J. Cent. South Univ. (2012) 19: 262-272

DOI: 10.1007/s11771-012-1000-y

Pull-out tests and slope stability analyses of nailing systems comprising single and multi rebars with grouted cement

Sang-Soo Jeon

Construction Technology Research Center, Department of Civil Engineering,

Inje University, Obang-dong 607, Kimhae, Kyungsangnam-Do #621-749, Korea

? Central South University Press and Springer-Verlag Berlin Heidelberg 2012

Abstract: The pull-out capacities for soil nailing systems comprising of one single 29 mm diameter (type A) and four 16 mm diameter (type B) rebars with grouted cement were examined. A field test and numerical analysis for the type A and type B systems were carried out to investigate the pull-out capacities and the slope stability reinforcement efficiency in soil and rock slopes. The results of the pull-out tests show the mobilized shear force and load transfer characteristics with respect to soil depth. The load-displacement relationship was examined for both type A and type B systems. Slope stability analyses were carried out to study the relationships between soil and nail reinforcement and bending stiffness as well as combined axial tension and shear forces. Factors of safety were calculated in relation to the number of nails and their outside diameters. Both soil and rock slopes were included in this evaluation.

Key words: soil nailing; bending resistance; pull-out test; finite difference method

1 Introduction

Nails have been widely used for excavation, tunnel, and slope stabilization. Nails have a high ratio of the circumference to the cross-section area, and therefore they rely essentially on frictional resistance for the load transfer. The bending moment resistance has been disregarded in most cases. Rebars used as nail tendons have been selected to provide adequate tensile strength based on the yield stress of the steel.

MILLIGAN and TEI [1] examined the fundamental interaction mechanisms between nail and soil during pull-out. The pull-out tests were carried out for nails embedded in different types of soil materials [2-10] to examine the strength characteristics, the degree of soil saturation, the grouting pressure associated with overburden stress, and the strain distribution and resistance of soil nail. Numerical slope stability analyses were carried out to explore the behavior of soil nails [11-16]. The factors influencing the shear resistance at the soil/nail interface and the mobilized nail forces were investigated.

MENKITI and LONG [4] observed that the short-term prefailure behavior of nailed slopes was governed more by the deformation pattern of the slope than by the large-scale development of failed wedges and the nails acted mostly in tension with only a limited amount of bending induced. ZHOU and YIN [17] proposed a simple mathematical model for the interaction analysis of a soil nail and the surrounding soil by taking into account a few key factors, namely the soil dilation, bending of the soil nail, vertical pressure, and non-linear subgrade reaction stiffness. The contributions of the bending of the soil nails to the pull-out resistance were of secondary importance as tension failure was dominant in the soil-nailed structures. Past studies [18-20] indicated that the bending resistance is minimal compared with the shaft resistance and the contribution of the bending resistance is usually less than 15%. Therefore, most of the resistance is contributed by shaft resistance, and the bending resistance is negligible in slope design.

In this work, field pull-out tests for type A and type B nailing systems were carried out to examine the mobilized shear force and load transfer characteristics with respect to soil depth. The soil depths tested in this work were in the range of 9-11 m. The load- displacement relationship can be used to represent the reinforcement efficiency of type A and type B systems. A verification and creep test of the soil nailing system based on the specification proposed by FHWA (Federal Highway Association) [21] were carried out. In the numerical analyses, the factor of safety was examined using cable and pile elements for type A and type B systems in relation to the number of nails and their outside diameters embedded in both soil and rock slopes. The number of nails was ranged from one to three and their outside diameters were ranged from 90 to 120 mm.

2 Field pull-out test

Field pull-out tests were carried out in Konjiam, a northern part of Korea. Pull-out tests were categorized into three types: verification test, proof test, and creep test. The verification test before the reinforcement of soil nailing was performed to validate the design method and strength of the nail. The pull-out load was applied up to the design load multiplied by the factor of safety. The creep test was carried out to examine long-term behavior of soil nailing system with respect to time in clayey and sandy soils. The load for creep test was progressively applied to 150% of design load and the displacement associated with applied load was measured at the top of nailing system.

Two types of soil nailing systems were tested at the same sites. The mechanical properties of colluviums soils at the site are listed in Table 1. The embedded lengths of the type A and type B systems were 9.6 and 10.7 m, respectively. The load-displacement relationship was evaluated using a load cell and a LVDT (linear variable differential transformer). The maximum design loads of the type A and type B nailing systems were 235.2 and 284.2 kN, respectively, which were above 90% of the yield strength.

