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Soil–structure interaction for landslide stabilizing piles
Computers and Geotechnics 29 (2002) 363–386 www.elsevier.com/locate/compgeo
Soil–structure interaction for landslide stabilizing piles C.-Y. Chen*, G.R. Martin University of Southern California, Los Angeles, CA, USA Received 21 May 2001; received in revised form 28 September 2001; accepted 27 November 2001
Abstract The mechanics of the mobilization of resistance from passive pile groups subjected to lateral soil movement is discussed from the standpoint of the arching effect. The existence of an arching zone around pile groups for granular and fine-grained soils is examined first using the finite difference computer code FLAC [Fast Lagrangian analysis of continua, version 3.4, manual (1998)]. Pile load-displacement curves and the arching effect are linked together to explain how the stresses transfer from the soil to the pile. The effect of parameter changes on pile/soil interaction are also explained by the changes in the arching phenomenon. The results reveal that the formation and shape of the arching zone are functions of pile arrangement, relative pile/soil displacement, pile shape, interface roughness, and soil dilation angle. Group effects in granular soil are significant but no significant effects in fine-grained soil under lateral active loading and lateral soil movement (passive loading) for one row of piles, was observed. # 2002 Elsevier Science Ltd. All rights reserved.
1. Introduction Based on model tests, it has been shown that for granular soils, the formation of the arching effect around pile groups is a significant stabilizing mechanism. To complement existing knowledge and to clarify issues related to arch formation, a plane-strain model using the finite difference analysis program FLAC [1] is adopted to simulate soil plastic flow around the piles. The model is used to evaluate the load transfer mechanism of stabilizing piles; especially the processes leading to formation
* Corresponding author at No. 26 Hsi-Shih Li, Changhua, Taiwan, 500, Taiwan ROC. E-mail address: [email protected] (C.-Y. Chen). 0266-352X/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0266-352X(01)00035-0
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of an arching zone. In addition, the role of landslide stabilizing piles for fine-grained soils is explored. The formation of an arch is explained by stress transfer from yielding (or moving) soil on to the piles. In examining the arching effect, the analyses show the development of a plastic zone around the piles under lateral soil movements (defined by load-displacement (‘‘p–’’) curves) and eventually failure modes between the pile/soil interface. Group effects are considered and are compared to the behavior of piles subjected to lateral loading from piles supporting a structure (‘‘active’’ piles). A three-dimensional analysis [2] is also conducted to demonstrate the applicability of the 2-D analyses.
2. Review of the arching phenomenon 2.1. Definition of arching Terzaghi [3] explained the phenomenon of pressure transfer from a yielding mass of soil to adjacent rigid boundaries by a trap door test. The pressure transfer was called arching. The trap door test has been discussed extensively using analytical and numerical methods [4–6]. In general, the definition of the arching effect is used to describe the phenomenon of stress transfer through the mobilization of shear strength [7]. In other words, arching is defined as the transfer of stress from yielding parts of a soil mass to adjoining less-yielding or restrained parts of soil mass [8]. The definition of the arching effect could be different for different applications. Low et al. [9] defined the arching phenomenon as the reduction of the vertical stress on the top of cap beams used for the design of a piled embankment. 2.2. Consideration of arching in engineering practice The arching phenomenon can be found on underground structures (e.g. tunnels, conduits, and anchor plates) caused by soil movement in the vertical direction. The most familiar application of the vertical arching effect is in the design of a tunnel [10]. The vertical direction of the arching phenomenon above a piled cap (Fig. 1) was also investigated to design a piled embankment [11]. In addition, using piles to
Fig. 1. Arched sand above pile caps [11].
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transfer embankment loading and to control differential settlements, the use of piles to stop slope movements are other analogous applications of the arching effect. 2.3. Development process of a soil arch Handy [12] studied soil arch action for a soil mass loaded between two walls, simulating a bin. Soil arching action was depicted as a trajectory of minor principal stress that approximates to a catenary. Its development can be initiated from the rotation of principal stresses. The second stage of arching reduces the vertical and horizontal pressures near the base of the wall. The result of the arching effect on pile caps [11] showed that static equilibrium requires arches to be semi-circular, of uniform thickness and with no overlap (Fig. 1). Within each arching zone, the tangential direction and the radial direction are the direction of major and minor principal stresses, respectively. The Adachi et al. [13] model test defined the arching zone by an equilateral triangular arch. Other shapes of arches had also been observed in different physical phenomena, including parabolic, hemispherical, domal and corbelled [14]. The following sections study the arching effect from the viewpoint of stress transfer in the pile-slope interaction analysis. Rigid piles in sand and clay slopes are modeled in the 2-D analyses. 2.4. Arching between slope stabilizing piles Wang and Yen [7] designed stabilizing piles in a rigid-plastic, infinite soil slope from the viewpoint of arching effects using an analytical method. Some important results from the Wang and Yen [7] analyses are summarized below: 1. 1. The maximum average arching pressure is equal to the pressure at rest in a slope. 2. 2. Arching is more prominent for larger c0 and 0 values when the other factors remain the same. 3. 3. Existence of a critical pile spacing was noted. Once pile spacing was larger than the critical value, no arching developed. 4. 4. An arching zone can exist in both sandy and clayey slopes. The principles of the trap door test were simulated by a series of model tests and numerical finite element analyses on landslide stabilizing piles by Adachi et al. [13]. They explained the development of the arching effect in granular soils, where the uphill pressure does not govern particles B, C, and D within the arching zone of soil, as shown in Fig. 2. Moreover, the existence of an arching foothold [zone (1)] in front of the circular pile will cause less pressure to act on these piles than on equivalent rectangular piles (i.e. dd, d=diameter). However, the deformation on the pile/soil interface, the effects of pile/soil parameters on the formation of arching zone and the different arching mechanisms between granular and fine-grained soils are unresolved. For this reason, numerical
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Fig. 2. Arching effect [13].
plane-strain finite difference analyses using FLAC [1] as described below, were adopted to simulate the processes when soil movements flow and squeeze into rows of piles. The results complement existing knowledge on the piled-slope interaction and clarify outstanding issues.
3. Numerical approach The finite difference analysis package, FLAC [1], was chosen for the numerical analysis. In this 2-D approach, beam elements are used to represent a rigid pile shaft and the nodes of pile interface elements are attached to the beam nodes to represent the possibility of slippage between the pile and the soil. Validation of the behavior of interface elements are examined first. The interface elements allow computation of normal and shear stresses on the pile interface. 3.1. Validation of the interface elements The interface elements in FLAC are characterized by Coulomb sliding and tensile separation with properties of friction, cohesion, dilation, normal and shear stiffness and tensile strength. The interface elements used in FLAC are similar to those used in the discrete element method as introduced by Cundall and Hart [15]. The Coulomb shear-strength criterion limits the shear force as: Fsmax ¼ c0 L þ tan0 Fn
ð1Þ
where L=effective contact length. The interface elements are allowed to separate if tension exists across the interface and exceeds the tension limit of the interface. Once gapping is formed between the pile/soil interface, the shear and normal forces are set to zero.
