Computers and Geotechnics 49 (2013) 253–263

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Computers and Geotechnics

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The effect of pressure-grouted nails on the stability of weathered soil slopes ⇑ Yongmin Kim a, Sungjune Lee b, Sangseom Jeong a, Jaehong Kim c, a Department of Civil Engineering, Yonsei University, Seoul 120-749, Republic of Korea b Department of Civil Engineering, Cheongju University, Cheongju 360-764, Republic of Korea c Department of Civil Engineering, Chonbuk National University, Jeonju 561-756, Republic of Korea article info abstract

Article history: Pressure-grouted soil nails have been increasingly used for stabilizing slopes. The pullout resistance of a Received 17 July 2012 soil nail is the main factor for reinforcing the slope stability. In this study, a two-dimensional axisymmet- Received in revised form 12 November 2012 ric finite element model is developed to simulate the pullout behavior of a pressure-grouted soil nail. This Accepted 6 December 2012 model is verified with field pullout tests result of a pressure-grouted soil nails by comparing with gravity- grouted soil nails. Based on the analysis, a three-dimensional finite element model is proposed for stabil- ity analysis of a slope reinforced with pressure-grouted soil nails using the reduction Keywords: method. A series of numerical slope stability analyses for a slope composed of weathered soil are per- Pressure-grouted soil nail formed to investigate the effects of grouting pressure on the slope stability and the behavior of the soil Pullout resistance Shear strength reduction method nails. Special attention is given to the installation effect of a pressure-grouted soil nails. It is found from Stability of reinforced slope the result of this study that the pressure-grouted soil nails increase the safety factor by fifty percent in a 3D finite element analysis slope by increasing the stiffness of the nailed slope system. Numerical analysis results confirm the fact that the pullout resistance of a soil nail is the main factor for stabilizing slopes rather than the shear resis- tance of the soil nail. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction shear resistance of the soil nails to resist the ground movement along the slope failure surface. Thus, many researchers have stud- Soil nails have been commonly used for slope stabilization by ied the pullout behavior of pressure-grouted soil nails through lab- enhancing the shear resistance of soil and/or the pullout resistance oratory or field tests. Main influencing factors on the fundamental at the interface between the and adjacent soil mass because mechanism of the pullout behavior of a soil nail were investigated of their low construction cost and simple installation procedure through laboratory model pullout tests [5,6,9,14,15,25,28–30]. The [4,18]. Although most of soil nails are installed without pressure pullout resistance of pressure-grouted soil nails was obtained from (gravity-grouted soil nails), pressure-grouted soil nails installed field pullout tests [17–19]. A numerical analysis method was also with a high grouting pressure (300–1000 kPa) have been increas- developed to investigate the effects of grouting pressure on the ingly used to improve slope stability in South Korea and other pullout resistance of a pressure-grouted soil nail [26]. However, places in the world. While pressure-grouted soil nail construction while these previous studies were mainly focused on the pullout requires additional equipment (such as a pump to place grout un- resistance of a pressure-grouted soil nail itself, few studies have der constant pressure and a packer system to attain the grouting been performed on the reinforcing effects of pressure-grouted soil pressure) and higher construction quality control than conven- nails for slope stability. tional soil nails, the pressure-grouted soil nail has many advanta- Some researchers performed numerical analyses for reinforced ges compared with the conventional gravity-grouted soil nail soil structures with gravity-grouted soil nails [21,23,24]. However, such as: (1) enhancement of grouting formation in a ; no information of numerical studies on reinforced slope with pres- (2) increase in diameter of a soil nail; (3) increase in shear strength sure-grouted soil nails is available. at the interface between the soil nail and the surrounding soil; and In order to investigate the reinforcing effects of pressure-grout- (4) reduction of the number of reinforcing soil nails [19]. ed soil nails for slope stability, a new numerical method for slope The pullout resistance of a pressure-grouted soil nail is the main stability analysis is developed. Special attention is given to the factor for designing a slope reinforced with soil nails rather than installation effect of a pressure-grouted soil nails using finite ele- ment (FE) analysis. Results of field pullout tests on pressure-grout- ed soil nails are compared with the analysis results for verification ⇑ Corresponding author. purpose. A series of numerical analyses for a slope without soil E-mail addresses: [email protected] (S. Jeong), [email protected] (J. Kim).