Table 1 Mechanical properties of colluvium soil

The pull-out tests were carried out based on the verification test proposed by FHWA. Figure 1 shows the system for the real-time monitoring and measuring of the load and displacement at the top of nail, including the resisting support system, the LVDT, and the load cell. The soil nails were instrumented with strain gauges attached to the steel tendon of each nail and readings were obtained and stored in a datalogger, which was downloaded at the site. The pull-out load transfer was estimated with respect to soil depth. Figure 2 shows the type A and type B soil nailing systems. The soil depth of 12 m was designed for both soil nailing systems. However, the bottom of the bore hole collapsed therefore, the reinforcement depths for the type A and B systems were 9.6 and 10.7 m, respectively.

As shown in Fig. 3, the coupler was reinforced and a single rebar was directly pulled out for the type A system and four rebars anchored at circular steel plate were pulled out for the type B system. As shown in   Fig. 4, the type A and type B systems were tested at borehole No.1 and No.2, respectively. Figure 4 shows the location of strain gauge in the diagonal direction.

Fig. 1 Real-time monitoring and measuring system of load and displacement

Fig. 2 Field test view of type A (a) and type B (b) nails

Figure 5 shows the results of standard penetration test (SPT) with respect to soil depth at the test site. The soil characteristics of test site were fine sandy soils mixed with boulders in colluvial soil deposits. The boring was stopped at a soil depth of 8 m due to the appearance of a 0.5 m-diameter boulder. SPT test results indicate that the measured N value was above 50 except at a soil depth of 6 m. The results indicated that the colluvium soil was very dense sandy soils mixed with boulders.

3 Field pull-out test results

The load-displacement curves obtained from the field pull-out tests are compared in Fig.6. When pull-out loads of 156.8, 176.4 and 196 kN were applied to the type A system, the displacements were 13.2, 15.3 and 20.9 mm, respectively. Figure 6 shows a yield state at a pull-out load of 196 kN. When pull-out loads of 284.2 kN were applied to type B nails, followed by stopping of the test, the displacement at this point was 15.8 mm. The displacements with respect to the stepwise load constantly increased. The results indicated that the failure pull-out load for type B system exceeded the pull-out load of 284.2 kN. The pull-out displacement required to achieve the peak pull-out strength was smaller for the type A system.

Fig. 3 View of coupler anchored at circular steel plate for type A (a) and type B (b) systems

Fig. 4 Location of strain gauges for type A and type B systems: (a) Borehole No.1; (b) Borehole No.2

Fig. 5 Standard penetration test associated with soil depth in test site

Fig. 6 Load-displacement relationship

As shown in Fig. 6, the load-displacement curves for the type A and type B systems were quite different. The failure occurred at the interfaces between the rebar and grouted cement for the type A system. However, the failure occurred at the nail/soil interface for the type B system. These results indicate that the applied load was well transferred to the entire length of soil nails, and there was good adhesion at the interfaces between the four rebars and grouted cement.

Based on FHWA specifications, the displacement at the top of nail induced by the pull-out load should exceed 80% of elastic displacement of unbonded length. The elastic displacement of unbonded length of nail can be estimated by the following equation:

                           (1)

where δ_E is the elastic displacement of the unbonded length, ?P is the pull-out load, L_u is the unbonded length of the nail, A is the cross-sectional area of the rebar, and E is the elastic modulus of the rebar. The elastic displacements of the type A and type B systems were 1.3 and 1.6 mm, respectively and exceeded 80% of the elastic displacement of the unbonded length.

The measured pull-out load was used to calculate the side resistance per unit length, q_s:

                              (2)

where p is the circumference of nail, and L_b is the bonded length of nail.

For the type A system, the maximum tensile force of the nail tendon generated in the nails and the side resistance at the nail/soil interface were 176.4 kN and 55.9 kN/m², respectively, for a bonded length of 9.6 m and a nail circumference of 0.33 m. For the type B system, the maximum tensile force generated in the nails and the side resistance at the nail/soil interface were 284.2 kN and 80.4 kN/m², respectively, for a bonded length of 10.7 m and a nail circumference of 0.33 m. Therefore, the side resistance per unit length for type B system was 30% larger than that for type A.

Figure 7 plots the results of the creep test. As shown in Fig. 7, the displacement induced by the pull-out load linearly increased with respect to time. For the type A and type B systems, the maximum displacements were 0.4 and 0.6 mm for pull-out loads of 176.4 and 284.2 kN, respectively. FHWA specification indicates that the creep displacement for 1-10 min should be less than 1 mm. Therefore, the creep test results for both type A and type B systems satisfied this specification.