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A plane-strain model that simulates the process of pushing a row of piles laterally into the soil is portrayed in Fig. 3 (active pile problem). The rigid piles are 0.762 m diameter steel pipes and are spaced at 6 m. The boundary space (10d, d=pile diameter) has been verified by observation of the development of the soil plasticity as sufficient to represent an isolated pile without inducing group effects. The pile is represented by beam elements located along the pile periphery and connected to the grid via interface elements. The pile is pushed into the soil by applying a constant negative y-direction velocity at the beam nodes. An initial confining stress corresponding to 3.5 m (z/d=4.6, d=pile diameter) below the ground surface is chosen to represent a field situation. This also coincides with the assumption by Randolph and Houlsby [16] that under plane-strain conditions soil will deform past a pile at a depth greater than 3d to avoid the near-ground surface effect in which the ultimate lateral soil resistance will be smaller than the plane-strain value [17]. The soil behavior is assumed to follow an elasto-plastic Mohr–Coulomb failure criterion, with zero tension force. Fine grained soil with a bulk modulus 7.5 104 kPa, a shear modulus 1.26 104 kPa, a unit weight 21 kN/m3, and an undrained shear strength cu of 25 kPa is used for the analysis. To simulate the condition of a perfectly smooth interface between the soil and pile, the interface was initially modeled with a normal stiffness Kn=1 107 kPa, a shear stiffness Ks=1 107 kPa, and without cohesive or frictional strength. To represent a perfectly rough pile surface, the interface properties were chosen as an undrained shear strength equal to 5cu. The high adhesion strength was chosen to model a perfectly rough interface between the pile and soil to avoid a separation between pile/soil interface since separation was not allowed in the analysis. This value was also adopted by Ng et al. [18] in their benchmark test on interface elements, which were intended to represent a rough pile interface.
Fig. 3. Conceptual model to estimate lateral pressure on piles.
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3-D pile and soil displacements for flexible piles under active loading will tend to lead to different load transfer mechanisms to rigid piles. Hence, a plane-strain analysis for rigid piles cannot deliver the load-transfer (p-y) curves for flexible piles directly [19,20]. Instead, a pile-displacement, , is defined relative to the external rigid boundaries. Although, the definition of ‘‘p–y’’ and ‘‘p–’’ is different, the ultimate soil pressure on the pile is the same [18–22]. The results of the analysis shown in Fig. 4 reveals that the normalized lateral pressure (p/cud) is 9.11 and 11.94 for the smooth and rough interface respectively, which is similar to the theoretical values of 9.14 and 11.94 based on classical plasticity [16]. 3.2. Plane-strain model for evaluation of arching (passive piles) One metre diameter steel pipe rigid piles, with spacing 4 m, were used to model the three-dimensional plastic flow around the piles. Fig. 5 shows the concept of this 2-D simulation model. To take advantage of the symmetric conditions, the boundary is adopted as 8 by 24 m. Fig. 6(a) shows the finite difference grid used for the analysis. The piles are represented by beam elements (rigid) located along the pile periphery and connected to the grid via interface elements as shown in Fig. 6(b). Interface elements are also used in this analysis to simulate the behavior of pile/soil separation. A total of 80 nodes and 80 beam elements are used in the analysis per pile. The nodes are fixed in space to model the rigid piles. The deformation was modeled as moving by fixing the two sides of boundaries (A–A and B–B) and applying a constant small velocity (1 106 m/step) at both sides at the same time. This simulates the situation of slope failure and causes soil to flow through the space between piles. This model was also adopted by Chaoui et al. [23] in a 2-D analysis to evaluate the behavior of piles in unstable slopes. The soil displacement is measured at the center of two adjacent piles. Soil pressures acting
Fig. 4. Normalized lateral pressure versus displacement curves.
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Fig. 5. Conceptual model to analyse the group mechanism of stabilizing piles.
Fig. 6. Grid used for the plane-strain analysis.
on the pile are calculated from the forces acting on the pile nodes. An initial confining stress at a point 3 m below the ground surface was chosen to represent the field situation. The soil behavior is assumed to follow the elasto-plastic (with tension cut-off) Mohr–Coulomb material using the large strain mode analysis with updating of the coordinates with each step. Two different kinds of soils, granular and finegrained soil, were used to study the different arching mechanisms. 3.3. Drained behaviour—granular soil A granular soil with a bulk modulus (K) 7.5 104 kPa, a shear modulus (G) 1.26 104 kPa, a unit weight () 21 kN/m3, and a friction angle (0 ) 30o (without tensile strength and dilatancy) is assumed for the analysis. The interface properties are modeled as a normal stiffness (Kn) 1 107 kN/m, shear stiffness (Ks) 1 107 kN/m and a friction angle 30o for a rough interface and zero for a smooth interface. Fig. 7 shows the velocity vectors of soil movement laterally around the piles when they are loaded with an applied displacement (corresponding to a velocity 1 106 m/step) at the two boundaries A–A and B–B. It shows that soil particles are ‘‘flowing’’
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Fig. 7. Velocity vectors for granular soil (at 5000 steps, =0.5 cm).
and squeezing around the pile shaft. The development of the plastic zone in the soil around the pile is depicted in Fig. 8 for increasing time steps. Soil yield begins from the two sides of pile shaft caused by the soil particles flowing around and squeezing toward the rear of the pile. With increasing soil movements, the accumulated zone of plastic yielding extends to the front of the pile and a small elastic zone is protected. This elastic zone (called an arching foothold) in front of the pile is also shown in Fig. 2 [zone (1)] and is used as a collapse mechanism in an upper bound analysis to determine tunnel pressures [10]. Ultimately, an elastic arch zone was formed between the two adjacent piles. The formation of the elastic arching zone can be explained by the concept that the pressure does not transmit through the inside of the arching zone. Thus, an elastic state is maintained within the arching zone and moves downward to the lower boundary (from A–A to B–B in Fig. 5). The transfer path of the stresses can be traced by the rotation of the principal stress directions as portrayed in Fig. 9. Within the elastic arching zone, the directions of the principal stresses change unduly and stresses in the two principal directions become more equal. Several of the principal stresses directions were changed, outside the arching zone, where larger principal stresses were directed towards the piles. Finally, the soil masses within the elastic arching zone yield but without significantly increasing the pressures acting on the piles. Failure mechanisms around the pile/soil interface in the granular soil are shown in Fig. 10. Soil squeezing around the pile shaft was observed and soil masses within the elastic arching zone behaved more downward movements compared to the masses outside the arching zone, while no separation between the pile/soil interface was found in the granular soil (Fig. 10). 3.4. Undrained behaviour—fine grained soil For undrained soil conditions, the definitions of interface roughness were the same as for the drained soil conditions. An undrained shear strength 25 kPa and a zero
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Fig. 8. Development of soil plastic failure in granular soil.
friction angle was used for the slope in fine grained material under undrained conditions. The development of the plastic zone and displacement contours are shown in Fig. 11 as a function of time. The soil started to yield at both sides of the pile shaft [Fig. 11(a)] and accumulated in front of the pile without the formation of an arching foothold as for the granular slope. Also, very shallow elastic arching zone within the two adjacent piles is noted in the fine grained soil. The existence of an arching effect is evident from the rotation of the principal stresses directions as depicted in Fig. 12. While, the more uniform principal stress vectors in front and behind the piles revealed that the effect of arching was less well developed under undrained conditions than the granular soil. Also, considerable soil mass moved behind the piles in the y-direction displacement contours [Fig. 11 (c)]. This was contributed to by the separation between the pile and the soil at the rear of the piles (e.g. Fig. 13). This
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Fig. 9. Rotation of principal stress directions in granular soil (=1.7 cm).
