Liang, Yamin, Al Bodour and Erfani 1docs.trb.org/prp/10-3582.pdf · Liang, Yamin, Al Bodour and...

Liang, Yamin, Al Bodour and Erfani 1

Topic: Analysis Method for Drilled Shafts Stabilized Slopes Using Arching Concept 1 2 3 4 5 6 7

Robert Y. Liang Professor, Department of Civil Engineering, Akron, Ohio 44325-3905, Tel.: (330) 972-7190 e-mail: [email protected] 8

9 10 11 12 13

Wassel Al Bodour Graduate Research Assistant, Department of Civil Engineering, Akron, Ohio 44325-3905, e-mail: [email protected] 14

15 16 17 18 19

Mohammad Yamin Graduate Research Assistant, Department of Civil Engineering, Akron, Ohio 44325-3905, e-mail: [email protected] 20

21 22 23 24 25 26

Arash Erfani Joorabchi Research Assistant, Department of Civil Engineering, Akron, Ohio 44325-3905, Tel.: (330) 957-9981 e-mail: [email protected] 27

28 29 30 31 32 33 34 35 36 37

Paper prepared for presentation and publication at the 89th Annual Transportation Research Board Meeting in Washington, DC, 2010 Total Words: 5,537 Figures: 13 Tables: 3 TOTAL: 9,845 Paper Submission Date: August 1st, 2009

TRB 2010 Annual Meeting CD-ROM Paper revised from original submittal.

mailto:[email protected]




ABSTRACT 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23

The use of drilled shafts to stabilize an unstable slope or to fix a failed slope has gained popularity in highway applications mainly due to the fact that it is a structural fix that does not require additional right of way, as compared to change in slope geometry (adding berms to the toe of the slope) or other methods of stabilization. The main purpose of this paper is to introduce an analysis method for determining the FS of a drilled shaft/slope system and for determining the earth thrust on the drilled shafts for structural design of the drilled shafts. The concept of the analysis is cast in the limiting equilibrium approach via. method of slices, while incorporating the drilled shafts induced arching effects as the soil mass moves down-slope and around the drilled shafts. The mathematical equations based on the limiting equilibrium calculation, together with the load transfer factor for accounting for the drilled shafts induced arching effects, is presented in this paper. The 3-dimensional FEM parametric study using ABAQUS program is used to derive the regression based semi-empirical equations for quantifying the arching effect through the load transfer factor. A UASLOPE computer program is written to incorporate the above mentioned algorithms for applications to real cases. A case study of a fully instrumented and monitored slope stabilization project, ATH-124, in Ohio, is presented. The analysis of the stabilized slope at the ATH-124 project site using FEM and the computer code UA Slope are presented, together with field monitored data. Based on field monitoring data and the comparison between the finite element analysis results and the computer code UA slope for the global factor of safety and shaft force , the suggested analysis and design approach appears to be reasonable.



INTRODUCTION 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

The use of drilled shafts to stabilize an unstable slope in highway applications has gained popularity in recent years (for example, Fukumoto, 1972 and 1973; Sommer, 1977; Ito et al., 1981 and 1982; Nethero, 1982; Morgenstern, 1982; Gudehus and Schwarz, 1985; Reese et al., 1992; Rollins and Rollins, 1992; Poulos, 1995 and 1999; Zeng and Liang, 2002). The drilled shafts offer structurally sound permanent stabilization elements that can be constructed in almost any type of soil or rock conditions (constructability issue is minimized) and can sustain huge lateral loads from the moving soil mass (being capable of stabilizing a long translational sliding mass or deep-seated slip zone with the accompanied huge driving forces). Moreover, the drilled shafts can be constructed on the original slopes, thus avoiding the need for acquiring additional right-of-way. Drilled shafts can also be combined with other slope stabilization techniques (such as lowering ground water table, use of ground anchors, among others), thus allowing a versatile slope stabilization approach. The development of suitable analysis and design methods for using the drilled shafts to stabilize a slope involves the consideration of two design issues: (a) to determine the factor of safety, FS, of the slope with the installed drilled shafts (i.e., a slope/drilled shaft system), and (b) to determine the design loads for structural design of the drilled shafts. The drilled shafts used for stabilizing a slope have often been referred to as passive shafts due to the fact that the lateral earth pressure acting on the shaft is dependent upon the movement of the slope and the interaction between the shaft and the surrounding soils. Ideally, this complex soil structure interaction mechanism could be studied using three-dimensional FEM simulation techniques, taking into account the nonlinear and plastic nature of soil constitutive behavior as well as the soil-shaft interactions.