0266-352X/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compgeo.2012.12.003 254 Y. Kim et al. / Computers and Geotechnics 49 (2013) 253–263 nails, reinforced with gravity-grouted soil nails and reinforced with (Fig. 1). These dimensions were considered adequate to eliminate pressure-grouted soil nails are performed and their results are the influence of boundary effects on the soil nail performance. Both compared to investigate the effects of pressure-grouted soil nails the soil and nail are represented by eight-node, second-order qua- for slope stability. dratic element. A relatively fine mesh was used near the interface between the soil nail and the surrounding soil, and became coarser farther from the soil nail. 2. Numerical analysis for simulating pullout behavior of a The linear-elastic model for the soil nail and the Mohr–Coulomb pressure-grouted soil nails model using non-associated flow rule for the surrounding soil are used for the FE model. For a structural component, a soil nail is The pullout resistance of a pressure-grouted soil nail is the constructed with a deformed steel bar and cement grout and it is dominant design factor for a soil nail reinforced slope. Thus a modeled as an equivalent elastic solid cylinder due to high ulti- numerical method, which can rationally estimate the pullout resis- mate bond strength between them [12,31]. The equivalent elastic tance of a pressure-grouted soil nail, is needed for the slope stabil- modulus of a soil nail is determined by: ity analysis. In this study, a numerical analysis method is developed to simulate the pullout behavior of a pressure-grouted Eg Ag þ EsAs soil nail. The pressurized grouting procedure during its installation Eeq ¼ ð1Þ Ag þ As is considered in this numerical method.

where Eeq is the equivalent elastic modulus; Eg and Es are the elastic 2.1. Finite element model modulus of cement grout and deformed steel bar, respectively; Ag and As are the cross-sectional area of cement grout and deformed A two-dimensional (2D) axisymmetric condition is used to steel bar, respectively. model a soil nail as a rigid cylinder and the surrounding as The interface between the soil nail and the surrounding soil is concentric hollow cylinders. The commercial FE computer program described as perfectly rough, thus no relative movement between ABAQUS [1] is used in the numerical analysis. To verify the FE mod- the nail and the soil is assumed to take place. While this assump- el, a result available for pullout tests on pressure-grouted soil nails tion, which does not allow the interface slippage behavior, may re- is compared with that of numerical analyses. sult in overestimating the shear strength of the smooth interface, it In this study, the typical 2D axisymmetric FE model for a pres- has been widely adopted for simulating the shear behavior of the sure-grouted soil nail is shown in Fig. 1. The overall dimensions of rough interface. Therefore, shear failure assumed to occur in the the model boundaries comprise a width of fifty times the soil nail soil near the soil nail rather than at the interface between grout diameter (D) from the nail center and a total height (HT) equal to and soil. The shear behavior between grout and soil is simulated the nail length (LT) plus a further 1.0LT below the soil nail toe level. by the material behavior of the soil. The finite element mesh of The outer boundary of the model is fixed against displacements the soil adjacent the soil nail is dimensioned with thin-layer ele-

Nail Diameter (D) ) T =1/3L U Length Length (L Unbonded ) T ) T Nail Length(L =2/3L B Length Nail Bonded (L ) T Total Hight (H Hight Total

Soil T L

Total Width (WT=50D)