Fig. 7 Creep behavior of soil nail

Figure 8 shows the load transfer induced by a pull-out load applied to the top of nailing system for the type A system. Figure 9 shows the load transfer induced by a pull-out load at the No. 1 and No. 2 rebars for the type B system. For the type A system, the load transfer occurred between the ground surface and a soil depth of 1.6 m. There was no load transfer below a soil depth of 3.6 m. This result indicates that most of the resistance to the pull-out load was at the top of nailing system. For the type B system, the load transfer linearly decreased from the top to the bottom of the nailing system.

The load transfer of the type A system induced by the maximum pull-out load was 5.5% at a soil depth of 3.6 m, and most of the resistance was at the top of the nailing system. The load transfer values of the type B system induced by the maximum pull-out load were 40.0% and 22.4% at soil depths of 4.7 and 6.7 m, respectively. These results showed that the reinforcement of the type B system was more effective.

Fig. 8 Load transfer vs soil depth for type A system

Fig. 9 Load transfer vs soil depth for type B system: (a) Steel No.1; (b) Steel No. 2

4 Finite difference analyses

The slope stability was examined for soil and rock slopes reinforced by the type B system. A 2-D finite difference model using the commercial program FLAC2D [22] was developed to evaluate the slope stability.

The bending resistance is minimal compared with the shaft resistance and the contribution of the bending resistance is usually less than 15%. Therefore, the resisting shear forces and bending moment occurring on the sliding surface of slopes have been disregarded for the design of slope stability. However, as the diameter of pile increases, the resisting bending moment makes up a larger portion of overall resisting forces and the applied load is well mobilized throughout the entire length of the soil nails for the type B system. Therefore, in this work, the slope stability analysis for the type B system associated with the bending resistance was carried out.

Table 2 lists the values of geotechnical parameters for soil and rock slopes obtained from TERZAGHI et al [23] used in our numerical analysis. Stability analyses were carried out at colluvial soil deposits and at sound rock subjected to the circular and plane failure. Table 3 gives the slope angles for colluvial soils and sound rocks associated with 0.2 m-thick planar seam layer, boundary conditions, number of meshes, lengths and diameters of nails, and the number of reinforcement nails.

Figure 10 shows the schematic configuration of the numerical models for the soil and rock slopes reinforced by the type B system. The slope stability for colluvial soil deposits was evaluated with various outside diameters of cement grout and the number of rebars under dry conditions. The slope stabilities for a sound rock with a slope angle of 60° and an inclined planar seam layer at 45° to the horizontal level were examined with various outside diameters of cement grout with a single soil nail. The number of finite difference meshes for soil slopes was 1 257 and the boundary conditions are shown in Fig. 10. The soil and rock underneath were modeled by an elasto-plastic model with a Mohr-coulomb failure criterion. No dilation was assumed for the soil and rock. Two-dimensional plane-strain finite difference models were set up to represent a 10 m-high soil slope with a face angle of 45° to the horizontal level, a reinforced nail length of 10 m, a horizontal nail spacing of 1 m, a vertical nail spacing of 2.5 m, a reinforcement slope angle of 15°, and one, two, or three reinforced nails and nail outside diameters of 90, 105, and 130 mm. The model employed in this study represents a typical slope geometry.

The locations of reinforcement were in the middle for a single nail, in the middle and at the bottom for two nails, and at the top and bottom and in the middle for three nails. The number of finite difference meshes for the rock slopes was 855 and the other conditions were the same for soil slopes. Just a single nail was reinforced with varied outside diameters of 90, 120, and 150 mm.

5 Results of finite difference analysis

5.1 Soil slopes

Figures 11 and 12 show the resisting forces of the nailing system for soil slopes when the slope stability analyses were carried out using a cable and pile element with a single reinforced nail.

When the reinforcement was carried out using a single nail of 90 mm in diameter, resisting axial forces of 37.1?10^-4 and 16.4?10^-3 kN were calculated using cable and pile element, respectively. The corresponding resisting shear forces on the nail grout surface in axial direction were 19.4?10^-3 and 56.4?10^-4 kN, respectively. The calculated resisting forces were relatively small because the applied load was partially mobilized in relatively stable slope. Using the pile element, the resisting axial force was 3.5 times larger than that using the cable element and the resisting shear force was 1.7 times smaller. It was found that as the outside diameter increased, the resisting axial force increased.