In the past, there were some practical approaches developed for addressing the design issues involved in the use of drilled shafts in stabilizing a slope. Ito et al. (1981) presented an approach to evaluate the stability for a slope using a single row of piles, by considering that the piles would provide an additional resisting force to the sliding of the unstable soil mass. The additional resistance force provided by the piles is estimated using the theory of plasticity by Ito and Matsui (1975). Hassiotis et al (1997) extended the friction circle method, with its inherent limitations such as homogeneous soil and circular slip surface, to the slope with the piles by considering the piles to exert an additional resistance force against sliding. Reese et al. (1992) illustrated a procedure by adding the passive ultimate forces provided by the drilled shafts to the resistant forces against sliding. Poulos (1995, 1999) demonstrated the procedure for a two-layer soil slope system with horizontal sliding plane, in which the upper soil layer is the unstable one and the lower layer is a stable soil layer. The lateral response of drilled shafts was assessed using Brom's method (1964), Viggianni (1981), and Ito and Matsui (1975) theories. Zeng and Liang (2002) presented a method by considering the arching effects induced by the drilled shafts in calculating the factor of safety of the slope/drilled shafts system. The arching was studied in Liang and Zeng (2002) by means of 2-D finite element simulations.

The main objective of this paper is to present an analysis method for using the drilled shafts to stabilize an unstable slope. The analysis method is based on a limit equilibrium method of slice approach, and supplemented by detailed and comprehensive 3-D finite element simulation results of the slope/drilled shafts system. Due to page limitations, the derivations of the theory of the mathematical equations as well as FE simulations results will be only briefly described herein; rather, the main focus of this paper is to present the analysis procedure with a case study.



FRAMEWORK OF ANALYSIS FOR SLOPE/DRILLED SHAFTS SYSTEM 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

The framework of analysis for a slope/drilled shafts system adopted in the current analysis procedure is based on the previous work by Zeng and Liang (2002) and Liang and Zeng (2002) and the subsequent expansion work by Al Bodour (2009). The overall concept of the method lies in the realization that the presence of the drilled shafts in the slope/drilled shafts system would create arching and thereby reduce the driving forces in the soils on the down-slope side of the drilled shafts due to transfer of earth pressure to the drilled shafts. As a result, the driving forces for the portion of the soils on the down-slope side of the drilled shafts are reduced, resulting in an increase in FS of the system. It should be pointed out that arching mechanisms have been observed and studied by many researchers, such as Terzaghi (1936 and 1943), Bosscher and Gray (1986), Finn (1963), Chelapati (1960), Getzler at al.(1968), Whitman and Luscher (1962), Wang and Yen (1974), Adachi (1989), Low et al.(1994), Chen et al. (1997), among others.

The current analysis method consists of the development of three key elements: (a) a mathematical formulation for the limiting equilibrium based method of slices approach, with the consideration of the drilled shafts induced arching effect, for determining the FS for the slope-drilled shafts system, (b) semi-empirical equations based on a comprehensive finite element parametric study to quantify the arching effects through a load transfer factor, which is dependent on such factors as strength parameters of the soils, the stiffness of the soil, the geometry (diameter and length of the shaft), the spacing and location of the shafts, the slip surface depth and the top of the rock elevation, and (c) a practical method for estimating the net earth thrust force on the drilled shafts for structural design of the drilled shafts . LIMITING EQUILIBRIUM FORMULATION FOR SLOPE/DRILLED SHAFTS SYSTEM Zeng and Liang (2002) developed a limiting equilibrium method (LEM) based solution for a slope/drilled shafts system, depicted in Figure 1, in which the drilled shafts induced arching effect is accounted for by the load reduction factor. The method is developed based on the following assumptions:

(1) FS is assumed to be the same along the original failure slip surface. (2) The normal force on the base of the slice acts at the midpoint of the slice base. (3) The location of the thrust line can be placed generally at one-third of the average

interslice height (hi) above the failure surface as in Janbu (1973). (4) The assumption by Zeng and Liang (2002) regarding the inclination of the interslice

forces was adopted. The right-interslice force (Ri) is assumed to be parallel to the inclination of the preceding slice base (i.e., i-1), and the left-interslice force is assumed to be parallel to the slice base (i.e., i).

Based on Force equilibrium and Mohr-Coulomb failure criteria of the soil, the following equations can be obtained for each slice i.



1 2

3 4

FIGURE 1 Slope with sliding soil mass divided into n vertical slices.

1iii

iiiiii

iii PkFS

tanlucosW

FS

lcsinWP

(1) 5

FS

tansincosk i

i1ii1ii

(2) 6

7

8 9

10

11

12

13

14

15

16

= load transfer factor to be discussed in the next section

i = the slice number Pi = the force acting on the side facing up-slope

Pi-1 = the force acting on the side facing down-slope

i = inclination of slice i base

1i = inclination of slice i-1 base

ui = pore water pressure at the base of the slice i

ci = soil cohesion at the base of slice i

i= soil friction angle at the base of slice i



η in Eq. 1 is the load transfer factor between two consecutive slices, which is used to quantify the transfer of the interslice forces from one slice to the adjacent slice. This load transfer factor (η) is set to 1.0 for all the interfaces between two consecutive slices when there are no drilled shafts at the interface. When the drilled shafts exist in a slope, this load transfer factor reflects the amount of the reduction in the forces due to the presence of the drilled shafts and is defined in Eq. 3.

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

FINITE ELEMENT STUDY OF LOAD TRANSFER FACTOR A comprehensive 3-D FEM parametric study of the drilled shaft/slope system has been carried out by the authors. The stability of slopes reinforced using a single row of drilled shaft is modeled and analyzed using Shear Strength Reduction Method (Zienkiewicz, 1973; Duncan, 1996; Griffiths and Lane 1999). The FE computer code ABAQUS (2006) is used to conduct this study. The numerical study is detailed in the following sections ABAQUS and Shear Strength Reduction Method (SSRM) Recently, Hügel et al (2008) have demonstrated the power of ABAQUS for slope analysis using SSRM by defining temperature field. Specifically, Qianjun et al. (2009) developed a virtual temperature-based method to reduce soil properties internally in ABAQUS; hence, there is no need for the iterative solution any more. In this study, the dimensionless horizontal displacement δ = Umax/H, where Umax is the maximum horizontal displacement of the slope, H is the slope height, is calculated in terms of the strength reduction factor (RF). The value of the reduction factor which corresponds to the point at which the dimensionless horizontal displacement begins to change rapidly (abrupt change) is the factor of safety. Finite Element Model 3D finite element model was constructed using ABAQUS program for studying the soil structure interaction behavior of the drilled shafts on a slope under the effect of shear strength reduction. The baseline finite element model was constructed for a slope without drilled shafts on the verge of failure (FS =1.0). The base line model was then reinforced with a row of drilled shafts to improve the factor of safety. From the SSRM, the factor of safety of the drilled shafts reinforced slope is determined. Material Model Soil is modeled as linear elastic-perfectly plastic material which obeys the Mohr-Coulomb failure criterion. The model properties are the angle of internal friction, cohesion, elastic modulus, and Poisson’s ratio. The thermal expansion coefficient is set to be equal to zero. The rock and the drilled shaft are modeled as linear elastic material. Modeling of the Interfaces Three contact interfaces were defined to account for the contact boundaries in the model: 1) soil-shaft interface, 2) rock-shaft interface, and 3) soil-rock interface. Two interface properties are needed; First, normal interaction property, where the " Hard Contact" was used, which means that contact pressure will be generated only if there is a full over-closure between the contact surfaces. Furthermore, this type of contact minimizes the penetration of the slave nodes into the



master surface, and it does not allow the transfer of the tensile stresses across the interface. If any separation takes place between the contact surfaces, no contact pressure will be generated, and tensile stresses will not be transferred. Second, tangential interaction property is defined by the friction coefficient at the interface.