Fig. 10. Exaggerated grid distortion of pile/soil interface in granular soil (=1.7 cm).
explains why the soil yielded in front of the piles since stresses cannot be transmitted across a gap.
4. Parametric study Important parameters affecting the pile-slope interaction analysis using a 2-D analysis include the failure criterion for the soil, initial stress conditions, Young’s modulus, interface properties and soil dilatancy. Although higher drained soil strength (c0 , 0 values) will cause stronger arching effects, it was found that strength values do not change the shape or prohibit the development of the arching zone once soil displacements are sufficient to initiate plastic flow. Similar results were found for a higher initial stress state and Young’s modulus values in this parametric
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Fig. 11. Development of undrained failure mechanism.
study. However, the effects of interface roughness and soil dilation angle play an important role in the development and formation of the soil arch. Their effects are explained in more detail below. 4.1. Effect of interface roughness on arching effect To understand the relationship between the formation of an arching zone and the pressures acting on the piles, the pressures acting on the pile in granular soil were measured during the stepping process leading to the formation of an arch. The resulting lateral loads p acting on the pile (per unit length) in the direction of soil movement for a rough (c0 int=c0 soil, 0 int=0 soil), an intermediate roughness (c0 int= 0.5c0 soil, 0 int=0.50 soil) and a smooth interface (c0 int=0, 0 int=0) versus relative pile/
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Fig. 12. Rotation of principal stress directions under undrained conditions.
Fig. 13. Deformation of pile/soil interface under undrained conditions.
soil displacement measured at the center of two adjacent piles (called p– curves herein) are shown in Fig. 14. The lateral load, p, on each pile includes the effects of the pressure at rest and the arching pressure transferred from the yielding soil to the pile. It is found that loads acting on the pile are close to the ultimate value in the p– curve whenever an apparent elastic arching zone is formed completely. As expected, a rougher pile interface stiffens the p–curves and leads to a higher value of ultimate soil resistance on the pile. The reduction of the ultimate soil resistance on a surface of intermediate roughness interface was minor compared with the significant reduction for a smooth interface. This reflects the fact that the shear drag force around the pile shaft was not considered in computing the forces acting on the piles. The pressure forces acting on the center of the right hand boundary versus the displacement at point B0 (as shown in Fig. 5) are recorded and depicted in Fig. 15. These curves reach their constant values whenever an arching zone was developed completely. For a rough interface, lower reaction forces act at point B0 compared
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Fig. 14. Load-displacement characteristic curves for various pile interface roughnesses.
Fig. 15. Pressures at the center of the right hand boundary (point B0 , ref. Fig. 5).
with a smooth interface. This verifies the fact that pressures are reduced in front of the arching zone, which causes less force to be transmitted to the right hand boundary. Fig. 15 implies that more soil displacement is needed to develop the arch fully for a smooth interface. This is also verified by Fig. 16, which shows that for the same
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Fig. 16. State of soil and Y-displacement contours for smooth interface in sandy soil at steps=17,000 (=1.7 cm).
boundary displacements the arching zone has not been formed completely for a smooth interface and the arching foothold in front of the piles is diminished. Pressure forces acting on the right and the left hand boundaries are depicted in Fig. 17. Less force acts on the top boundary yet higher forces act on the bottom boundary, which explains why less pressure acts on the pile when the interface is smooth. 4.2. Effect of soil dilatancy on arching effect In addition to the interface roughness, dilatancy will affect the ultimate lateral pressure acting on a pile. The dilation angle is believed also to affect the arch development. Fig. 18 shows the ‘‘p–’’ curves in granular soil with different dilation angle values for a pile with a rough interface. A higher dilation angle will cause volumetric dilation and more soil squeezing will be induced in front of the pile, which causes a higher pressure acting on the top boundary (Fig. 19). More severe arching effects and a wider elastic arching zone is observed in Fig. 20 for soil exhibiting a higher dilation angle.
5. Group effects Pile group effects are considered for one row of stabilizing piles in drained conditions using the same pile and soil properties previously described. The pressure acting on the piles are shown in Fig. 21 for pile spacings from 2d (d=pile diameter) to 6d. Smaller pile spacing increases initial stiffness of the p– curves, and decreases the ultimate lateral pressure. The closer the pile spacing, the greater is the arching effect. Arch development is limited by the pile spacing and is fully mobilized at smaller soil displacements for closer pile spacing, as shown in Fig. 22. The state of the soil is depicted in Fig. 23(a) and (b) for pile spacings of 2d and 3d, respectively. A narrower (2d) pile spacing shows no visible elastic arching zone within the two adjacent piles
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Fig. 17. Pressures at the left and right of boundaries.
Fig. 18. Load-displacement curves with and without dilation angle.
when pile pressures reach their ultimate value. The elastic arching zone inside the two adjacent piles will also form earlier than the arching foothold in front of the piles in a closer pile spacing, as shown in Figs. 23 and 8 (pile spacing=4d). 5.1. Behavior of passive piles and active piles Piles subjected to active loading from superstructures (active piles) are compared with the response of piles undergoing lateral soil movements (passive piles) for one
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Fig. 19. Pressures with changing of dilation angle at boundaries.
Fig. 20. State of soil and Y-direction displacement contours in granular soil with =15 .
row of piles, using the setup and parameters previously described for piles with a rough interface. Simulation of the superstructure loading on the piles is modeled by applying a small constant velocity to the pile nodes, as shown in Fig. 24. The p–y (y=pile deflection) curves for active piles and the p– (=relative soil movement) curves for passive piles are shown in Fig. 21. The p– curves derived from the passive piles show a stiffer response compared with the behavior of p–y curves from the active piles, which is contributed by the strong arching effect in passive pile response for granular soil. The ultimate soil resistances seem to coincide closely, regardless of the two different modes of achieving differential pile-soil movement under undrained conditions. Chen and Poulos [22] showed that for passive pile response ultimate
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Fig. 21. Group effects in granular soil.
Fig. 22. Pressures at point B0 with changing pile spacing in granular soil.
pressures acting on one row of piles were found to reduce with increasing pile spacing. To verify this result, piles subjected to lateral loading and soil movement under undrained plane-strain conditions are re-examined and shown in Fig. 25. As predicted,closer pile spacings will cause an increase in the pressure on the piles in soils under undrained conditions. Pile–soil separation as shown in Fig. 13 causes the ultimate pressure acting on the pile less than 12 cu=300 KN/m. A dramatic reduction of pressure at point B0 (Fig. 26) reveals that a decrease in the pile spacing
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Fig. 23. State of soil at pile spacings of 2d and 3d in granular soil.
Fig. 24. Modeling of active pile response with velocity applied to the pile nodes.
will cause a stronger arching effect, which causes a reduction of pressure being transferred to the soil masses behind the pile. The arching effect is also reduced at a specific free field displacement. This helps explain why no visible elastic arching zone was found for a 2d pile spacing case and why the arching effect vanished sooner. This led to similar ultimate pressures on the pile and their normalized pressure (p/cud)
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Fig. 25. Group effects for undrained conditions.
