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    The effect of pressure-grouted soil 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 Koreab Department of Civil Engineering, Cheongju University, Cheongju 360-764, Republic of Koreac Department of Civil Engineering, Chonbuk National University, Jeonju 561-756, Republic of Korea

    a r t i c l e i n f o

     Article history:

    Received 17 July 2012

    Received in revised form12 November 2012

    Accepted 6 December 2012

    Available online 16 January 2013

    Keywords:

    Pressure-grouted soil nail

    Pullout resistance

    Shear strength reduction method

    Stability of reinforced slope

    3D finite element analysis

    a b s t r a c t

    Pressure-grouted soil nails have been increasingly used for stabilizing slopes. The pullout resistance of a

    soil nail is the main factor for reinforcing the slope stability. In this study, a two-dimensional axisymmet-

    ric finite element model is developed to simulate thepullout behavior of a pressure-grouted soil nail. This

    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 shear strength reduction

    method. A series of numerical slope stability analyses for a slope composed of weathered soil are per-

    formed to investigate the effects of grouting pressure on the slope stability and the behavior of the soil

    nails. Special attention is given to the installation effect of a pressure-grouted soil nails. It is found from

    the result of this study that the pressure-grouted soil nails increase the safety factor by fifty percent in a

    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 themain factor for stabilizing slopes rather than the shear resis-

    tance of the soil nail.

     2012 Elsevier Ltd. All rights reserved.

    1. Introduction

    Soil nails have been commonly used for slope stabilization by

    enhancing the shear resistance of soil and/or the pullout resistance

    at the interface between the grout and adjacent soil mass because

    of their low construction cost and simple installation procedure

    [4,18]. Although most of soil nails are installed without pressure

    (gravity-grouted soil nails), pressure-grouted soil nails installed

    with a high grouting pressure (300–1000 kPa) have been increas-

    ingly used to improve slope stability in South Korea and other

    places in the world. While pressure-grouted soil nail construction

    requires additional equipment (such as a pump to place grout un-

    der constant pressure and a packer system to attain the groutingpressure) and higher construction quality control than conven-

    tional soil nails, the pressure-grouted soil nail has many advanta-

    ges compared with the conventional gravity-grouted soil nail

    such as: (1) enhancement of grouting formation in a borehole;

    (2) increase in diameter of a soil nail; (3) increase in shear strength

    at the interface between the soil nail and the surrounding soil; and

    (4) reduction of the number of reinforcing soil nails  [19].

    The pullout resistance of a pressure-grouted soil nail is the main

    factor for designing a slope reinforced with soil nails rather than

    shear resistance of the soil nails to resist the ground movement

    along the slope failure surface. Thus, many researchers have stud-

    ied the pullout behavior of pressure-grouted soil nails through lab-

    oratory or field tests. Main influencing factors on the fundamental

    mechanism of the pullout behavior of a soil nail were investigated

    through laboratory model pullout tests  [5,6,9,14,15,25,28–30]. The

    pullout resistance of pressure-grouted soil nails was obtained from

    field pullout tests [17–19]. A numerical analysis method was also

    developed to investigate the effects of grouting pressure on the

    pullout resistance of a pressure-grouted soil nail  [26]. However,

    while these previous studies were mainly focused on the pullout

    resistance of a pressure-grouted soil nail itself, few studies have

    been performed on the reinforcing effects of pressure-grouted soilnails for slope stability.

    Some researchers performed numerical analyses for reinforced

    soil structures with gravity-grouted soil nails   [21,23,24]. However,

    no information of numerical studies on reinforced slope with pres-

    sure-grouted soil nails is available.

    In order to investigate the reinforcing effects of pressure-grout-

    ed soil nails for slope stability, a new numerical method for slope

    stability analysis is developed. Special attention is given to the

    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

    purpose. A series of numerical analyses for a slope without soil

    0266-352X/$ - see front matter     2012 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.compgeo.2012.12.003

    ⇑ Corresponding author.

    E-mail addresses: [email protected] (S. Jeong), [email protected] (J. Kim).