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

Loads and Boundary Conditions The only load used in this analysis is the gravity load. The boundary conditions are modeled as follows: The bottom of the rock is fixed in all directions. For all the vertical boundaries the soil movement is prohibited (fixed) in the normal direction. The left and right vertical boundaries are considered being lines of symmetry. All the boundary conditions are shown in Figure 2-a, and 2-b. FEM Mesh The mesh generated for the problem is depicted in Figure 3. It consists of 7696 hexahedral elements for soil body, 23600 similar elements for rock, and 420 similar elements for the drilled shafts. The mesh of the shaft and the adjacent area was finer than the other zones because this region was expected to be a high stress zone. The mesh was refined based on the convergence of the numerically computed factor of safety. At the beginning, a trial mesh was made and the corresponding factor of safety was found, then the mesh was refined incrementally and the factor of safety was computed. When the obtained value of the factor of safety becomes stable (almost constant value), then the mesh with the minimum number of elements corresponding to this safety factor is used. Parametric Study Based on the above mentioned finite element model, the effect of fifteen parameters on the load transfer process was investigated. These parameters are classified into five groups; 1) Soil parameters (cohesion c, internal friction , elastic modulus Es, and unit weight ); 2) Rock properties (elastic modulus Er, and Poisson's ratio r); 3) Shaft properties (total shaft length Lp, rock socket length Lr, diameter D, elastic modulus Ep, and Poisson's ratio p); 4) Geometry (spacing to diameter ratio S/D, slope angle , Dimensionless shaft location xi/X); and finally 5) The soil-shaft interface friction angle . The base line model geometry and the parameters for this study were selected such that the non-reinforced slope has a factor of safety equal to one. Each parameter was investigated by changing its value over a reasonable range. For each different value of each parameter the model was analyzed using FEM and SSRM. At failure the factor of safety, the up-slope and down-slope horizontal soil stresses around the shaft perimeter, the depth of the failure surface at the drilled shaft location were obtained. The importance of each parameter was investigated, and the load transfer factor was calculated based on these computations. The results show that the important parameters which control the load transfer factor are a) The soil properties [cohesion(c), angle of internal friction (), and the modulus of elasticity (Es)], b) the Drilled shaft parameters [diameter (D), and the total shaft length (Lp)] and, c) Arrangement and geometry [Spacing to diameter ratio(S/D), slope angle (), location of the shaft (). The order of these parameters starting from the most important parameter is[C, , S/D, , D, , Es, Lp] The load transfer factor is quantitatively defined in this study by dividing the horizontal resultant force on the sahft, in the direction of the soil movement down slope, by the horizontal resultant



1 2

force on the shaft in the direction of soil movement up slope. Accordingly the load transfer factor is computed as:

up

Down

F

F (3) 3

4 5 6 7 8 9

10 11 12 13 14

15

16 17

18

19 20 21 22 23 24 25 26 27 28 29 30 31 32

Fup = the resultant horizontal force (in the direction of the soil movement) on the up-slope side of the shaft Fdown = is the resultant horizontal force (in the direction of the soil movement) on the down-slope side of the shaft The resultant force in the soil up-slope and down-slope around the shaft is estimated by integrating the horizontal soil stresses around the perimeter of the shaft as shown in Figure 4-a and from the top of the shaft down to the failure surface as shown in Figure 4-b:

fL

0

2/D

0

xxup dz.ds.F (4)

fL

0

2/D

0xxDown dz.ds.F (5)

where D = the diameter of the drilled shaft Lf = the distance from the top of the shaft down to the failure surface xx = S11= the horizontal soil stresses right up-slope the shaft xx =S'11= the horizontal soil stresses down-slope the shaft.