Fig. 26. Pressures at point B0 with changing of pile spacing for undrained conditions.
is equal to 9.0. The minor group effect for one row of piles in soil under undrained conditions is also verified by Yegian and Wright [24] and Chen and Poulos [22] using the finite element analysis.
6. Two rows of piles Groups containing two rows of piles are analyzed to investigate the effect on the load transfer mechanisms for passively loaded piles. An analysis is performed for
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drained conditions, a rough interface and with the same soil properties as the aforementioned case for one row of piles. Parallel and zigzag arrangements are examined as shown in Fig. 27. From the y-direction displacement contours, it was found that the ‘‘parallel arrangement’’ piles extend the soil movement to the rear row of the piles but the mechanism is similar to the case using one row of piles. However, the multiple soil arching effects, which can develop for a zigzag arrangement of piles,
Fig. 27. State of soil and y-direction displacement contours on two rows of piles in granular soil/drained conditions.
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Fig. 28. Conceptual model of 3-D pile-slope stability analysis.
Fig. 29. y-Direction displacement contours in 3-D slope stability analysis.
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provide much more resistance to soil movement as previously found by Chen and Poulos [21], Bransby and Springman [20].
7. 3-D analysis The previous results are applicable to ground displacements which are uniform with depth (plane-strain) and with enough lateral soil movement to cause the soil to yield and flow. To verify if the plane-strain model used can simulate the characteristics of 3-D slope displacements interacting with stabilizing piles, a 3-D analysis using FLAC3D [2] was performed as shown in Fig. 28. One row of 1 m diameter piles with bending stiffness EpIp=1.23 106 kN m2 and a pile spacing of 3 m are wishedin-place from the crest to stabilize a 30o inclined embankment slope. The interface elements are incorporated between the pile and the soil to simulate the possibility of slippage between the pile/soil interface. The pile end was fixed at the bottom to model the situation of pile embedded into a stiff layer. A strength reduction method is used to induce failure of the slope, whereby soil strength parameters, c0 =3 kPa and 0 =20 are reduced using the same ratio until the slope failure occurs. The resulting slope sliding surface is shown in Fig. 29(a). Displacement contours along the direction of soil movement are depicted in Fig. 29(b). It was concluded that the plane-strain model can simulate the characteristics of the 3-D piled-slope stability analysis after comparing the plane-strain displacement contours and the 3-D results.
8. Conclusion A plane-strain model is used to simulate the development of plastic yielding and failure modes for the pile-soil interaction as well as the preventive mechanism of landslide stabilizing piles for different soil conditions. The so-called ‘‘arching effect’’ is found for both drained and undrained soil conditions from the standpoint of stress transfer. It is noted that the results are for ultimate state analyses, in which enough soil movement occurs to cause soil plastic flow. A small strain condition may not induce the formation of an arching zone and will cause less pressures acting on the pile. The important findings include: 8.1. Arching effects The following conclusions were drawn about the characteristics of arching effects in a piled slope: 1. An arching zone can be traced by viewing the contours of displacement along the direction of soil movement and the rotation of principal stress directions. 2. The arching effect exists under both drained and undrained conditions. 3. Under undrained conditions, with no dilatancy, a double arching effect is found whereby the stresses arch around an elastic zone in front of the piles
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and between the two neighboring piles. The shape of the arching zone between the two adjacent piles is appears to be hyperbolic. 4. A flatter arching zone is found under undrained conditions. 5. Soil dilatancy is found to have considerable effects on the formation of an arch, since higher soil dilatancy will cause an increase in volume around the pile shaft. In addition, a rougher interface leads to accelerate the formation of arch.
8.2. Group effects on pile forces
1. Closer pile spacing leads to higher initial stiffness for p-dcurves for drained conditions. The development of arching is limited by the pile spacing, which leads to lower ultimate lateral forces on the piles with reduced spacing. 2. In contrast to the pile response under undrained conditions, forces acting on a pile are higher for closer pile spacing when no drainage is permitted (undrained). In this case, no significant group effects occur if pile spacing is over 4d. 3. As expected, group effects are more significant for drained rather than undrained conditions. References [1] Itasca, FLAC. Fast Lagrangian analysis of continua, version 3.4, manual. Itasca, Minnesota; 1998. [2] Itasca, FLAC3D. Fast Lagrangian analysis of continua in 3-dimensions, version 2.0, manual. Itasca, Minnesota; 1997. [3] Terzaghi K. Theoretical soil mechanics. New York, NY: John Wiley & Sons, 1943. [4] Ladanyi B, Hoyaux B. A study of the trap door problem in a granular mass. Canadian Geotechnical Journal 1969;6(1):1–14. [5] Vardoulakis I, Graf B, Gudehus G. Trap door problem with dry sand: a static approach based upon model kinematics. Int J Numer Analy Mech Geomech 1981;5:57–78. [6] Koutsabeloulis NC, Griffiths DV. Numerical modeling of the trap door problem. Geotechnique 1989;39(1):77–89. [7] Wang WL, Yen BC. Soil arching in slopes. Journal of the Geotechnical Engineering Division, ASCE 1974;100(No. GT1):61–78. [8] Committee on Glossary of Terms and Definitions in Soil Mechanics. Glossary of terms and definitions in soil mechanics. Journal of the Soil Mechanics and Foundations Division, ASCE 1958;84(4): 1–43. [9] Low BK, Tang SK, Choa V. Arching in piled embankments. Journal of Geotechnical Engineering 1994;120(11):1917–37. [10] Atkinson JH, Potts DM. Stability of a shallow circular tunnel in cohesionless soil. Geotechnique 1977;27(2):203–15. [11] Hewlett WJ, Randolph MF. Analysis of piled embankments. Ground Engineering, London, England 1988;21(3):12–18. [12] Handy RL. The arch in soil arching. Journal of Geotechnical Engineering, ASCE 1985;111( 3):302–18. [13] Adachi T, Kimura M., Tada S. Analysis on the preventive mechanism of landslide stabilizing piles. Numerical models in geomechanics, numog III, Elsevier; 1989. p. 691–8.
