Numerical Analysis of the Load Transfer and Deformation in a Soil Nailed Slope

Michael Z. Yang~ and Eric C. Drumm, 2 Member ASCE

Abstract."

A mine waste slope that had failed previously was cut back and stabilized with soil nails. The lower section of the slope was steepened from 1H:IV to about 1 H'3.7V, and the slope was monitored with slope inclinometers. To evaluate the load transfer process in the nails during the excavation of the lower slope, a finite element analysis was conducted. A typical 3-D section of the slope was analyzed, with the width equal to the horizontal nail spacing. Staged material property replacement and removal of elements was used to simulate the construction and excavation process. The analysis results were compared with slope inclinometer data from the field site, and the axial nail forces were evaluated. The build up of tension in the nails was represented in the model. To observe the load transfer mechanisms as failure was approached, a surcharge loading was then incrementally applied on the top of the finite element model of the slope. The results suggest the development of a yield zone leading to a global failure of the slope.

Introduction

Prior to 1977 when the U.S. Surface Mining Act mandated surface mine reclamation, the extraction of coal from the southern Appalachian mountains of the United States often left unstable or marginally stable waste-rock slopes. These slopes were created when waste-rock was dumped down the hillside below the mine

Geotechnical Engineer, Michael Baker Jr., Inc., 555 Business Dr., Suite 100, Horsham, PA 19044. Formerly Grad. Res. Asst., Dept. of Civil & Environ. Engrg., Univ. of Tenn., Knoxville, TN 37916

2 Professor, Dept. of Civil & Environ. Engrg., Univ. of Tenn., Knoxville, TN 37916

102

Dow

nloa

ded

from

asc

elib

rary

.org

by

Dre

xel U

nive

rsity

on

03/2

3/13

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

NUMERICAL METHODS IN GEOTECHNICAL ENGINEERING 103

operations. This mine spoil is often comprised of random size material ranging from clay size to boulder size, and generally exists at low density. Many of these slopes are still active, with down slope movement carrying trees and vegetation. This movement may occur very slowly over periods of years, or may occur rapidly corresponding to periods of high rainfall or construction activities. Access to these slopes is often difficult, making conventional repair methods involving movement of large volumes of material demanding and expensive. An investigation (Drumm et al. 1997) was conducted to evaluate the application of established soil nailing techniques to mine waste slopes.

An existing, marginally stable 1 H: 1V slope about 8 m high was stabilized with nails. The lower 4 m of the slope was steepened to 1H:3.7V (75 degrees), thus creating a "cut-slope" requiring support, Figure 1. Boulders and debris in the mine spoil forced the relocation of many nails, resulting in an irregular nailing pattern (Drumm et al. 1998). However, one section of the slope was designed with 3 m long nails in the upper natural slope and 6 m nails in the lower cut slope and can be idealized as shown in Figure 1. The design specified 1.5 m horizontal and vertical nail spacing. The 25 mm diameter steel nails were grouted into 200 mm diameter holes augered into the mine spoil. Although nail installation followed conventional soil nail practice, the surface did not receive shotcrete. Instead, to encourage the growth of vegetation, a layer of geo-grid was applied to the surface, and held in place by 0.5 m square plates on the end of each nail. Slope inclinometers were installed to measure the deformations in the nailed slope. Figure 1 depicts the approximate location of the inclinometer casing. The deformations in the slope were monitored during construction, and for a period of 800 days following completion of the slope excavation. To investigate the stress distribution in the nails, and investigate the mechanisms contributing to the stability of the soil nailed slope, a series of numerical analyzes was performed.

Both 2 dimensional and 3 dimensional finite element approximations have been utilized to analyze the deformation and stress conditions in reinforced soil systems (Mino et al., 1988; Nagao et al., 1988; Jewell and Pedley, 1992; Asaoka et al., 1996; Ehrlich et al., 1996; Kenny and Kawai, 1996; Briaud and Lim, 1997). When the 3 dimensional soil-nail system is idealized in 2-D, the nails are often represented by continuous reinforced plate with an equivalent stiffness (Nagao et al., 1988; Enrlich et al., 1996; Kenny and Kawai, 1996). When the nails are replaced by a continuous plate, the contact area between the soil and nails is over estimated and the resulting modified interface parameters may have little physical meaning (Asaoka et al., 1996). The soil-nail interaction effects can be more accurately characterized using a 3-D finite element approximation in which the individual nails can be modeled (Asaoka et al., 1996; Briand and Lim, 1997).