    Computers and Geotechnics 49 (2013) 253–263

    Contents lists available at SciVerse ScienceDirect

    Computers and Geotechnics

    j o u r n a l h o m e p a g e :   w w w . e l s e v i e r . c o m / l o c a t e / c o m p g e o

    http://dx.doi.org/10.1016/j.compgeo.2012.12.003mailto:[email protected]:[email protected]://dx.doi.org/10.1016/j.compgeo.2012.12.003http://www.sciencedirect.com/science/journal/0266352Xhttp://www.elsevier.com/locate/compgeohttp://www.elsevier.com/locate/compgeohttp://www.sciencedirect.com/science/journal/0266352Xhttp://dx.doi.org/10.1016/j.compgeo.2012.12.003mailto:[email protected]:[email protected]://dx.doi.org/10.1016/j.compgeo.2012.12.003http://crossmark.dyndns.org/dialog/?doi=10.1016/j.compgeo.2012.12.003&domain=pdf

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    ment (thickness of 4 mm) to simulate the thin localized shear zone

    [3,7,10,16,20].

     2.2. Numerical procedure for simulating pressure-grouted soil nail

    installation

    The installation procedure of a pressure-grouted soil nail is sim-

    ulated in the model described above to investigate the effects of 

    grouting pressure on its pullout behavior. In this study, seven steps

    are applied to simulate the installation procedure of the pressure-

    grouted soil nail (Fig. 2):

    Step 1: The 2D axisymmetric FE mesh including the soil nail is

    generated with boundary conditions. Initial ground stresses

    are applied to the FE model (Fig. 2a).

    Step 2: The elements of the nail are removed to simulate the

    procedure of drilling a borehole (Fig. 2b).

    Step 3: The grouting pressure is applied to the borehole surface

    for the bonded zone while the borehole surface for the

    unbounded zone is fixed against displacements (Fig. 2c).

    Step 4: The grouting pressure acting on the borehole surface is

    removed and replaced by fixed boundary condition to lock the

    stresses and displacement generated by the grouting pressure

    in the elements surrounding the borehole (Fig. 2d).

    Step 5: The soil nail elements are added in the borehole with the

    model properties of the soil nail. The fixed boundary conditions

    employed by previous step are not changed (Fig. 2d).

    Step 6 : The fixed boundary conditions for the borehole surface

    are removed. This process causes the locked-in stresses and dis-

    placement to be released and transmitted to the soil nail ele-

    ments (Fig. 2e).

    Step 7 : The pullout test process is simulated in this step (Fig. 2f).

    On the other hand, the analysis procedure described above

    excluding the pressure grouting simulation steps (step 3 and step

    4) is used for the analysis of a gravity-grouted soil nail.

     2.3. Pullout behavior of pressure-grouted soil nails in weathered soil

    The FE analysis model described above is verified with the re-

    sults from the field pullout tests performed in two test sites in

    South Korea (Pusan and Gyeonggi case). The analysis results are

    compared with those from the tests to investigate the pullout

    behavior of the pressure-grouted soil nails.

    nail

    soil

    gravity

    initial ground stress

    remove

    nail element

    grouting pressure

    fixed boundary

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

    fixed boundary

    add nail element

    remove

    fixed boundary

    pullout

    (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.

    Y. Kim et al. / Computers and Geotechnics 49 (2013) 253–263   255

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     2.3.1. Pusan case

    Four instrumented pressure-grouted soil nails and three instru-

    mented gravity-grouted soil nails were installed in the moderately

    to completely weathered soil [19]. Fig. 3 shows information about

    the soil and soil nails of Pusan case. All tested soil nails have a

    diameter of 105 mm and a total length of 3 m including the unb-

    onded length of 1 m and the bonded length of 2 m. The tested soil

    nails were constructed with placing a deformed steel bar (30 mm

    in diameter) in the middle of a borehole and then with placing neat

    cement grout (water-to-cement ratio of 0.42) under the grouting

    pressure of 500 kPa. Material properties of the equivalent soil nail

    and weathered soil used for FE analysis are summarized in Tables 1and 2, where the following parameters are listed: diameter (D),

    cross-sectional area ( A), elastic modulus (E ), Poisson’s ratio (m), fric-tion angle (/), dilatancy angle (w), cohesion (c ), unit weight (c).

    Fig. 4 shows a comparison of load–displacement relationships

    determined from the pullout tests and those from the numerical

    analysis for the pressure-grouted and gravity-grouted soil nails.

    Each average load–displacement relationship for the four pres-

    sure-grouted soil nails and three gravity-grouted soil nails is used

    in these comparisons. Although the FE analysis results show stiffer

    pull-out behavior than the measured, a reasonably good agreement

    of load–displacement relationships (especially ultimate pull-out

    resistances) is obtained between the numerical analysis results

    and pullout test results for both types of soil nails.