Fig. 1. 2D axisymmetric FE model for a pressure-grouted soil nail. Y. Kim et al. / Computers and Geotechnics 49 (2013) 253–263 255 ment (thickness of 4 mm) to simulate the thin localized shear zone stresses and displacement generated by the grouting pressure [3,7,10,16,20]. in the elements surrounding the borehole (Fig. 2d). Step 5: The soil nail elements are added in the borehole with the 2.2. Numerical procedure for simulating pressure-grouted soil nail model properties of the soil nail. The fixed boundary conditions installation employed by previous step are not changed (Fig. 2d). Step 6: The fixed boundary conditions for the borehole surface The installation procedure of a pressure-grouted soil nail is sim- are removed. This process causes the locked-in stresses and dis- ulated in the model described above to investigate the effects of placement to be released and transmitted to the soil nail ele- grouting pressure on its pullout behavior. In this study, seven steps ments (Fig. 2e). are applied to simulate the installation procedure of the pressure- Step 7: The pullout test process is simulated in this step (Fig. 2f). grouted soil nail (Fig. 2): On the other hand, the analysis procedure described above Step 1: The 2D axisymmetric FE mesh including the soil nail is excluding the pressure grouting simulation steps (step 3 and step generated with boundary conditions. Initial ground stresses 4) is used for the analysis of a gravity-grouted soil nail. are applied to the FE model (Fig. 2a). Step 2: The elements of the nail are removed to simulate the 2.3. Pullout behavior of pressure-grouted soil nails in weathered soil procedure of drilling a borehole (Fig. 2b). Step 3: The grouting pressure is applied to the borehole surface The FE analysis model described above is verified with the re- for the bonded zone while the borehole surface for the sults from the field pullout tests performed in two test sites in unbounded zone is fixed against displacements (Fig. 2c). South Korea (Pusan and Gyeonggi case). The analysis results are Step 4: The grouting pressure acting on the borehole surface is compared with those from the tests to investigate the pullout removed and replaced by fixed boundary condition to lock the behavior of the pressure-grouted soil nails.

initial ground stress

nail gravity remove fixed boundary nail element grouting pressure

soil

(a) Step 1 (b) Step 2 (c) Step 3-4

pullout

fixed boundary

remove fixed boundary add nail element

(d) Step 5 (e) Step 6 (f) Step 7

Fig. 2. Numerical analysis procedure for simulating construction process and pullout test for a pressure-grouted soil nail: (a) step 1, (b) step 2, (c) steps 3–4, (d) step 5, (e) step 6, and (f) step 7. 256 Y. Kim et al. / Computers and Geotechnics 49 (2013) 253–263

Pressure-Grouted Gravity-Grouted 250 Soil Nails Soil Nails Pressure-Grouted Gravity-Grouted This study(FEM) This study(FEM) Measured(average) Measured(average) 200

105mm 150 Unbonded Length=1m 105mm

100

Steel bar Pullout load, kN

50 Length=3m Weathered Soil

Bonded 0 Length=2m 0 1020304050 Vertical displacement, mm

Fig. 4. Comparisons of predicted and measured load–displacement relationships (Pusan case).

Fig. 3. Information about the soil and test soil nails (Pusan case). resistances) is obtained between the numerical analysis results 2.3.1. Pusan case and pullout test results for both types of soil nails. Four instrumented pressure-grouted soil nails and three instru- As expected, the pressure-grouted soil nail shows around 36% mented gravity-grouted soil nails were installed in the moderately higher pullout load than the gravity-grouted soil nail. to completely weathered soil [19]. Fig. 3 shows information about the soil and soil nails of Pusan case. All tested soil nails have a 2.3.2. Gyeonggi case diameter of 105 mm and a total length of 3 m including the unb- The load transfer characteristics of two instrumented pressure- onded length of 1 m and the bonded length of 2 m. The tested soil grouted soil nails installed in weathered soil are compared with nails were constructed with placing a deformed steel bar (30 mm those predicted by the proposed numerical analysis. Information in diameter) in the middle of a borehole and then with placing neat about the soil and soil nails of Gyeonggi case are shown in Fig. 5. cement grout (water-to-cement ratio of 0.42) under the grouting The test pressure-grouted soil nails of PNG1 and PNG2 have length pressure of 500 kPa. Material properties of the equivalent soil nail of 3 m and 4 m, respectively. Both of them have a same unbonded and weathered soil used for FE analysis are summarized in Tables 1 length of 1 m. These soil nails were constructed with same instal- and 2, where the following parameters are listed: diameter (D), lation procedure of the pressure-grouted soil nails in Pusan case as cross-sectional area (A), elastic modulus (E), Poisson’s ratio (m), fric- described above. Material properties of the weathered soil and soil tion angle (/), dilatancy angle (w), (c), unit weight (c). nails used for FE analysis are summarized in Table 3. Fig. 4 shows a comparison of load–displacement relationships Fig. 6 illustrates comparisons of predicted and measured load– determined from the pullout tests and those from the numerical displacement relationships for the two pressure-grouted soil nails. analysis for the pressure-grouted and gravity-grouted soil nails. Stiffer field load–displacement relationships compared with those Each average load–displacement relationship for the four pres- from numerical analyses are observed in this case but opposite re- sure-grouted soil nails and three gravity-grouted soil nails is used sults were shown in the previous Pusan case. This indicates the in these comparisons. Although the FE analysis results show stiffer limitation of the numerical analysis method used in this study. pull-out behavior than the measured, a reasonably good agreement The complicated pullout behavior of a pressure-grouted soil nail, of load–displacement relationships (especially ultimate pull-out which depends on types of soil, geometry of the irregular expanded