Dow

nloa

ded

from

asc

elib

rary

.org

by

Dre

xel U

nive

rsity

on

03/2

3/13

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

104 NUMERICAL METHODS IN GEOTECHNICAL ENGINEERING

Figure 1 Schematic Section Through Nailed Slope

3-D finite element analysis of a nailed slope

A numerical analysis was conducted to model the deformation of the slope, and to investigate the stress distribution in the nails and resulting improvement in stability. The commercial finite element code ABAQUS (H., K., & S., 1998) was used for the analysis. A 3-D section of the slope was idealized as shown in Figure 2a, with a model width in the x coordinate direction equal to the 1.5 m horizontal nail spacing. The subsurface conditions were approximated by considering a homogeneous mine waste overlying sandstone bedrock (Drumm et al., 1997). Eight- node brick and six-node tetrahedral elements were used to represent the mine spoil, sandstone and soil nails. In addition to evaluating the conditions under the gravitational service loads, the stresses as the slope approached instability were evaluated by incrementally applying a surcharge loading at the top of the slope. Therefore a large deformation algorithm was used in each analytical step.

The mine spoil was represented by a Drucker-Prager hardening elastic-plastic model (Desai and Siriwardane, 1984), with the strength parameter and elastic modulus assigned based on CU triaxial tests performed on the fine-grained portion of the mine waste. The measured q0 and c were used to obtain the Drucker-Prager yield function for plane strain conditions. A non-associative flow rule was used in order to assure that the material would not be dilative. The steel/grout nails were modeled as a single uniform material with equivalent linear elastic properties. The nails were modeled as square in cross section, with an area equal to that of the grout hole (200 mm in diameter). Zero thickness contact elements surrounded the nails, with the shear strength of the interface assigned based on the results of nail pull-out tests (Dmmmet al., 1997). The limited constraint provided to the soil by the geogrid

Dow

nloa

ded

from

asc

elib

rary

.org

by

Dre

xel U

nive

rsity

on

03/2

3/13

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

NUMERICAL METHODS IN GEOTECHNICAL ENGINEERING 105

installed on the slope surface and the plate at each nail head was approximated by an elastic strip on the slope face. The elastic strip was 1.5 m wide (width of finite element model) and 0.15 m high and attached to the nail with a spring element of low stiffness (4000 kN/m). The sandstone at the lower level was assumed to act a strong stiff layer, and modeled as a linear elastic material. The material properties used in the analysis are summarized in Table 1. The elastic-plastic material model used for the mine spoil and the contact elements used with the soil nails require an incremental process. For this reason, the initial stress state must be estimated and the loading sequence must be approximated.

Table 1. Summary of Material Properties

Material Cohesion Friction Angle Elastic Modulus Poisson's Ratio Description c (kPa) ip (deg) E (MPa) la

Mine Waste 20 20 11 0.33

Sandstone NA NA 180 0.25 Nail & Grout NA NA 8,000 0.23

Grout/mine 0 20 NA NA waste interface

Plate NA NA 400 0.23 Determination o f initial stresses and Simulation o f Nail Installation

Soil nails act as passive reinforcement elements in the nailed slope system. As the soil slope deforms under loading, external loads are transferred to the nails and the induced stresses in the nail improve stability. To properly model the load transfer mechanisms in a nailed slope, it is important to account for the initial stress conditions in the soil, and to simulate the sequential slope excavation and nail installation process. Relative displacements at the interface between the nail/grout

Figure 2 (a) Mesh of Initial Slope (b) Mesh of Soil Nailed Slope

Dow

nloa

ded

from

asc

elib

rary

.org

by

Dre

xel U

nive

rsity

on

03/2

3/13

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

106 NUMERICAL METHODS IN GEOTECHNICAL ENGINEERING

and the surrounding soil must be included. Without slip taking place along the nails, very high stresses would be generated at the ends of the nails, and tensile stress would be produced in the soil. This would lead to an unrealistic stress distribution and a poor representation of the field behavior.

The analysis procedure employed here is illustrated in Figure 3. The first analytical step (Stepl) was to determine the geostatic stresses in the mine waste, which was accomplished by fixing all the nodes and applying the gravitational loading. For this step all the elements (including the soil nails) were assigned properties corresponding to the mine waste. In Step 2, the initial boundary conditions were imposed, and the remaining nodes were released to allow the slope to deform. This established the initial stress and deformation conditions in the natural slope, and provided the baseline deformations for the calculation of the incremental displacement, strains, and stresses due to the subsequent excavation and loading steps. The staged nail installation and slope excavation process were then simulated in Steps 3 to 5. The nail installation was simulated in Step 3 by simultaneously removing the soil elements and replacing with nail elements, and the response under the gravity loading was determined. The stresses in the nails were then used to determine the baseline nail forces from which incremental increases due to subsequent excavation (Steps 4 and 5) could be compared. To observe the load transfer mechanisms as failure was approached, a surcharge loading was then incrementally applied on the top of nailed slope (Step 6).

