group performed at the Salt Lake City Airport, USA (Rollins et al, 1998, Snyder, 2004). The idealized soil profile at the test site is shown in Figure 14. The evaluated shear strength of clay in the upper three clay layers from the unconsolicated undrained (UU) triaxial tests and cone penetration test ranged from 30 to 40 kPa, whereas those for the clay layers at 5 to 6 meters below the ground surface ranged from 30 to 60 kPa. Inter-nal friction angle of sand layer at a depth of 3 to 5 m was evaluated from the standard penetration test as 38 degrees, whereas that below 6 m as 33 degrees.
For the full scale model tests, steel pipe piles were driven closed end to an embedment depth of 11.6 m.
The test pile has a 0.324 m outside diameter with a 9.5 mm wall thickness. The piles in the group were driven in a 3× 5 pattern with a nominal spacing of 3.92 pile diameters center to center in the loading direction and of 3.29 pile diameter perpendicular to it. The lateral load was applied 495 mm above the ground surface. A photograph of the overall layout of the 15-pile group, with a reference single pile in front, is shown in Figure 15. The piles and the load frame are pin-connected so that the rotation is free at the pile head. For static loading, the piles were pushed against reaction wall with two 1.34 MN hydraulic jacks powered by a hydraulic pump of a maximum pressure of 69,000 kPa.
Figure 14. Idealized soil profile at the Salt Lake City International Airport Site, USA.
In the analysis of the full scale group pile test, the finite element mesh shown in Figure 16 was used for the computation. The lateral load is statically applied at pile heads (0.495 m above the ground surface) until the displacement of 90 mm is achieved at the loading point.
Figure 17 shows computed and measured response of a single pile with and without soil-pile separation.
Figure 15. Full-scale lateral load test layout; a reference single pile in front of 3× 5 group pile.
Figure 16. Finite element mesh for the group pile under lateral load test.
Figure 17. Single pile response under static load: load-deflection curve (a), load-maximum bending moment curve (b), and bending moment distribution (c).
The analysis without separation highly overestimates the lateral load-carrying capacity of the pile. In fact, the soil-pile gap was observed in-situ at the full scale test sites as shown in Figure 18. In the analysis, when soil-pile separation is considered, the
Figure 18. Photograph of a gap formation behind the pile (the pile is deflected laterally to the right and the gap is formed on the left of the pile in the photo).
load-deflection curve agrees well with those measured.
The separation between soil and pile occurs in the analysis when the normal stress at the interface goes into tension regime as stated previously. The computed load-maximum bending moment curve and the bend-ing moment distribution with soil-pile separation also agree well with the measured values. At the same load level, the analysis without soil-pile separation underestimates both deflection and maximum bend-ing moment. At target deflection of 90 mm, ignorbend-ing soil-pile separation leads to 43% overestimation of the ultimate lateral load-carrying capacity of the pile.
Computed and measured load as an average per pile are shown in Figure 19. In the figure, the leading pile is designated as pile no (1), while the trailing pile as pile no (5). In comparison to the results for a single pile, the effect of the pile-soil separation is not significant for most of the piles in pile group except for the trailing pile, where the computed result with the effect of pile-soil separation effect agrees well with those measured.
The computed results without this effect resulted in 73% overestimation of load-carrying capacity at the target deflection of 84 mm.
Figure 19. Group pile response under static load: load-deflection curves for piles no (1) through (5).
Figure 20. Earth pressures in front of and at the back of piles at depth 0.3 m below the ground surface; (a) with soil-pile separation, (b) without a separation.
In order study further the mechanism that causes the difference in the effect of pile-soil separation among the piles within the pile group, lateral earth pressures computed in front of and at the back of a pile at a depth of 0.3 m from the ground surface are shown in Figure 20. The trailing pile shows that the potential tensile force that would be acting if the pile-soil sep-aration is not allowed as shown on the right side of Figure 20(b) is released to zero when the pile-soil sep-aration is allowed as shown in Figure 20(a). the positive earth pressure in front of the pile is not very sensitive to the effect of pile-soil separation. The leading pile and middle pile show little effects of soil-pile separa-tion not only in front of the piles but also at the back of the piles. In the analysis, soils in active side (extension side) of each pile move in the direction of pile deflec-tion due to the deformadeflec-tion of the next column of pile behind the pile in question, and therefore a gap cannot be formed behind the pile in a relatively closely spaced pile group as analyzed in this study. The soil-pile gap that could have been formed for these piles appeared to be closed by the soil mass that were actually pushed forward by the column of pile trailing behind.