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[14] Kellogg CG. Discussions—the arch in soil arching. Journal of Geotechnical Engineering, ASCE 1987;113( 3):269–71. [15] Cundall PA, Hart RD. Numerical modeling of discontinua. Engineering Computer 1992;9:101–13. [16] Randolph MF, Houlsby GT. The limiting pressure on a circular pile loaded laterally in cohesive soil. G’eotechnique 1984;34(4):613–23. [17] Stevens JB, Audibert JME. Re-examination of p–y curve formulations. Proceedings, 11th Annual Offshore Technology Conference, Paper No. 3402, 397–403. [18] Ng PCF, Pyrah IC, Anderson WF. Assessment of three interface elements and modification of the interface element in CRISP90. Computers and Geotechnics 1997;21(4):315–39. [19] Bransby MF. The difference between load-transfer relationships for laterally loaded pile groups: active p–y or passive p–. Journal of Geotechnical Engineering 1996;122(12):1015–8. [20] Bransby MF, Springman SM. Selection of load-transfer functions for passive lateral loading of pile groups. Computers and Geotechnics 1999;24:155–84. [21] Chen LT, Poulos HG. Analysis of pile-soil interaction under lateral loading using infinite and finite elements. Computers and Geotechnics 1993;15:189–220. [22] Chen L, Poulos HG. A method of pile-soil interaction analysis for piles subjected to lateral soil movement. Proc, 8th Int Conf on Computer Methods and Advances in Geomechanics 1994;3:2311– 6. [23] Chaoui F, Magnan JP, Mestat Ph, Delmas Ph. Three-dimensional analysis of the behavior of piles in unstable slopes. Proc, 8th Int Conf on Computer Methods and Advances in Geomechanics 1994;3: 2297–302. [24] Yegian M, Wright SG (1973). Lateral soil resistance—displacement relationships for pile foundations in soft clays. In: Proceedings 5th Annual Offshore Technology Conference, OTC 1893, vol. 2. Offshore Technology Conference, Houston; 1973. p. 663–76.
Soil–structure interaction for landslide stabilizing piles C.-Y. Chen*, G.R. Martin University of Southern California, Los Angeles, CA, USA Received 21 May 2001; received in revised form 28 September 2001; accepted 27 November 2001
Abstract The mechanics of the mobilization of resistance from passive pile groups subjected to lateral soil movement is discussed from the standpoint of the arching effect. The existence of an arching zone around pile groups for granular and fine-grained soils is examined first using the finite difference computer code FLAC [Fast Lagrangian analysis of continua, version 3.4, manual (1998)]. Pile load-displacement curves and the arching effect are linked together to explain how the stresses transfer from the soil to the pile. The effect of parameter changes on pile/soil interaction are also explained by the changes in the arching phenomenon. The results reveal that the formation and shape of the arching zone are functions of pile arrangement, relative pile/soil displacement, pile shape, interface roughness, and soil dilation angle. Group effects in granular soil are significant but no significant effects in fine-grained soil under lateral active loading and lateral soil movement (passive loading) for one row of piles, was observed. # 2002 Elsevier Science Ltd. All rights reserved.
1. Introduction Based on model tests, it has been shown that for granular soils, the formation of the arching effect around pile groups is a significant stabilizing mechanism. To complement existing knowledge and to clarify issues related to arch formation, a plane-strain model using the finite difference analysis program FLAC [1] is adopted to simulate soil plastic flow around the piles. The model is used to evaluate the load transfer mechanism of stabilizing piles; especially the processes leading to formation
* Corresponding author at No. 26 Hsi-Shih Li, Changhua, Taiwan, 500, Taiwan ROC. E-mail address: [email protected] (C.-Y. Chen). 0266-352X/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0266-352X(01)00035-0
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of an arching zone. In addition, the role of landslide stabilizing piles for fine-grained soils is explored. The formation of an arch is explained by stress transfer from yielding (or moving) soil on to the piles. In examining the arching effect, the analyses show the development of a plastic zone around the piles under lateral soil movements (defined by load-displacement (‘‘p–’’) curves) and eventually failure modes between the pile/soil interface. Group effects are considered and are compared to the behavior of piles subjected to lateral loading from piles supporting a structure (‘‘active’’ piles). A three-dimensional analysis [2] is also conducted to demonstrate the applicability of the 2-D analyses.
2. Review of the arching phenomenon 2.1. Definition of arching Terzaghi [3] explained the phenomenon of pressure transfer from a yielding mass of soil to adjacent rigid boundaries by a trap door test. The pressure transfer was called arching. The trap door test has been discussed extensively using analytical and numerical methods [4–6]. In general, the definition of the arching effect is used to describe the phenomenon of stress transfer through the mobilization of shear strength [7]. In other words, arching is defined as the transfer of stress from yielding parts of a soil mass to adjoining less-yielding or restrained parts of soil mass [8]. The definition of the arching effect could be different for different applications. Low et al. [9] defined the arching phenomenon as the reduction of the vertical stress on the top of cap beams used for the design of a piled embankment. 2.2. Consideration of arching in engineering practice The arching phenomenon can be found on underground structures (e.g. tunnels, conduits, and anchor plates) caused by soil movement in the vertical direction. The most familiar application of the vertical arching effect is in the design of a tunnel [10]. The vertical direction of the arching phenomenon above a piled cap (Fig. 1) was also investigated to design a piled embankment [11]. In addition, using piles to
Fig. 1. Arched sand above pile caps [11].
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transfer embankment loading and to control differential settlements, the use of piles to stop slope movements are other analogous applications of the arching effect. 2.3. Development process of a soil arch Handy [12] studied soil arch action for a soil mass loaded between two walls, simulating a bin. Soil arching action was depicted as a trajectory of minor principal stress that approximates to a catenary. Its development can be initiated from the rotation of principal stresses. The second stage of arching reduces the vertical and horizontal pressures near the base of the wall. The result of the arching effect on pile caps [11] showed that static equilibrium requires arches to be semi-circular, of uniform thickness and with no overlap (Fig. 1). Within each arching zone, the tangential direction and the radial direction are the direction of major and minor principal stresses, respectively. The Adachi et al. [13] model test defined the arching zone by an equilateral triangular arch. Other shapes of arches had also been observed in different physical phenomena, including parabolic, hemispherical, domal and corbelled [14]. The following sections study the arching effect from the viewpoint of stress transfer in the pile-slope interaction analysis. Rigid piles in sand and clay slopes are modeled in the 2-D analyses. 2.4. Arching between slope stabilizing piles Wang and Yen [7] designed stabilizing piles in a rigid-plastic, infinite soil slope from the viewpoint of arching effects using an analytical method. Some important results from the Wang and Yen [7] analyses are summarized below: 1. 1. The maximum average arching pressure is equal to the pressure at rest in a slope. 2. 2. Arching is more prominent for larger c0 and 0 values when the other factors remain the same. 3. 3. Existence of a critical pile spacing was noted. Once pile spacing was larger than the critical value, no arching developed. 4. 4. An arching zone can exist in both sandy and clayey slopes. The principles of the trap door test were simulated by a series of model tests and numerical finite element analyses on landslide stabilizing piles by Adachi et al. [13]. They explained the development of the arching effect in granular soils, where the uphill pressure does not govern particles B, C, and D within the arching zone of soil, as shown in Fig. 2. Moreover, the existence of an arching foothold [zone (1)] in front of the circular pile will cause less pressure to act on these piles than on equivalent rectangular piles (i.e. dd, d=diameter). However, the deformation on the pile/soil interface, the effects of pile/soil parameters on the formation of arching zone and the different arching mechanisms between granular and fine-grained soils are unresolved. For this reason, numerical
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Fig. 2. Arching effect [13].
plane-strain finite difference analyses using FLAC [1] as described below, were adopted to simulate the processes when soil movements flow and squeeze into rows of piles. The results complement existing knowledge on the piled-slope interaction and clarify outstanding issues.