Table 2 Geotechnical parameters used in numerical analysis

Table 3 Characteristics of slope geometry and nails used in numerical model

Fig. 10 Schematic configuration of numerical models for soil and rock slopes: (a) Soil slope; (b) Rock slope

Fig. 11 Resisting axial force (a and a′) and shear force on nail grout surface in axial direction (b and b′) using cable and pile element of nailing system for soil slopes

Fig. 12 Resisting forces using pile element of nailing system for soil slopes:      (a) Resisting shear force mobilized on cross-section of nail; (b) Resisting normal force mobilized on nail grout surface in axial direction; (c) Resisting bending moment

Numerical analyses were carried out for the nails of 105 mm and 130 mm in diameter, and the results were compared with those of 90 mm-diameter nail. When a cable element was used for analysis, the resisting axial force increased by 24% and 39%, and the resisting shear forces on the nail grout surface in axial direction decreased by 34% and 56% for the 105 mm and 130 mm diameter nails, respectively, compared with the forces for the 90 mm nail. When a pile element was used for analysis, the resisting axial force increased by 3.6% and 4.8%, and the resisting shear forces on the nail grout surface in axial direction increased by 3.0% and 4.2% for the 105 mm and 130 mm diameter nails, respectively. The induced shear force on the cross-section of the nail increased by 68% and 230%, and the resisting bending moment increased by 78% and 300% for the 105 mm and 130 mm diameter nails, respectively. The normal forces mobilized on the nail grout surface in axial direction increased by 54% and 210% for 105 mm and 130 mm diameter nails, respectively. Numerical results using the pile element instead of the cable element showed a small increment in the resisting axial forces and shear forces on the nail grout surface in axial direction but a large increment in the normal forces mobilized on the nail grout surface in axial direction, shear force in the cross-section of the nail, and resisting bending moment.

When the reinforcement was carried out using two 90 mm diameter nails at the middle and bottom of slopes, the numerical results using the cable and pile elements showed the resisting axial forces of 4.55?10^-3 and 2.51?10^-3 kN at the middle and bottom of the slope, respectively, and corresponding resisting shear forces on the nail grout surface in axial direction at the nail/soil interface of 8.55?10^-3 and 4.70?10^-3 kN, respectively. The results indicated that the nail at the middle took up a larger portion of applied load than the nail at the bottom. Similarly, when the reinforcements were carried out using three 90 mm diameter nails at the top, middle, and bottom of the slope, the nail at the top took up a larger portion of applied load than that at the middle and bottom.

Figures 13 and 14 show the critical slide surfaces and the factors of safety (FSs) obtained from a numerical analysis associated with the number of reinforcement nails under dry conditions. Numerical analysis using a cable and pile element provided FSs of 2.29 and 2.41, respectively, for a single 90 mm diameter nail reinforcement, and FSs of 2.65 and 2.69, respectively, for a three 90 mm diameter nail reinforcement. Numerical analyses were performed for 105 and 130 mm diameter nails, and the numerical results were compared with those of the 90 mm diameter nail. Using the cable element, the FSs of the 105 and 130 mm diameter nails increased by 1.7% and 4.4%, respectively, for a one-nail reinforcement, by 1.5% and 3.1%, respectively, for a two-nail reinforcement, and by 0% and 3.1%, respectively, for a three nail reinforcement. Using the pile element, the FSs of 105 mm and 130 mm diameter nails increased by 1.2% and 2.9%, respectively, for a one-nail reinforcement, by 0.7% and 2.6%, respectively, for a two-nail reinforcement, and by 1.1% and 1.9% respectively, for a three-nail reinforcement.

5.2 Rock slopes

The resisting forces using both cable and pile elements with a single 90, 120, 150 mm diameter nails embedded in rock slopes were calculated, as shown in Figs. 15 and 16 and are tabulated in Table 4. It is clearly seen that when cable element was used, the resisting shear force on the nail grout surface in axial direction was significantly higher, and the bending resistance was enhanced.

Figures 17 and 18 show the resisting forces for a 90 mm diameter nail. The FSs using both cable and pile elements were about one, and the resisting forces were almost same. The resisting axial force and shear forces on the nail grout surface in axial direction for a 90 mm diameter nail at the nail/soil interface were 129.3 and 124.6 kN, respectively, using the cable element, and 154.6 and 66.5 kN, respectively, using the pile element. The resisting axial forces increased by 20% when using the pile element, but the shear forces generated at the interfaces decreased by 46% due in part to the redistribution of shear force mobilized on the cross-section of the nail, the resisting bending moment of the nail, and the normal force mobilized on the nail grout surface in axial direction.