    As expected, the pressure-grouted soil nail shows around 36%

    higher pullout load than the gravity-grouted soil nail.

     2.3.2. Gyeonggi case

    The load transfer characteristics of two instrumented pressure-

    grouted soil nails installed in weathered soil are compared with

    those predicted by the proposed numerical analysis. Information

    about the soil and soil nails of Gyeonggi case are shown in Fig. 5.

    The test pressure-grouted soil nails of PNG1 and PNG2 have length

    of 3 m and 4 m, respectively. Both of them have a same unbonded

    length of 1 m. These soil nails were constructed with same instal-lation procedure of the pressure-grouted soil nails in Pusan case as

    described above. Material properties of the weathered soil and soil

    nails used for FE analysis are summarized in Table 3.

    Fig. 6 illustrates comparisons of predicted and measured load–

    displacement relationships for the two pressure-grouted soil nails.

    Stiffer field load–displacement relationships compared with those

    from numerical analyses are observed in this case but opposite re-

    sults were shown in the previous Pusan case. This indicates the

    limitation of the numerical analysis method used in this study.

    The complicated pullout behavior of a pressure-grouted soil nail,

    which depends on types of soil, geometry of the irregular expanded

    105mm

    Weathered Soil

    Pressure-Grouted

    Soil Nails

    Gravity-Grouted

    Soil Nails

    Steel bar 

    105mm

       U  n   b  o  n   d  e   d

       L  e

      n  g   t   h  =   1  m

       B  o  n   d  e   d

       L  e  n  g   t   h  =   2  m

       L  e  n  g   t   h  =   3  m

    Fig. 3.  Information about the soil and test soil nails (Pusan case).

     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   Friction 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

    0 10 20 30 40 50

    Vertical displacement, mm

    0

    50

    100

    150

    200

    250

       P  u   l   l  o  u   t   l  o  a

       d ,

       k   N

    Pressure-GroutedThis study(FEM)

    Measured(average)

    Gravity-GroutedThis study(FEM)

    Measured(average)

    Fig. 4.   Comparisons of predicted and measured load–displacement relationships

    (Pusan case).

    256   Y. Kim et al. / Computers and Geotechnics 49 (2013) 253–263

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    soil nail, types of grouting, cannot be simply simulated through the

    numerical method in an idealized condition. Although the pro-

    posed numerical analysis method has such limitation, the general

    trend of the measured pullout behavior of the soil nails (especially

    for the ultimate pullout resistance) is fairly well predicted. Stiffer

    load–displacement relationship and lower pullout load for the

    shorter pressure-grouted soil nail of PNG1 than the longer one of 

    PNG2 are obtained from the comparisons as shown in Fig. 6.

    3. Slope stability analysis for a reinforced slope with pressure-

    grouted soil nails

    A 3D FE model for the slope stability analysis of a slope rein-

    forced with pressure-grouted soil nails is proposed to obtain the

    safety factor of the reinforced slope and to investigate their rein-

    forcing effects on the slope stability. The numerical technique for

    simulating pullout behavior of soil nails described in previous sec-

    tion is implemented in this 3D FE model. The shear strength reduc-

    tion method is used for the slope stability analysis to obtain the

    safety factor of a slope.

     3.1. 3D FE model of a reinforce slope with pressure-grouted soil nails

    A 3D FE model to simulate the slope stability analysis for a rein-

    forced slope reinforced with pressure-grouted soil nails using ABA-

    QUS is developed in this study. The 3D FE mesh used in analysis is

    shown in Fig. 7. The slope composed of weathered soil has an angle

    of 60  to the horizontal plane, a slope height of 10 m, and a slope

    width of 3 m. The soil nails installed vertically to the slope surface

    has a diameter of 105 mm and a total length of 12 m with an unb-

    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

    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

    to help the soil nails mobilize their pullout resistance fully. The

    geometry and the boundary conditions applied to the 3D FE model

    (Fig. 7) are selected considering the pressure grouting effects and

    slope stability analysis. An 8-node linear brick element with re-

    duced integration is used for modeling the 3D FE model.

    The soil nails and plates are modeled as linear elastic solids. The

    Mohr–Coulomb model with non-associated flow rule is used for

    the weathered soil. The material properties used in the 3D FE mod-

    el are summarized in Table 4.