Results and Discussions

The numerical results from the end of analysis Step 5 (end of excavation) were compared with the observed deformation profiles from the inclinometer measurements. The nodal displacements obtained along a vertical line about 2 meters behind the edge of the slope, corresponding to the location of the inclinometer casing (Figure 1), are compared with the measured inclinometer deflections in Figure 4. The maximum computed displacement at the surface was about 1.7 mm, whereas the displacement measured at the end of construction (about 60 days after the start of construction) was about 0.6 mm. The measured displacements are relative to the bottom of the inclinometer casing (depth of about 7 m), which was the refusal depth during the installation. The numerical results indicate displacements extending to a depth of over 10 m, with a displacement of nearly one mm at the depth corresponding to the bottom of the inclinometer casing. This would suggest that the bottom of the inclinometer casing was at insufficient depth and it may have translated with the mine waste as the displacement took place. If it is assumed that the bottom of the inclinometer casing translated by about one mm, an amount equal to the computed FE displacement at this depth, the measured displacement profile can be "corrected" by applying a one mm translation to the displacements as indicated by the corrected measurements shown in Figure 4. With this correction to the field measurements, the

Dow

nloa

ded

from

asc

elib

rary

.org

by

Dre

xel U

nive

rsity

on

03/2

3/13

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

NUMERICAL METHODS IN GEOTECHNICAL ENGINEERING 107

Figure 3 Steps in Analysis Procedure

Dow

nloa

ded

from

asc

elib

rary

.org

by

Dre

xel U

nive

rsity

on

03/2

3/13

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

108 NUMERICAL METHODS IN GEOTECHNICAL ENGINEERING

Figure 4 Comparison of Measured and Predicted Displacement

predicted displacements above the 7 m depth seem to agree very well with the field measurements at the end of construction.

Also shown in Figure 4 is the corrected displacement profile measured 800 days after construction. The additional deformations which took place after construction have been attributed largely to creep (Drummet al., 1998), which was not considered in the numerical analysis. However, it is observed that the additional long term deformations seem to be occurring primarily in the material above a depth of 4 m, or in the natural slope with the shorter 3 m nails. Very little additional deformation was measured by the inclinometer at depths from about 4 m to 7 m, corresponding to the portion of the lower cut slope with the longer 6 m nails. In the initial design of the nail system, the shorter 3 m nails installed in the upper 4 m of the natural slope were not considered to contribute to the overall stability, but were installed to control local deformations. The observed deformations suggest that the these short nails were not effective in controlling the long term creep deformation in the upper slope, but the 6 m nails in the lower slope effectively limited slope deformation. It will be shown below that the short upper nails are of insufficient

Dow

nloa

ded

from

asc

elib

rary

.org

by

Dre

xel U

nive

rsity

on

03/2

3/13

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

NUMERICAL METHODS IN GEOTECHNICAL ENGINEERING 109

length to extend across the region of concentrated plastic strains that would be developed as the slope approaches failure due to a surcharge loading.

Yielding in the slope was investigated in terms of the computed plastic strain magnitude e;:

~p = ~pl~pl

where e pt is the plastic strain. The results of the analysis suggested that the plastic strains were very small throughout the mine waste under the service load. Figure 5a illustrates the computed yielded zone under the service (gravitational) load. Only a small plastic zone (maximum strain magnitude equals 5%) occurred at the toe of the nailed slope. This suggests that the nailed slope has a high global factor of safety, which is consistent with the results from limit equilibrium analysis which yielded a FS=I.7 (Drumm et al., 1997).

To observe the load transfer mechanisms in the nailed slope as failure was approached, a surcharge loading was incrementally applied on the top of the slope. Figure 5b illustrates a continuous yielded zone under a 90 kPa surcharge load at the top bench of the nailed slope. This was the smallest value of the surcharge loading such that a continuous zone of plastic strains were computed. The scale of the plastic strains is the same as that in Figure 5a. Below this level of surcharge, the yielded zone was discontinuous. A probable slip surface, indicated in Figure 5b, was obtained by connecting the locus of largest plastic strain magnitude computed at each elevation. This slip surface had a parabolic form, which is the assumed shape in many global limit equilibrium stability analysis methods (Shen et al., 1981; G~sler, 1988). It is noted that the short nails in the upper slope are completely contained within this zone of large plastic strain. A surcharge loading of 160 kPa was the maximum for which a solution could be obtained. At this level of loading, a limit equilibrium analysis provided a similar failure surface and a FS = 1.07.