a

b

FIGURE 2 The boundary conditions used in the finite element model. 1

2 3 FIGURE 3 The finite element model and mesh representation.



a

b

1

3

1 2

3

4 5 6 7 8 9

FIGURE 4 The soil stressess distribution a) Around the shaft perimeter b) From the top of

the shaft down to the failure surface

The parametric study of the 3D FEM simulations resulted in a compilation of factor. A statistical regression analysis was performed to yield the following set of equations for estimating factor.



1 , 2

76.03

7.01 ln96.023.3 0.10 (6) 2

3 4

where

tan256.0018.0E

C418.0

287.0

1 5

6

(7)

6

s

10

EE (8) 7

8 9

10 11

(9) tan047.0D/Sln24.0 95.3

2

X

x i (10) 12

13

D

412.0p

2.11

3 091.0L

D004.0 14

15

16

17

18

19

20

21

22

23

24

25

26 27

, (11) pr L15.0L

Also,

E = Soil Modulus

c = Soil cohesion

= Soil friction angle

S = Drilled shafts spacing

D = Drilled shafts diameter

Xi = Drilled shaft location

X = Length of slope

β = Slope angle

Lp = Total drilled shaft length

Lr = length of Rock socket



A PC based computer program (UA SLOPE Version 2.0), incorporating the arching concept (load transfer factor) and the limit equilibrium approach, has been developed to allow for computation of FS of the slope with or without the drilled shafts.

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23

CASE STUDY – ATH-124 Site Condition and Soil Investigation The existing failed slope at the State Route ATH-124, from station 107 + 40 to 108 + 60, was selected for field testing. The slope failure was first observed in the fall of 2004 with the evidence of sudden slope movement clearly visible in the form of tension cracks and scarps The triggering mechanism for slope failure was attributed to a sudden drawdown of the water level in the adjacent Ohio River. Initial site investigation after slope failure included a total of eight boreholes for determining the site soil profile and obtaining undisturbed Shelby tube samples for laboratory testing of soil properties. In addition, five inclinometer borehole casings were installed to monitor any continuing slope movement and to delineate the location of the slip zone. The plan view of the site is schematically illustrated in Figure 5. The State Rt. 124 was eventually relocated and the site was abandoned. In June 2007, as part of this study, this site was further investigated with four additional soil boreholes and laboratory testing. The laboratory tests of soil samples retrieved from the field included specific gravity, natural water content, direct shear test, CIU test, and UC test. For rock cores, RQD and unconfined compression strength of rock core were obtained. Three additional inclinometer casings were installed at the slope site. Based on the two site investigation reports, the soil profile at the failed slope was determined and shown in Figure 6. The pertinent soil and rock properties, including strength parameters, are summarized in Table 1.



1

2 FIGURE 5: Plane view of test Site and instrumentation layout



Zone Description

1 Cohesive fill 2 Granular fill 3 Colluvium/Alluvium 4 Cohesive Soil 5 Rock

1

2

3 4 5

FIGURE 6: Cross-section A-A: simplified soil profile

TABLE 1 Summary of the input material parameters in FEM analysis

Zone Material Description C (PSF) o (PCF) 1 Cohesive fill(A-6b) 200 30 133.5 0.2 2 Granular fill (A-1-b) 0 40 135.5 0.2 3 Colluvium/Alluvium 100 28 125 0.2 4 Cohesive (A-7-6) 0 15 130 0.2 5 Bed Rock qu =68948 kPa 155 0.18

6 7 8 9

10 11 12 13 14 15 16 17 18 19

Determining the Slip Zone The slip zone of the failed slope was determined from the inclinometer readings during the two years of monitoring after the occurrence of the first slippage in 2004. The four points defining the slip zone in Figure 6 were determined from the inclinometer reading without ambiguity. The last point defining the exit point of the slip surface, however, was determined by stability analysis using the computer code Gstable7 with STEDwin [Slope Stability Analysis System, version 2.004, Manual (2003)]. The angle of internal friction at the failure surface, associated with a factor of safety equal to one at a rapid drawdown condition, was determined to be 15.5o. Construction of Drilled Shafts The four drilled shafts were installed at the failed slope site in two types of arrangement. One arrangement includes a single isolated drilled shaft (labeled as Sh#4 in Figure 5), and the second arrangement involves a row of three drilled shafts (labeled as Sh#1, Sh#2, Sh#3) in Figure 5.