     3.2. Shear strength reduction method

    To calculate the safety factor of a slope defined in the shear

    strength reduction method which was proposed as early as 1975

    by Zienkiewicz et al.   [32], a series of slope stability analyses are

    performed with the reduced shear strength parameters   c 0trial   and

    /0trial  defined as follows:

    c 0trial ¼  1

    F trial c 0 ð2Þ

    u0trial ¼  arctan  1

    trial  tan/0

      ð3Þ

    where c 0 and/0 are real shear strength parameters and F trial is a trial

    safety factor.

    The essence of the finite element method with shear strength

    reduction method is the reduction of the soil shear strength

    parameters until the slope fails. Usually, initial F trial is setto be suf-

    ficiently small so as to guarantee that the systemis stable. Then the

    value of  F trial is increased by  F inc  values until the slope fails. After

    Pressure-Grouted

    Soil Nails

    105mm

    105mm

       U  n   b  o  n   d  e   d

       L  e  n  g   t   h  =   1  m

       B  o  n   d  e   d

       L  e  n  g   t   h  =   2  m

       U  n   b  o  n   d  e   d

       L  e  n  g   t   h  =   1  m

       B  o  n   d  e   d

       L  e  n  g   t   h  =   3  m

    PNG

    1

    PNG2

    Weathered Soil

    Fig. 5.  Information about the soil and test soil nails (Gyeonggi case).

     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

    0 5 10 15 20

    Vertical displacement, mm

    0

    50

    100

    150

    200

    250

       P  u   l   l  o  u   t   l  o  a

       d ,

       k   N

    Nail Length=3mThis study(FEM)

    Measured

    Nail Length=4mThis study(FEM)

    Measured

    Pressure-Grouted Soil Nails

    Fig. 6.   Comparisons of predicted and measured load–displacement relationships

    (Gyeonggi case).

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    the slope fails, the F start  is replaced by the previous  F low and F inc  is

    reduced by 1/5. Then the same procedure is repeated until the F inc is less than user-specified tolerance (e). Fig. 8 shows the flowchartof the procedure to calculate a safety factor [27]. This iterative pro-

    Soil Nail

         1     5    m

         2     5    m

    20m

    20m

    Plate

    Unbonded

    Length=3m

    Bonded

    Length=9m

    (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

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    cedure is based on the incremental search method. This final value

    of  F low, by definition, is identical to the one in limit equilibrium

    analysis. The finite element method with shear strength reduction

    technique used in slope stability analysis relies strongly on the

    determination of global instability of soil slopes, i.e. definition of 

    a failure [11]. Generally, the failure of slope is defined as: (1) swell-

    ing of slope surface [22]; (2) reaching ultimate shear stress of fail-

    ure surface [8]; and (3) non-convergence of solutions  [33]. In this

    study, the slope failure is defined by non-convergence of solution,

    and the failure surface of slope is presumed by plotting the ele-

    ments where maximum plastic strain occurs. The analysis resultsare represented by relationship between dimensionless displace-

    ment (E sdmax/cH 2) and factor of safety, where   E s   is the Young’s

    modulus of soil,  dmax   is the maximum displacement of the slope,

    H   is the slope height [33].

     3.3. Numerical procedure of the stability analysis

    Slope stability analysis including the installation process of 

    pressure-grouted soil nails are performed based on the 3D FE mod-

    el described above to obtain the safety factor for a reinforced slope.

    The following seven steps are required for the slope stability anal-

    ysis (Fig. 9):

    Step 1: The 3D FE mesh including the soil nail and the plate isgenerated (Fig. 9a).

    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 boreholes 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 slopeand 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

    slope stability with increasing the safety factor by around fifty

    and eleven percent compared with safety factors for natural slope

    and gravity-grouted reinforced slope, respectively.

    Fig. 11 shows developed slope failure surfaces for the gravity-

    grouted and pressure-grouted soil nails from the maximum plastic

    strain distribution plots. The slope reinforced with pressure-grout-

    ed soil nails exhibits expanded failure surface from the slope sur-

    face compared with that for the gravity-grouted reinforced slope.

    This expanded failure surface was also observed in the laboratory

    load tests on the model soil nail reinforced retaining wall per-

    formed by Kim et al. [13]. It was found fromtheir tests that the fail-ure surface expanded toward the backfill as the stiffness of the wall

    increased. Therefore, it is presumed that the grouting pressure may

    increase the stiffness of the reinforced slope system.