Table 1 Equivalent material properties of the soil nail used in numerical analysis.

Material properties Diameter D (m) Area, A (m2) Unit weight, c (kN/m3) Elastic modulus, E (MPa) Poisson’s ratio, m Steel bar Original property 0.029 0.00066 77.0 210,000 0.2 Grout 0.076 0.008 24.0 23,000 0.3 Soil nail Equivalent property – 28 37,250 0.29

Table 2 Material properties of the weathered soil and soil nail (Pusan case).

Material properties Elastic modulus, E (MPa) Poisson’s ratio, m angle, / (°) Dilatancy angle, w (°) Cohesion, c (kPa) Unit weight, c (kN/m3) Weathered soil 33.32 0.34 31 10.5 15.88 16.66 Y. Kim et al. / Computers and Geotechnics 49 (2013) 253–263 257

250 Pressure-Grouted Soil Nails Pressure-Grouted Soil Nails 200

105mm Unbonded Unbonded Length=1m Length=1m 150 105mm

100 Pullout load, kN

50 Nail Length=3m Nail Length=4m Weathered Soil This study(FEM) This study(FEM) Bonded Bonded Length=2m Length=3m Measured Measured 0 0 5 10 15 20 Vertical displacement, mm

Fig. 6. Comparisons of predicted and measured load–displacement relationships (Gyeonggi case). PNG1

PNG2 onded length of 3 m and a bonded length of 9 m. A 5.0 mm thick thin layer of material surrounding the nail is used to simulate Fig. 5. Information about the soil and test soil nails (Gyeonggi case). the thin localized shear zone. The plates of 2.0 2.0 0.5 m con- nected to the head of the soil nails are placed on the slope surface soil nail, types of grouting, cannot be simply simulated through the to help the soil nails mobilize their pullout resistance fully. The numerical method in an idealized condition. Although the pro- geometry and the boundary conditions applied to the 3D FE model posed numerical analysis method has such limitation, the general (Fig. 7) are selected considering the pressure grouting effects and trend of the measured pullout behavior of the soil nails (especially . An 8-node linear brick element with re- for the ultimate pullout resistance) is fairly predicted. Stiffer duced integration is used for modeling the 3D FE model. load–displacement relationship and lower pullout load for the The soil nails and plates are modeled as linear elastic solids. The Mohr–Coulomb model with non-associated flow rule is used for shorter pressure-grouted soil nail of PNG1 than the longer one of the weathered soil. The material properties used in the 3D FE mod- PNG2 are obtained from the comparisons as shown in Fig. 6. el are summarized in Table 4.