The as-built properties and geometries of the drilled shafts are as follows: shaft diameter D = 33 inches, shaft length L = 50 ft, rock socket length L

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

Socket = 15 ft, center to center spacing S = 7.5 ft, S/D = 2.75, the 28 day compressive strength of concrete fc = 4570 psi, modulus of elasticity of concrete E conc = 2.6 x 106 psi, steel section = Hp 10x42, the equivalent flexural modulus of the drilled shaft (EI ) = 1.57389 x 1011 lb-in2. The moment capacity of the drilled shaft is computed using the computer code LPILE [LPILE plus, version 5.0.7, Manual (2004)] as 14000 inch-kip, while the shear capacity is computed as 500 kips. It should be noted that the distance between the three shafts in a row and the single isolated drilled shaft is 27.5 ft. All four drilled shafts were placed at the same offset (36 ft) from the edge of the slope crest. Instrumentation Layout For this study, the movement of the slope and the constructed drilled shafts were instrumented with various sensors and inclinometer casings. The general layout of the instrumentation is shown in Figure 5. Altogether, four inclinometer casings were installed (INC#1, INC#2, INC#3, and INC#4) on the slope about two months prior to the construction of the drilled shafts to establish baseline readings. INC#1 and INC#4 were located at the top of the slope, about 10 ft upslope from the location of the drilled shafts. The total length of INC#1 is 57 ft with about 20 ft into rock; and the total length of INC#4 is 54 ft, with 20 ft into rock. Inclinometer INC#2 was installed between shaft #1 and shaft #2 to capture the possible effect of the arching on the soil movements between the shafts. It has a total length of 68 ft, with 30 ft into the rock. Inclinometer INC#3 is located 13 ft down slope from the drilled shafts and has a total length of 50 ft with 15 ft into the rock. Three piezometers (PZ#1, PZ#2, and PZ #3) were installed to observe the fluctuations of the ground water level. PZ#1 was installed in the upper third of the slope at the depth of 26 ft. PZ#2 was installed in the middle portion of the slope at the depth of 26 ft. PZ#3 was located near the toe of the slope at 24.5ft below ground surface. Each constructed drilled shaft was instrumented with conventional inclinometer casings (Sh#1 with INC#5, Sh#2 with INC#6, Sh#3 with INC#7, and Sh#4 with INC#8). In addition, a total of 30 vibrating wire based strain gages (Geocon Model 4000) were installed on the H-beam in shaft #2, i.e., 15 gages on the anticipated tension side (up-slope side) and 15 gages on the anticipated compression side (down-slope side). The vertical spacing of the strain gages was 3-foot apart. . Application of Surcharge Loading The surcharge load at the slope crest area was applied in two stages as follows. Stage 1 loading occurred between 11/19/2007 and 11/27/2007 with an equivalent of 750 psf uniform pressure covering an area of roughly 16 ft by 7 3ft. Stage 2 loading occurred from 10/20/08 to 10/22/08 with additional 848 psf uniform surcharge pressure added to the existing surcharge load from Stage 1. Thus, the total surcharge load provides a roughly uniform pressure of 1598 psf at the end of stage 2 loading. FEM Analysis Results A 3D finite element model was established to model the test site slope with a row of drilled shafts installed. The finite element mesh is shown in Figure 7. The results of FEM model simulation of the slope was compared with the measured for the two loading stages.