3. Numerical approach The finite difference analysis package, FLAC [1], was chosen for the numerical analysis. In this 2-D approach, beam elements are used to represent a rigid pile shaft and the nodes of pile interface elements are attached to the beam nodes to represent the possibility of slippage between the pile and the soil. Validation of the behavior of interface elements are examined first. The interface elements allow computation of normal and shear stresses on the pile interface. 3.1. Validation of the interface elements The interface elements in FLAC are characterized by Coulomb sliding and tensile separation with properties of friction, cohesion, dilation, normal and shear stiffness and tensile strength. The interface elements used in FLAC are similar to those used in the discrete element method as introduced by Cundall and Hart [15]. The Coulomb shear-strength criterion limits the shear force as: Fsmax ¼ c0 L þ tan0 Fn
ð1Þ
where L=effective contact length. The interface elements are allowed to separate if tension exists across the interface and exceeds the tension limit of the interface. Once gapping is formed between the pile/soil interface, the shear and normal forces are set to zero.
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A plane-strain model that simulates the process of pushing a row of piles laterally into the soil is portrayed in Fig. 3 (active pile problem). The rigid piles are 0.762 m diameter steel pipes and are spaced at 6 m. The boundary space (10d, d=pile diameter) has been verified by observation of the development of the soil plasticity as sufficient to represent an isolated pile without inducing group effects. The pile is represented by beam elements located along the pile periphery and connected to the grid via interface elements. The pile is pushed into the soil by applying a constant negative y-direction velocity at the beam nodes. An initial confining stress corresponding to 3.5 m (z/d=4.6, d=pile diameter) below the ground surface is chosen to represent a field situation. This also coincides with the assumption by Randolph and Houlsby [16] that under plane-strain conditions soil will deform past a pile at a depth greater than 3d to avoid the near-ground surface effect in which the ultimate lateral soil resistance will be smaller than the plane-strain value [17]. The soil behavior is assumed to follow an elasto-plastic Mohr–Coulomb failure criterion, with zero tension force. Fine grained soil with a bulk modulus 7.5 104 kPa, a shear modulus 1.26 104 kPa, a unit weight 21 kN/m3, and an undrained shear strength cu of 25 kPa is used for the analysis. To simulate the condition of a perfectly smooth interface between the soil and pile, the interface was initially modeled with a normal stiffness Kn=1 107 kPa, a shear stiffness Ks=1 107 kPa, and without cohesive or frictional strength. To represent a perfectly rough pile surface, the interface properties were chosen as an undrained shear strength equal to 5cu. The high adhesion strength was chosen to model a perfectly rough interface between the pile and soil to avoid a separation between pile/soil interface since separation was not allowed in the analysis. This value was also adopted by Ng et al. [18] in their benchmark test on interface elements, which were intended to represent a rough pile interface.
Fig. 3. Conceptual model to estimate lateral pressure on piles.
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3-D pile and soil displacements for flexible piles under active loading will tend to lead to different load transfer mechanisms to rigid piles. Hence, a plane-strain analysis for rigid piles cannot deliver the load-transfer (p-y) curves for flexible piles directly [19,20]. Instead, a pile-displacement, , is defined relative to the external rigid boundaries. Although, the definition of ‘‘p–y’’ and ‘‘p–’’ is different, the ultimate soil pressure on the pile is the same [18–22]. The results of the analysis shown in Fig. 4 reveals that the normalized lateral pressure (p/cud) is 9.11 and 11.94 for the smooth and rough interface respectively, which is similar to the theoretical values of 9.14 and 11.94 based on classical plasticity [16]. 3.2. Plane-strain model for evaluation of arching (passive piles) One metre diameter steel pipe rigid piles, with spacing 4 m, were used to model the three-dimensional plastic flow around the piles. Fig. 5 shows the concept of this 2-D simulation model. To take advantage of the symmetric conditions, the boundary is adopted as 8 by 24 m. Fig. 6(a) shows the finite difference grid used for the analysis. The piles are represented by beam elements (rigid) located along the pile periphery and connected to the grid via interface elements as shown in Fig. 6(b). Interface elements are also used in this analysis to simulate the behavior of pile/soil separation. A total of 80 nodes and 80 beam elements are used in the analysis per pile. The nodes are fixed in space to model the rigid piles. The deformation was modeled as moving by fixing the two sides of boundaries (A–A and B–B) and applying a constant small velocity (1 106 m/step) at both sides at the same time. This simulates the situation of slope failure and causes soil to flow through the space between piles. This model was also adopted by Chaoui et al. [23] in a 2-D analysis to evaluate the behavior of piles in unstable slopes. The soil displacement is measured at the center of two adjacent piles. Soil pressures acting
Fig. 4. Normalized lateral pressure versus displacement curves.
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Fig. 5. Conceptual model to analyse the group mechanism of stabilizing piles.
Fig. 6. Grid used for the plane-strain analysis.
on the pile are calculated from the forces acting on the pile nodes. An initial confining stress at a point 3 m below the ground surface was chosen to represent the field situation. The soil behavior is assumed to follow the elasto-plastic (with tension cut-off) Mohr–Coulomb material using the large strain mode analysis with updating of the coordinates with each step. Two different kinds of soils, granular and finegrained soil, were used to study the different arching mechanisms. 3.3. Drained behaviour—granular soil A granular soil with a bulk modulus (K) 7.5 104 kPa, a shear modulus (G) 1.26 104 kPa, a unit weight () 21 kN/m3, and a friction angle (0 ) 30o (without tensile strength and dilatancy) is assumed for the analysis. The interface properties are modeled as a normal stiffness (Kn) 1 107 kN/m, shear stiffness (Ks) 1 107 kN/m and a friction angle 30o for a rough interface and zero for a smooth interface. Fig. 7 shows the velocity vectors of soil movement laterally around the piles when they are loaded with an applied displacement (corresponding to a velocity 1 106 m/step) at the two boundaries A–A and B–B. It shows that soil particles are ‘‘flowing’’
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Fig. 7. Velocity vectors for granular soil (at 5000 steps, =0.5 cm).
and squeezing around the pile shaft. The development of the plastic zone in the soil around the pile is depicted in Fig. 8 for increasing time steps. Soil yield begins from the two sides of pile shaft caused by the soil particles flowing around and squeezing toward the rear of the pile. With increasing soil movements, the accumulated zone of plastic yielding extends to the front of the pile and a small elastic zone is protected. This elastic zone (called an arching foothold) in front of the pile is also shown in Fig. 2 [zone (1)] and is used as a collapse mechanism in an upper bound analysis to determine tunnel pressures [10]. Ultimately, an elastic arch zone was formed between the two adjacent piles. The formation of the elastic arching zone can be explained by the concept that the pressure does not transmit through the inside of the arching zone. Thus, an elastic state is maintained within the arching zone and moves downward to the lower boundary (from A–A to B–B in Fig. 5). The transfer path of the stresses can be traced by the rotation of the principal stress directions as portrayed in Fig. 9. Within the elastic arching zone, the directions of the principal stresses change unduly and stresses in the two principal directions become more equal. Several of the principal stresses directions were changed, outside the arching zone, where larger principal stresses were directed towards the piles. Finally, the soil masses within the elastic arching zone yield but without significantly increasing the pressures acting on the piles. Failure mechanisms around the pile/soil interface in the granular soil are shown in Fig. 10. Soil squeezing around the pile shaft was observed and soil masses within the elastic arching zone behaved more downward movements compared to the masses outside the arching zone, while no separation between the pile/soil interface was found in the granular soil (Fig. 10). 3.4. Undrained behaviour—fine grained soil For undrained soil conditions, the definitions of interface roughness were the same as for the drained soil conditions. An undrained shear strength 25 kPa and a zero
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Fig. 8. Development of soil plastic failure in granular soil.