The axial tension force computed in each nail under different loading conditions is presented in Figure 6. Although tension was developed in the nails as the lower slope was excavated, the predicted tensile forces were very small, both in the short upper nails and longer lower nails. At the end of construction, the maximum tension force predicted was about 5 kN near the center of nail 5. This can be compared with the anticipated range of nail capacity of 25 to 60 kN, based on field nail pullout tests (Drumm et al., 1997) and an assumed development length of 3 m. The interface elements around the nails assured that the stresses were nearly zero at the end of the nails away from the slope face, which is expected. Due to the presence of the plate on the end of the nail at the slope face, small tensile forces were developed at the head of the lower nails.

Dow

nloa

ded

from

asc

elib

rary

.org

by

Dre

xel U

nive

rsity

on

03/2

3/13

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

110 N U M E R I C A L M E T H O D S IN G E O T E C H N I C A L E N G I N E E R I N G

O

O tt~

O *-.,

,,.-, O

e0

Dow

nloa

ded

from

asc

elib

rary

.org

by

Dre

xel U

nive

rsity

on

03/2

3/13

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

NUMERICAL METHODS IN GEOTECHNICAL ENGINEERING 11 l

Figure 6 Predicted Axial Force in Each Nail under Service and Surcharge Load

Dow

nloa

ded

from

asc

elib

rary

.org

by

Dre

xel U

nive

rsity

on

03/2

3/13

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

112 NUMERICAL METHODS IN GEOTECHNICAL ENGINEERING

Figure 6 also illustrates the increase in nail force as the surcharge on the top of the slope is increased. With a 60 kPa surcharge, a maximum tension force of about 14 kN was predicted in the center of nail 5, and a force of about 12 kN was generated at the center of nail 4. Even under the higher surcharge loading the tensile forces in the upper nails was very small, suggesting that they contributed little to the stability of the slope.

In Figure 7, a section through the slope is shown, onto which the computed nail forces from Figure 6 are superimposed on the relevant nail. The probable slip surface obtained from the maximum plastic strains in Figure 5b is also shown. The slip surface passes through nails 4 and 5 near the area where the maximum nail tensile forces were generated, which is consistent with common design assumptions (Shen, et al., 1981; Juran, and Beech, 1984; G~ssler, 1988). Nail number 6 at the bottom of slope was installed in anticipation of additional excavation, which did not take place due to the sandstone layer. The probable slip surface crosses this nail near its head.

Summary and Conclusions

A 3 dimensional finite element analysis was conducted to model the deformations and to investigate the stress distribution in a nailed slope excavated in mine waste. The method used to estimate the initial stresses and to incorporate the construction sequence was described, and the modeling of the nail/soil interface and nail face plate was discussed. The analysis results were compared with field measured deformations under the gravitational service loading, and the analysis was extended to evaluate conditions near failure through the application of a surcharge load. Results from the analysis lead to the following conclusions:

The computed deformations agreed very well with field measurements from inclinometers, provided the field measurements were corrected for deformations that may have occurred blow the lowest point in the inclinometer casing. Most of the long term deformations occurred in the upper slope which was supported by the short (3 m) nails suggesting that these nails were not effective.

2. Other than a small zone of plastic strains at the toe, the computed strains were small under the gravity service load conditions. This indicates the effectiveness of the soil nailing method. The nail forces were generally small, but tensile forces were developed in the longer lower nails installed in the cut slope.

Dow

nloa

ded

from

asc

elib

rary

.org

by

Dre

xel U

nive

rsity

on

03/2

3/13

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

N U M E R I C A L M E T H O D S IN G E O T E C H N I C A L E N G I N E E R I N G 113

119

._qo

cD

O

O

e~

rgJ

z

O

t".-

Dow

nloa

ded

from

asc

elib

rary

.org

by

Dre

xel U

nive

rsity

on

03/2

3/13

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

114 NUMERICAL METHODS IN GEOTECHNICAL ENGINEERING

3. Under the surcharge loading, a potential failure surface was obtained by connecting the locus of the points with the largest plastic strain magnitude. This surface was parabolic in form, which is consistent with the assumption in many conventional limit equilibrium analysis methods.