1 2 3 4

The FEM analysis results, including soil movements at the top of the slope, and the deflections of shaft #2, are plotted against the measured in Figure 8 and Figure 9, respectively. As can be seen the FEM predictions seem to agree well with the measured during the two stages of loading

5

6 FIGURE 7: FEM mesh modeling of test site



0

10

20

30

40

50

60

0 0.05 0.1 0.15Displacement (Inch)

Dep

th (

Fee

t)

FEM

Mesured

0

10

20

30

40

50

60

0 0.2 0.4 0.6

Displacement (Inch)

Dep

th (

Fee

t)

Measured

FEM

a b 1

2

3

4

FIGURE 8: Comparison between measured and FEM computed ground displacement at

INC #1: (a) due to first loading, and (b) due to second loading



0

10

20

30

40

50

60

0 0.1 0.2 0.3

Displ.(inch)D

epth

(fe

et)

Measured

FEM

0

10

20

30

40

50

60

0 0.1 0.2 0.3 0.4

Displ.(inch)

Dep

th (

feet

) Measured

FEM

a b

1 2

3

4 5 6 7 8 9

10 11 12 13 14

FIGURE 1 Comparison between measured and FEM computed shaft deflections for shaft

#2: (a) due to first loading, and (b) due to second loading

U A Slope Analysis versus FEM Analysis Results The previously validated FEM model of the test site was used to find the F.S. and the resultant force of the drilled shafts by adding surcharge load until the reinforced slope is on the verge of failure. The UA SLOPE 2.0 program was also used to determine the F.S. and the resultant force on the drilled shafts. Table 3 provides a comparison between the UA SLOPE 2.0 and the FEM simulation results. As can be seen, the computed FS and the resultant forces are very close from the two methods.

Table 3 Comparison of F.S. and the resultant force on the shaft using UA SLOPE 2.0 program and FEM model

Method Resultant Shaft force (kN) Global Factor of Safety FEM 132.5 1.3 UA SLOPE 121.5 1.2

15 16



SUMMARY AND CONCLUSIONS 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

An approach for analysis and design of a slope reinforced with a row of equally spaced drilled shafts was presented in this paper. The concept of the analysis was based on the notion that the installed drilled shafts in the slope provide relatively rigid inclusions so that arching develops when the soil mass moves downslope. The arching effect due to the presence of the drilled shafts was studied using 3-dimensional finite element simulation techniques in which the slope geometry, the soil parameters, the rock properties, the drilled shaft configurations were varied to establish regression based semi-empirical equations for quantifying the load transfer effect due to arching and drilled shafts. Furthermore, the conventional method of limit equilibrium method of slice was modified to incorporate the load transfer concept in determining the FS of the drilled shaft reinforced slope. The PC based computer program, UA SLOPE (Version 2.0) was developed to incorporate the above mentioned analysis principles. To provide a validation of the developed UA SLOPE 2.0 program, both the FEM simulation technique and the UA SLOPE analysis were carried out for a test site: ATH-124 in Ohio. The monitored field data are in good agreement with the FEM modeling results. Moreover, the results obtained from the UA SLOPE code are comparable to the FEM results. Based on the presented validation case study, the developed method of analysis, together with the accompanied computer program UA SLOPE (Version 2.0), could be used for analysis and design of the drilled shafts to stabilize an unstable slope.

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International Conference on Soil Mechanics and Foundation Engineering, Tokyo, pp. 113-118.

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landslide—one row of piles.” Soils and Foundations, Vol. 21, No. 1, pp. 21-37.

7. Ito, T., Matsui, T. and Hong, P. W. (1982). “Extended design method for multi-row stabilizing piles against landslide.” Soils and Foundations, Vol. 22, No. 1, pp. 1-13.

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control problems, Edited by Reeves, R. B., ASCE, pp. 61-76.



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7 8 9

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9. Morgenstern, N. R. (1982). “The analysis of wall supports to stabilize slopes.” In 2 application of walls to landslide control problems, Edited by Reeves, R. B., ASCE, pp. 19-29.

10. Gudehus, G. and Schwarz, W. (1985). “Stabilization of creeping slopes by dowels.” Proc. 6

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