friction angle was used for the slope in fine grained material under undrained conditions. The development of the plastic zone and displacement contours are shown in Fig. 11 as a function of time. The soil started to yield at both sides of the pile shaft [Fig. 11(a)] and accumulated in front of the pile without the formation of an arching foothold as for the granular slope. Also, very shallow elastic arching zone within the two adjacent piles is noted in the fine grained soil. The existence of an arching effect is evident from the rotation of the principal stresses directions as depicted in Fig. 12. While, the more uniform principal stress vectors in front and behind the piles revealed that the effect of arching was less well developed under undrained conditions than the granular soil. Also, considerable soil mass moved behind the piles in the y-direction displacement contours [Fig. 11 (c)]. This was contributed to by the separation between the pile and the soil at the rear of the piles (e.g. Fig. 13). This
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Fig. 9. Rotation of principal stress directions in granular soil (=1.7 cm).
Fig. 10. Exaggerated grid distortion of pile/soil interface in granular soil (=1.7 cm).
explains why the soil yielded in front of the piles since stresses cannot be transmitted across a gap.
4. Parametric study Important parameters affecting the pile-slope interaction analysis using a 2-D analysis include the failure criterion for the soil, initial stress conditions, Young’s modulus, interface properties and soil dilatancy. Although higher drained soil strength (c0 , 0 values) will cause stronger arching effects, it was found that strength values do not change the shape or prohibit the development of the arching zone once soil displacements are sufficient to initiate plastic flow. Similar results were found for a higher initial stress state and Young’s modulus values in this parametric
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Fig. 11. Development of undrained failure mechanism.
study. However, the effects of interface roughness and soil dilation angle play an important role in the development and formation of the soil arch. Their effects are explained in more detail below. 4.1. Effect of interface roughness on arching effect To understand the relationship between the formation of an arching zone and the pressures acting on the piles, the pressures acting on the pile in granular soil were measured during the stepping process leading to the formation of an arch. The resulting lateral loads p acting on the pile (per unit length) in the direction of soil movement for a rough (c0 int=c0 soil, 0 int=0 soil), an intermediate roughness (c0 int= 0.5c0 soil, 0 int=0.50 soil) and a smooth interface (c0 int=0, 0 int=0) versus relative pile/
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Fig. 12. Rotation of principal stress directions under undrained conditions.
Fig. 13. Deformation of pile/soil interface under undrained conditions.
soil displacement measured at the center of two adjacent piles (called p– curves herein) are shown in Fig. 14. The lateral load, p, on each pile includes the effects of the pressure at rest and the arching pressure transferred from the yielding soil to the pile. It is found that loads acting on the pile are close to the ultimate value in the p– curve whenever an apparent elastic arching zone is formed completely. As expected, a rougher pile interface stiffens the p–curves and leads to a higher value of ultimate soil resistance on the pile. The reduction of the ultimate soil resistance on a surface of intermediate roughness interface was minor compared with the significant reduction for a smooth interface. This reflects the fact that the shear drag force around the pile shaft was not considered in computing the forces acting on the piles. The pressure forces acting on the center of the right hand boundary versus the displacement at point B0 (as shown in Fig. 5) are recorded and depicted in Fig. 15. These curves reach their constant values whenever an arching zone was developed completely. For a rough interface, lower reaction forces act at point B0 compared
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Fig. 14. Load-displacement characteristic curves for various pile interface roughnesses.
Fig. 15. Pressures at the center of the right hand boundary (point B0 , ref. Fig. 5).
with a smooth interface. This verifies the fact that pressures are reduced in front of the arching zone, which causes less force to be transmitted to the right hand boundary. Fig. 15 implies that more soil displacement is needed to develop the arch fully for a smooth interface. This is also verified by Fig. 16, which shows that for the same
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Fig. 16. State of soil and Y-displacement contours for smooth interface in sandy soil at steps=17,000 (=1.7 cm).
boundary displacements the arching zone has not been formed completely for a smooth interface and the arching foothold in front of the piles is diminished. Pressure forces acting on the right and the left hand boundaries are depicted in Fig. 17. Less force acts on the top boundary yet higher forces act on the bottom boundary, which explains why less pressure acts on the pile when the interface is smooth. 4.2. Effect of soil dilatancy on arching effect In addition to the interface roughness, dilatancy will affect the ultimate lateral pressure acting on a pile. The dilation angle is believed also to affect the arch development. Fig. 18 shows the ‘‘p–’’ curves in granular soil with different dilation angle values for a pile with a rough interface. A higher dilation angle will cause volumetric dilation and more soil squeezing will be induced in front of the pile, which causes a higher pressure acting on the top boundary (Fig. 19). More severe arching effects and a wider elastic arching zone is observed in Fig. 20 for soil exhibiting a higher dilation angle.
5. Group effects Pile group effects are considered for one row of stabilizing piles in drained conditions using the same pile and soil properties previously described. The pressure acting on the piles are shown in Fig. 21 for pile spacings from 2d (d=pile diameter) to 6d. Smaller pile spacing increases initial stiffness of the p– curves, and decreases the ultimate lateral pressure. The closer the pile spacing, the greater is the arching effect. Arch development is limited by the pile spacing and is fully mobilized at smaller soil displacements for closer pile spacing, as shown in Fig. 22. The state of the soil is depicted in Fig. 23(a) and (b) for pile spacings of 2d and 3d, respectively. A narrower (2d) pile spacing shows no visible elastic arching zone within the two adjacent piles
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Fig. 17. Pressures at the left and right of boundaries.
Fig. 18. Load-displacement curves with and without dilation angle.
when pile pressures reach their ultimate value. The elastic arching zone inside the two adjacent piles will also form earlier than the arching foothold in front of the piles in a closer pile spacing, as shown in Figs. 23 and 8 (pile spacing=4d). 5.1. Behavior of passive piles and active piles Piles subjected to active loading from superstructures (active piles) are compared with the response of piles undergoing lateral soil movements (passive piles) for one
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Fig. 19. Pressures with changing of dilation angle at boundaries.
Fig. 20. State of soil and Y-direction displacement contours in granular soil with =15 .
row of piles, using the setup and parameters previously described for piles with a rough interface. Simulation of the superstructure loading on the piles is modeled by applying a small constant velocity to the pile nodes, as shown in Fig. 24. The p–y (y=pile deflection) curves for active piles and the p– (=relative soil movement) curves for passive piles are shown in Fig. 21. The p– curves derived from the passive piles show a stiffer response compared with the behavior of p–y curves from the active piles, which is contributed by the strong arching effect in passive pile response for granular soil. The ultimate soil resistances seem to coincide closely, regardless of the two different modes of achieving differential pile-soil movement under undrained conditions. Chen and Poulos [22] showed that for passive pile response ultimate
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Fig. 21. Group effects in granular soil.