As shown in Figs. 17 and 18, the resisting axial forces and shear forces on the nail grout surface in axial direction were concentrated on the sliding surfaces of the seam zone and were relatively uniformly distributed along the nail. Using the cable element, the resisting axial forces and shear forces on the nail grout surface in axial direction were partially mobilized near to the critical slide surface and did not vary with the diameter of nail. However, by using the pile element, the resisting forces were fully mobilized and evenly distributed throughout the entire length of the soil nails. The resisting axial force and shear force on the nail grout surface in axial direction at the nail/soil interface for  120 mm diameter nail increased by 35% and 30%, respectively, compared with those for 90 mm diameter of nail, and those for 150 mm diameter nail increased by 33% and 65%, respectively. As the nail diameter increased, the shear force on the cross-section of the nail, bending moment of the nail, and the force mobilized on the nail grout surface in the axial direction decreased.

Fig. 13 Critical slide surfaces associated with number of reinforcement nails and factor of safety (FS)

Fig. 14 FS associated with number of nails under dry condition

Figure 19 shows the change in the FS with the nail diameter. The FSs of 0.92 using both cable and pile elements were calculated for 90 mm diameter nail. The FS calculated using the cable element did not vary with the nail diameter. However, because the resisting shear force mobilized on the cross-section of the nail and resisting bending moment of the nail increased, the FS calculated using the pile element increased substantially by 9% and 15% for 120 and 150 mm diameter nails, respectively, compared with that for the 90 mm diameter nail. Hence, the slope stability analysis using the pile element should be carried out for economic construction as a large diameter of nail for the type B system is used.

Fig. 15 Resisting axial and shear force on nail grout surface in axial direction using cable and pile element of nailing system for rock slopes: (a) Resisting axial force; (b) Resisting shear force mobilized on nail grout surface in axial direction

Fig. 16 Resisting forces using pile element of nailing system for rock slopes: (a) Resisting shear force mobilized on cross-section of nail; (b) Resisting normal force mobilized on nail grout surface in axial direction; (c) Resisting bending moment

Table 4 Resisting force of soil nail embedded in rock slopes

Fig.17 Resisting forces using pile element and 90 mm diameter nail embedded in rock slopes : (a) Resisting axial force; (b) Resisting shear force mobilized on nail grout surface in axial direction

Fig.18 Resisting forces using pile element for 90 mm diameter nail embedded in rock slopes: (a) Resisting axial force; (b) Resisting shear force mobilized on nail grout surface in axial direction; (c) Resisting normal force on nail grout surface in axial direction;    (d) Resisting bending moment

Fig.19 FS with respect to diameter of nail

6 Conclusions

1) The pull-out failure load was relatively high for the type B system and the large displacement for type A system occurred at the same pull-out load.

2) Most of resisting force against the pull-out load occurred at the top for the type A system, while it was well developed through the entire length of soil nails for the type B system.

3) The resisting axial forces using the pile element substantially increased compared with those using the cable element. The resisting shear forces on the nail grout surface in axial direction were well developed through the entire length of soil nails. The resisting shear forces mobilized on the cross-section of the nail and the bending moment of the nail were decreased.

4) The numerical results using the cable element showed that the axial forces of nail increased as the nail diameter increased. The numerical results using the pile element showed that the increment in the resisting axial force and shear force on the nail grout surface in axial direction was relatively small, but the increment in the resisting shear force mobilized on the cross-section of the nail, bending moment of the nail and the normal force mobilized on the nail grout surface in axial direction increased. As the nail diameter increased, a large portion of the driving forces was resisted by bending. This result suggested that bending played a key role in the stabilizing mechanism.

5) The factor of safety calculated from the slope stability analysis using the pile element was about 10% higher than that using the cable element. Numerical results for rock slopes showed that the factors of safety calculated were similar for both cable and pile elements, and the factors of safety substantially increased as the nail diameter increased.

Acknowledgements

This work was supported by Grant from INJE University, 2010. The financial support is gratefully acknowledged.

References

[1] MILLIGAN G W E, TEI K. The pull-out resistance of model soil nails [J]. Soils Found, 1998, 38(2): 179-190.