4. The upper nails contributed little towards global stability, which was consistent with the original design assumptions. However, the measured long term creep deformations seemed to occur primarily in the upper portion of the slope, which suggests that if these nails had been extended, the long term deformations would have been smaller. The short upper nails were completely contained within the potential failure surface constructed from the computed plastic strains under the surcharge loading.

5. The nail tensile forces were very small under the service loading, but under the surcharge loading the locations of the maximum tensile forces corresponded to the point where the potential failure surface intersected the nails.

Acknowledgments

The construction, instrumentation and monitoring of the nailed slope was funded by the U.S. Bureau of Mines, Abandoned Mine Land (AML) Research Program, Contract #1432-J0240002. Much of the analysis described here was performed while the first author was a visiting scholar at the University of Tennessee on leave from the Institute for Rock and Soil Mechanics, Wuhan, China. The authors are grateful to the Institute for the financial support provided during this period.

References:

Asaoka, A., Pokharel G. and Ochiai, T. (1996). "Stability analysis of reinforced Structures introducing some linear constraint contions upon the 3-D velocity field." Proc. Earth Reinforcement, Yasufuku & Omine (eds), Balkema, Rotterdam, 717-722.

Briaud, J. L. and Lim, Y. (1997). "Soil-nailed wall under piled bridge abutment: simulation and guidelines." J. Geotech. & Geoenviron. Engrg., ASCE 123(11), 1043-1050.

Desai, C. S. and Siriwardane, H.J. (1984) Constitutive Laws for Engineering Materials with Emphasis on Geologic Materials, Prentice-Hall, Inc., Englewood Cliffs, NJ 468 pp.

Drumm, E. C., Mauldon, M., and Berry, R. M. (1997). "Application of earth inclusions for Slope Stabilization." Report to the U. S. Department of Energy, Pittsburgh Research Center, Contract No. 1432-J0240002, 163 pp.

Dow

nloa

ded

from

asc

elib

rary

.org

by

Dre

xel U

nive

rsity

on

03/2

3/13

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.

NUMERICAL METHODS IN GEOTECHNICAL ENGINEERING 115

Drumm, E. C., Mauldon, M., and Tant, C. R. (1998). "Stabilization of coat mine waste with soil nails." Ground Improvement, No. 2, 147-156.

Ehrlich, M., Almeida, M. S., and Lima, A. M. (1996) "Parametric analysis of soil nailing systems." Earth Reinforcement, Yasufuku & Omine (eds), Balkema, Rotterdam, 747-752.

G/~ssler, G. (1988). "Soil nailing - theoretical basis and practical design." Int. Geotech. Sym On Theo. & Pract. Of Earth Reinforc. Fukuoka, Japan, 283-288.

H., K., & S. (1998) ABAQUS User's and Theory Manuals. Version 5.7, Hibbit, Karlson & Sorensen Inc. Pawtucket, R.I.

Juran, I. And Beech, J. (1984). "Theoretical analysis of nailed soil retaining structures." Int. Sym. In-situ Soil & Rock Reinforc., Paris.

Jewell, R. A., Pedley, M. J. (1992). "Analysis for soil reinforcement with bending stiffness." J. Geotech. Engrg., 118(10), 1505-1528.

Kenny, M. J. and Kawai, Y. (1996). "The effect of bending stiffness of soil nails on wall deformation." Earth Reinforcement, Yasufuku & Omine (eds), Balkema, Rotterdam, 771-774.

Mino, S., Noritake, K. and Innami, S. (1988). " Field monitoring procedure of cut slopes reinforcement with steel bars." Int. Geotech. Sym. On Theo. & Pract. Of Earth Reinforc. Fukuoka, Japan, 323-329

Nagao, A. Kitamura, T. and Mizutani, J. (1988). "Field experiment on reinforced earth and its evaluation using FEM analysis." Int. Geotech. Sym. On Theo. & Pract. Of Earth Reinforc. Fukuoka, Japan, 329-334.

Shen, C. K., Bang, S. and Herrmann, L. R. (1981). "Ground movement analysis of an Earth Support System." J. Geotech. Engrg. ASCE 107(12).

Dow

nloa

ded

from

asc

elib

rary

.org

by

Dre

xel U

nive

rsity

on

03/2

3/13

. Cop

yrig

ht A

SCE

. For

per

sona

l use

onl

y; a

ll ri

ghts

res

erve

d.