Fig. 22. Pressures at point B0 with changing pile spacing in granular soil.
pressures acting on one row of piles were found to reduce with increasing pile spacing. To verify this result, piles subjected to lateral loading and soil movement under undrained plane-strain conditions are re-examined and shown in Fig. 25. As predicted,closer pile spacings will cause an increase in the pressure on the piles in soils under undrained conditions. Pile–soil separation as shown in Fig. 13 causes the ultimate pressure acting on the pile less than 12 cu=300 KN/m. A dramatic reduction of pressure at point B0 (Fig. 26) reveals that a decrease in the pile spacing
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Fig. 23. State of soil at pile spacings of 2d and 3d in granular soil.
Fig. 24. Modeling of active pile response with velocity applied to the pile nodes.
will cause a stronger arching effect, which causes a reduction of pressure being transferred to the soil masses behind the pile. The arching effect is also reduced at a specific free field displacement. This helps explain why no visible elastic arching zone was found for a 2d pile spacing case and why the arching effect vanished sooner. This led to similar ultimate pressures on the pile and their normalized pressure (p/cud)
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Fig. 25. Group effects for undrained conditions.
Fig. 26. Pressures at point B0 with changing of pile spacing for undrained conditions.
is equal to 9.0. The minor group effect for one row of piles in soil under undrained conditions is also verified by Yegian and Wright [24] and Chen and Poulos [22] using the finite element analysis.
6. Two rows of piles Groups containing two rows of piles are analyzed to investigate the effect on the load transfer mechanisms for passively loaded piles. An analysis is performed for
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drained conditions, a rough interface and with the same soil properties as the aforementioned case for one row of piles. Parallel and zigzag arrangements are examined as shown in Fig. 27. From the y-direction displacement contours, it was found that the ‘‘parallel arrangement’’ piles extend the soil movement to the rear row of the piles but the mechanism is similar to the case using one row of piles. However, the multiple soil arching effects, which can develop for a zigzag arrangement of piles,
Fig. 27. State of soil and y-direction displacement contours on two rows of piles in granular soil/drained conditions.
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Fig. 28. Conceptual model of 3-D pile-slope stability analysis.
Fig. 29. y-Direction displacement contours in 3-D slope stability analysis.
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provide much more resistance to soil movement as previously found by Chen and Poulos [21], Bransby and Springman [20].
7. 3-D analysis The previous results are applicable to ground displacements which are uniform with depth (plane-strain) and with enough lateral soil movement to cause the soil to yield and flow. To verify if the plane-strain model used can simulate the characteristics of 3-D slope displacements interacting with stabilizing piles, a 3-D analysis using FLAC3D [2] was performed as shown in Fig. 28. One row of 1 m diameter piles with bending stiffness EpIp=1.23 106 kN m2 and a pile spacing of 3 m are wishedin-place from the crest to stabilize a 30o inclined embankment slope. The interface elements are incorporated between the pile and the soil to simulate the possibility of slippage between the pile/soil interface. The pile end was fixed at the bottom to model the situation of pile embedded into a stiff layer. A strength reduction method is used to induce failure of the slope, whereby soil strength parameters, c0 =3 kPa and 0 =20 are reduced using the same ratio until the slope failure occurs. The resulting slope sliding surface is shown in Fig. 29(a). Displacement contours along the direction of soil movement are depicted in Fig. 29(b). It was concluded that the plane-strain model can simulate the characteristics of the 3-D piled-slope stability analysis after comparing the plane-strain displacement contours and the 3-D results.
8. Conclusion A plane-strain model is used to simulate the development of plastic yielding and failure modes for the pile-soil interaction as well as the preventive mechanism of landslide stabilizing piles for different soil conditions. The so-called ‘‘arching effect’’ is found for both drained and undrained soil conditions from the standpoint of stress transfer. It is noted that the results are for ultimate state analyses, in which enough soil movement occurs to cause soil plastic flow. A small strain condition may not induce the formation of an arching zone and will cause less pressures acting on the pile. The important findings include: 8.1. Arching effects The following conclusions were drawn about the characteristics of arching effects in a piled slope: 1. An arching zone can be traced by viewing the contours of displacement along the direction of soil movement and the rotation of principal stress directions. 2. The arching effect exists under both drained and undrained conditions. 3. Under undrained conditions, with no dilatancy, a double arching effect is found whereby the stresses arch around an elastic zone in front of the piles
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and between the two neighboring piles. The shape of the arching zone between the two adjacent piles is appears to be hyperbolic. 4. A flatter arching zone is found under undrained conditions. 5. Soil dilatancy is found to have considerable effects on the formation of an arch, since higher soil dilatancy will cause an increase in volume around the pile shaft. In addition, a rougher interface leads to accelerate the formation of arch.
8.2. Group effects on pile forces
1. Closer pile spacing leads to higher initial stiffness for p-dcurves for drained conditions. The development of arching is limited by the pile spacing, which leads to lower ultimate lateral forces on the piles with reduced spacing. 2. In contrast to the pile response under undrained conditions, forces acting on a pile are higher for closer pile spacing when no drainage is permitted (undrained). In this case, no significant group effects occur if pile spacing is over 4d. 3. As expected, group effects are more significant for drained rather than undrained conditions. References [1] Itasca, FLAC. Fast Lagrangian analysis of continua, version 3.4, manual. Itasca, Minnesota; 1998. [2] Itasca, FLAC3D. Fast Lagrangian analysis of continua in 3-dimensions, version 2.0, manual. Itasca, Minnesota; 1997. [3] Terzaghi K. Theoretical soil mechanics. New York, NY: John Wiley & Sons, 1943. [4] Ladanyi B, Hoyaux B. A study of the trap door problem in a granular mass. Canadian Geotechnical Journal 1969;6(1):1–14. [5] Vardoulakis I, Graf B, Gudehus G. Trap door problem with dry sand: a static approach based upon model kinematics. Int J Numer Analy Mech Geomech 1981;5:57–78. [6] Koutsabeloulis NC, Griffiths DV. Numerical modeling of the trap door problem. Geotechnique 1989;39(1):77–89. [7] Wang WL, Yen BC. Soil arching in slopes. Journal of the Geotechnical Engineering Division, ASCE 1974;100(No. GT1):61–78. [8] Committee on Glossary of Terms and Definitions in Soil Mechanics. Glossary of terms and definitions in soil mechanics. Journal of the Soil Mechanics and Foundations Division, ASCE 1958;84(4): 1–43. [9] Low BK, Tang SK, Choa V. Arching in piled embankments. Journal of Geotechnical Engineering 1994;120(11):1917–37. [10] Atkinson JH, Potts DM. Stability of a shallow circular tunnel in cohesionless soil. Geotechnique 1977;27(2):203–15. [11] Hewlett WJ, Randolph MF. Analysis of piled embankments. Ground Engineering, London, England 1988;21(3):12–18. [12] Handy RL. The arch in soil arching. Journal of Geotechnical Engineering, ASCE 1985;111( 3):302–18. [13] Adachi T, Kimura M., Tada S. Analysis on the preventive mechanism of landslide stabilizing piles. Numerical models in geomechanics, numog III, Elsevier; 1989. p. 691–8.
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