[2] HOSSAIN M A, YIN J H. Shear strength and dilative characteristics of an unsaturated compacted completely decomposed granite soil [J]. Canadian Geotechnical Journal, 2010, 47(10): 1112-1126

[3] JUNAIDEEN S M, THAM L G, LAWE K T, LEE C F, YUE Z Q. Laboratory study of soil-nail interaction in loose, completely decomposed granite [J]. Canadian Geotechnical Journal, 2004, 41(2): 274-286.

[4] MENKITI C O, LONG M. Performance of soil nails in Dublin glacial till [J]. Canadian Geotechnical Journal, 2008, 45(12): 1685-1698.

[5] PRADHAN B, THAM L G, YUE Z Q, JUNAIDEEN S M, LEE C F. Soil-nail pull-out interaction in loose fill materials [J]. International Journal of Geomechanics, ASCE, 2006, 6(4): 238-247.

[6] SU L J, CHAN T C F, SHIU Y K, CHEUNG T, YIN J H. Influence of degree of saturation on soil nail pull-out resistance in compacted completely decomposed granite fill [J]. Canadian Geotechnical Journal, 2007, 44(11): 1314-1328.

[7] TAN S A, OOI P H, PARK T S, CHEANG W L. Rapid pull-out test of soil nail [J]. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 2008, 134(9): 1327-1338.

[8] WEI W B, CHENG Y M, LI L. Three-dimensional slope failure analysis by the strength reduction and limit equilibrium methods [J]. Computer and Geotechnics, 2009, 36(1): 70-80.

[9] YIN J H, ZHOU W H. Influence of grouting pressure and overburden stress on the interface resistance of a soil nail [J]. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 2009, 135(9): 1198-1208.

[10] ZHENG H, SUN G, LIU D. A practical procedure for searching critical slip surfaces of slopes based on the strength reduction technique [J]. Computer and Geotechnics, 2009, 36(1): 1-5.

[11] CHEUK C Y, NG C W W, SUN H W. Numerical experiments of soil nails in loose fill slopes subjected to rainfall infiltration effects [J]. Computer and Geotechnics, 2005, 32(4): 290-303.

[12] CHU L M, YIN J H. A laboratory device to test the pull-out behavior of soil-nails [J]. Geotechnical Testing Journal, ASTM, 2005, 28(5): 1-15.

[13] HUANG M, JIA C Q. Strength reduction FEM in stability analysis of soil slopes subjected to transient unsaturated seepage [J]. Computer and Geotechnics, 2009, 36(1): 93-101.

[14] PATRA C R, BASUDHAR P K. Optimum design of nailed soil slopes [J]. Geotechnical and Geological Engineering, 2005, 23(3): 279-296.

[15] SU L J, YIN J H, ZHOU W H. Influences of overburden pressure and soil- dilation on soil nail pull-out resistance [J]. Computer and Geotechnics, 2010, 37(3): 555-564.

[16] ZHOU Y D, CHEUK C Y, THAM L G. Numerical modeling of soil nails in loose fill slope under surcharge loading [J]. Computer and Geotechnics, 2009, 36(5): 837-850.

[17] ZHOU W H, YIN J H. A simple mathematical model for soil nail and soil interaction analysis [J]. Computer and Geotechnics, 2008, 35(3): 479-488.

[18] GASSLER G. State of the art: In-situ technique of reinforced soil [C]// Proceedings of the International Conference on Reinforced Soil. Glasgow, 1990: 185-196.

[19] SCHLOSSER F. Behavior and design of soil nailing [C]// Proceedings of the Symposium on Recent Development in Ground Improvement Techniques. Bangkok, 1982: 399-413.

[20] JEWELL R A, PEDLEY M J. Analysis for soil reinforcement with bending stiffness [R]. Soil Mechanics Report No. 106/90, Oxford: Department of Engineering Science, University of Oxford, 1990.

[21] FHWA. Soil nailing field inspectors manual [R]. Publication No. FHWA-SA-93-068. 1994: 46-53

[22] Itasca consulting group inc. FLAC2D User manual (Version 4.0) [R]. Itasca Consulting Group Inc, 2002: 1-4.

[23] TERZAGHI, K, PECK R B, MESRI G. Soil mechanics in engineering practice [M]. New York: John Wiley & Sons, 1984.

(Edited by YANG Bing)

Received date: 2011-04-29; Accepted date: 2011-06-24

Corresponding author: Sang-Soo Jeon, Assistant Professor, PhD; Tel: +82-55-320-3651; Fax: +83-55-321-3410; E-mail: ssj@inje.ac.kr