3. Slope stability analysis for a reinforced slope with pressure- 3.2. Shear strength reduction method grouted soil nails

To calculate the safety factor of a slope defined in the shear A 3D FE model for the slope stability analysis of a slope rein- strength reduction method which was proposed as early as 1975 forced with pressure-grouted soil nails is proposed to obtain the by Zienkiewicz et al. [32], a series of slope stability analyses are safety factor of the reinforced slope and to investigate their rein- performed with the reduced shear strength parameters c0 and forcing effects on the slope stability. The numerical technique for trial /0 defined as follows: simulating pullout behavior of soil nails described in previous sec- trial tion is implemented in this 3D FE model. The shear strength reduc- 1 c0 c0 2 tion method is used for the slope stability analysis to obtain the trial ¼ trial ð Þ F safety factor of a slope.  0 1 0 3.1. 3D FE model of a reinforce slope with pressure-grouted soil nails utrial ¼ arctan tan / ð3Þ Ftrial A 3D FE model to simulate the slope stability analysis for a rein- where c0 and /0 are real shear strength parameters and Ftrial is a trial forced slope reinforced with pressure-grouted soil nails using ABA- safety factor. QUS is developed in this study. The 3D FE mesh used in analysis is The essence of the finite element method with shear strength shown in Fig. 7. The slope composed of weathered soil has an angle reduction method is the reduction of the soil shear strength of 60° to the horizontal plane, a slope height of 10 m, and a slope parameters until the slope fails. Usually, initial Ftrial is set to be suf- width of 3 m. The soil nails installed vertically to the slope surface ficiently small so as to guarantee that the system is stable. Then the has a diameter of 105 mm and a total length of 12 m with an unb- value of Ftrial is increased by Finc values until the slope fails. After

Table 3 Material properties of the weathered soil and soil nail (Gyeonggi case).

Material properties Elastic modulus, E (MPa) Poisson’s ratio, m Friction angle, / (°) Dilatancy angle, w (°) Cohesion, c (kPa) Unit weight, c (kN/m3) Weathered soil 34.37 0.30 42 5 6.0 17.67 258 Y. Kim et al. / Computers and Geotechnics 49 (2013) 253–263

20m

Plate

20m

Unbonded Length=3m 25m

Bonded Soil Nail Length=9m 15m

(a) Plan view (X-Z direction)

3m

Soil Nail

(b) 3D view (X-Y-Z direction)

Fig. 7. 3D FE mesh for a slope reinforced with soil nails: (a) plan view (X–Z direction) and (b) 3D view (X–Y–Z direction).

Table 4 Material properties for the 3D FE model for slope stability analysis.

Material properties Elastic modulus, E (MPa) Poisson’s ratio, m Friction angle, / (°) Dilatancy angle, w (°) Cohesion, c (kPa) Unit weight, c (kN/m3) Weathered soil 100 0.30 25 0 20.0 20.0

the slope fails, the Fstart is replaced by the previous Flow and Finc is is less than user-specified tolerance (e). Fig. 8 shows the flowchart reduced by 1/5. Then the same procedure is repeated until the Finc of the procedure to calculate a safety factor [27]. This iterative pro- Y. Kim et al. / Computers and Geotechnics 49 (2013) 253–263 259

Step 2: The natural slope is modeled by removing the plate ele- ments and by using soil properties for the soil nail elements. All boundaries of the model are fixed against displacements. Initial ground stresses are applied to the 3D FE model (Fig. 9b). Step 3: The elements for the soil nails are removed to simulate the drilling process, then grouting pressures are applied at the boundaries of the for the bonded zone while the boundaries of boreholes for the unbounded zone are fixed against displacements (Fig. 9c). Step 4: The boundaries of the borehole for the bonded zone are fixed against displacements after finishing the pressure grout- ing process (Fig. 9d). Step 5: The elements for the plates and the soil nails are added with their material properties while the displacement bound- aries for the shafts of the soil nails remain fixed (Fig. 9e). Step 6: The displacement boundaries for the shafts of the soil nails are removed to release and transmit the locked-in stresses and displacement in the surrounding soil to the soil nail ele- ments (Fig. 9f). Step 7: The slope stability analysis is performed by applying the gravity forces with unfixed boundaries for the upper sides of the model (Fig. 9g).

On the other hand, same analysis procedure except the steps for the pressure grouting is used for the stability analysis of a slope reinforced with gravity-grouted soil nails.

3.4. Reinforcing effects of pressure-grouted soils on slope stability

In order to investigate the reinforcing effects of the pressure- grouted soil nails, numerical slope stability analyses for a slope are performed under three different conditions: (1) natural slope without any reinforcement; (2) reinforced slope with gravity-gro- uted soil nails; and (3) reinforced slope with pressure-grouted soil nails. Fig. 10 shows results of stability analyses for a slope under these three different reinforcement conditions. Safety factors for the natural slope, the gravity-grouted soil nail reinforced slope Fig. 8. Flowchart for calculation of a safety factor. and the pressure-grouted soil nail reinforced slope are 1.15, 1.55 and 1.72 respectively. Based on the analysis results, using pres- sure-grouted soil nails exhibits obvious reinforcing effect for the cedure is based on the incremental search method. This final value slope stability with increasing the safety factor by around fifty of Flow, by definition, is identical to the one in limit equilibrium and eleven percent compared with safety factors for natural slope analysis. The finite element method with shear strength reduction and gravity-grouted reinforced slope, respectively. technique used in slope stability analysis relies strongly on the Fig. 11 shows developed slope failure surfaces for the gravity- determination of global instability of soil slopes, i.e. definition of grouted and pressure-grouted soil nails from the maximum plastic a failure [11]. Generally, the failure of slope is defined as: (1) swell- strain distribution plots. The slope reinforced with pressure-grout- ing of slope surface [22]; (2) reaching ultimate shear stress of fail- ed soil nails exhibits expanded failure surface from the slope sur- ure surface [8]; and (3) non-convergence of solutions [33]. In this face compared with that for the gravity-grouted reinforced slope. study, the slope failure is defined by non-convergence of solution, This expanded failure surface was also observed in the laboratory and the failure surface of slope is presumed by plotting the ele- load tests on the model soil nail reinforced per- ments where maximum plastic strain occurs. The analysis results formed by Kim et al. [13]. It was found from their tests that the fail- are represented by relationship between dimensionless displace- ure surface expanded toward the backfill as the stiffness of the wall 2 ment (Esdmax/cH ) and factor of safety, where Es is the Young’s increased. Therefore, it is presumed that the grouting pressure may modulus of soil, dmax is the maximum displacement of the slope, increase the stiffness of the reinforced slope system. H is the slope height [33]. 3.5. Behavior of a pressure-grouted soil nail installed in the reinforced 3.3. Numerical procedure of the stability analysis slope

Slope stability analysis including the installation process of The axial and shear loads developed along the soil nails are ob- pressure-grouted soil nails are performed based on the 3D FE mod- tained from the previous analysis results to investigate the rein- el described above to obtain the safety factor for a reinforced slope. forcing effects of soil nails for slope stability. Fig. 12 illustrates The following seven steps are required for the slope stability anal- the distributions of axial loads and shear loads developed along ysis (Fig. 9): the lower soil nails for both gravity-grouted and pressure-grouted soil nail reinforced slopes at the limit state. It is noted that higher Step 1: The 3D FE mesh including the soil nail and the plate is axial loads distribution is observed for the pressure-grouted soil generated (Fig. 9a). nail than the gravity-grouted soil nail, whereas the shear loads 260 Y. Kim et al. / Computers and Geotechnics 49 (2013) 253–263

Initial ground stress remove plate elements

modeled with soil properties

(a) Step 1 (b) Step 2

fixed boundaies

grouting pressure

remove soil nail elements fixed boundaries

(c) Step 3 (d) Step 4

add plate elements fixed boundaries

add soil nail elements remove fixed boundaries

(e) Step 5 (f) Step 6

gravity

(g) Step 7

Fig. 9. Numerical procedure of slope stability analysis for a slope reinforced with pressuregrouted soil nails: (a) step 1, (b) step 2, (c) step 3, (d) step 4, (e) step 5, (f) step 6, and (g) step 7. Y. Kim et al. / Computers and Geotechnics 49 (2013) 253–263 261

3 140 Type of Reinforcement Natural Slope FS=1.72 120 2.5 Gravity-Grouted Soil Nails Maximum axial load=113kN Pressure-Grouted Soil Nails 100 2 Maximum axial load=85kN 80 FS=1.55 1.5 60 Axial load, kN 1 FS=1.15 40

0.5 20 Type of Soil Nails Pressure-Grouted Gravity-Grouted 0 0 0 0.4 0.8 1.2 1.6 2 02468101214 Safety factor Distance from the head of soil nail, m (a) Axial loads Fig. 10. Safety factors for a slope under three different reinforcement conditions.

0.12 Type of Soil Nails developed along both types of soil nails are very low and can be Pressure-Grouted ignored. 0.1 Gravity-Grouted Basically, the axial loads may develop at the soil–grout interface in the form of shear stresses around the soil nail perimeter. These shear stresses are represented by the axial loads within the soil 0.08 nail. Since the shear stresses act along the circumferential area of the soil nail, the axial loads at the ends of the soil nails must be 0.06 zero. And the maximum axial loads were developed at the upper part of soil nail (2–4 m from the soil nail head) where shear stres- ses at the soil–grout interface reverse directions. The location of Shear load, kN 0.04 maximum axial loads may coincide with the divide between the active soil wedge and the stationary soil mass. However, the actual magnitude and location of maximum axial loads varies with the 0.02 soil deformation pattern, construction sequence, and required reinforcement [2]. 0 Additional slope stability analyses are performed for three dif- 02468101214 ferent slope angles of 45°,60° and 80° to investigate the effects Distance from the head of soil nail, m of slope angle on the behavior of soil nails. Fig. 13 shows the distri- butions of axial and shear loads developed along the soil nails with (b) Shear loads different slope angles. The distribution of axial resistance increases Fig. 12. Distribution of loads developed along the soil nail for two different types of with increase in the slope angle. Changes in the distributions of soil nails: (a) axial loads and (b) shear loads. shear loads with different slope angles are negligible and the over- all values of shear loads are very low and can be ignored. Therefore, as shown in Figs. 12 and 13, it is shown that the pullout resistance rather than shear resistance along the failure surface, regardless of a soil nails is the main factor for reinforcing the slope stability of the nail location and angle of soil nail.

Failure Surface (Gravity-Grouted Failure Surface Soil Nail) (Gravity-Grouted Soil Nail) Failure Surface (Pressure-Grouted Soil Nail)

Soil Nail Effect of grouting preesure

(a) Gravity-grouted soil nails (b) Pressure-grouted soil nails

Fig. 11. Failure surfaces for a reinforced slope with (a) gravity-grouted soil nails and (b) pressure-grouted soil nails from the maximum plastic strain distribution plots. 262 Y. Kim et al. / Computers and Geotechnics 49 (2013) 253–263

140 sure-grouted soil nails. Moreover, the load–displacement Slope=80o behavior with different length of pressure-grouted soil nail is o 120 Slope=60 well predicted by the proposed 2D FE model. Slope=45o 2. The pressure-grouted soil nails exhibits obvious reinforcing effects for the slope stability with increasing the safety factor 100 by around fifty and eleven percent compared with safety factors for natural slope and gravity-grouted reinforced slope, respec- 80 tively. The slope reinforced with pressure-grouted soil nails exhibits expanded failure surface from the slope surface com- 60 pared with that for the gravity-grouted reinforced slope. The

Axial load, kN expanded failure surface can be explained by the increased stiffness of the reinforced slope system due to grouting 40 pressure. 3. Higher pullout resistance distribution is observed for the pres- 20 sure-grouted soil nail than the gravity-grouted soil nail. The shear resistance developed along both types of soil nails are 0 very low and can be ignored. The distribution of pullout resis- 02468101214 tance increases with increase in the slope angle while the neg- Distance from the head of soil nail, m ligibly low shear resistance is developed along the soil nail (a) Axial loads without reference to the slope angle. These analysis results con- firm the fact that the pullout resistance of a soil nail is the main 0.2 factor for stabilizing slopes.

0 Acknowledgments

This work was supported by the National Research of Korea (NRF) grant funded by the Korea government (MEST) (No. -0.2 2011-0030842).

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