     3.5. Behavior of a pressure-grouted soil nail installed in the reinforced

    slope

    The axial and shear loads developed along the soil nails are ob-

    tained from the previous analysis results to investigate the rein-

    forcing effects of soil nails for slope stability.   Fig. 12 illustrates

    the distributions of axial loads and shear loads developed along

    the lower soil nails for both gravity-grouted and pressure-grouted

    soil nail reinforced slopes at the limit state. It is noted that higher

    axial loads distribution is observed for the pressure-grouted soilnail than the gravity-grouted soil nail, whereas the shear loads

    Fig. 8.  Flowchart for calculation of a safety factor.

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    (a) Step 1

    modeled with soil properties

    remove plate elements

    Initial ground stress

    (b) Step 2

    grouting pressure

    remove soil nail elements

    fixed boundaies

    (c) Step 3

    fixed boundaries

    (d) Step 4

    add plate elements

    add soil nail elements

    fixed boundaries

    (e) Step 5

    remove fixed boundaries

    (f) Step 6

    gravity

    (g) Step 7

    Fig. 9.   Numerical procedureof slope stabilityanalysis for a slope reinforcedwith pressuregroutedsoil nails: (a) step 1, (b)step 2, (c)step 3, (d)step 4, (e)step 5, (f) step 6, and

    (g) step 7.

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    developed along both types of soil nails are very low and can be

    ignored.

    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

    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

    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 

    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

    soil deformation pattern, construction sequence, and requiredreinforcement [2].

    Additional slope stability analyses are performed for three dif-

    ferent slope angles of 45, 60   and 80  to investigate the effects

    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

    different slope angles. The distribution of axial resistance increases

    with increase in the slope angle. Changes in the distributions of 

    shear loads with different slope angles are negligible and the over-

    all values of shear loads are very lowand can be ignored. Therefore,

    as shown in Figs. 12 and 13, it is shown that the pullout resistance

    of a soil nails is the main factor for reinforcing the slope stability

    rather than shear resistance along the failure surface, regardless

    of the nail location and angle of soil nail.

    0 0.4 0.8 1.2 1.6 2

    Safety factor 

    0

    0.5

    1

    1.5

    2

    2.5

    3

    Type of ReinforcementNatural Slope

    Gravity-Grouted Soil Nails

    Pressure-Grouted Soil Nails

    FS=1.15

    FS=1.55

    FS=1.72

    Fig. 10.   Safety factors for a slope under three different reinforcement conditions.

    Failure Surface

    (Gravity-Grouted

    Soil Nail)

    Soil Nail

    (a) Gravity-grouted soil nails

    Failure Surface

    (Pressure-Grouted

    Soil Nail)

    Effect of grouting preesure

    Failure Surface

    (Gravity-Grouted

    Soil Nail)

    (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.

    0 2 4 6 8 10 12 14

    Distance from the head of soil nail, m

    0

    20

    40

    60

    80

    100

    120

    140

       A  x   i  a   l   l  o  a   d

     ,   k   N

    Type of Soil NailsPressure-Grouted

    Gravity-Grouted

    Maximum axial load=113kN

    Maximum axial load=85kN

    (a) Axial loads

    0 2 4 6 8 10 12 14

    Distance from the head of soil nail, m

    0

    0.02

    0.04

    0.06

    0.08

    0.1

    0.12

       S   h  e  a  r   l  o  a   d ,

       k   N

    Type of Soil NailsPressure-Grouted

    Gravity-Grouted

    (b) Shear loads

    Fig. 12.   Distribution of loads developedalong thesoil nail for twodifferenttypes of 

    soil nails: (a) axial loads and (b) shear loads.

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    4. Conclusions

    In this study, a 2D axisymmetric FE model is developed to sim-

    ulate the pullout behavior of a pressure-grouted soil nails. The sim-

    ulation of the pressure grouting process is included in the FEmodel. This numerical model and analysis result is favorably veri-

    fied by field pullout test results. Based on the analysis, a 3D FE

    model for stability analysis of a slope reinforced with pressure-gro-

    uted soil nails is proposed implementing the numerical analysis

    technique used in the 2D FE model using the shear strength reduc-

    tion method. A series of numerical slope stability analyses are per-

    formed for three different types of slopes to investigate the effects

    of grouting pressure on the slope stability and the behavior of the

    soil nails at the limit state. Based on the findings of this study, the

    following conclusions can be drawn:

    1. Based on the analysis results from the soil nail pullout simula-

    tions, a reasonably good agreement of load–displacement rela-

    tionships is obtained between the numerical analysis resultsand field pullout test results for both gravity-grouted and pres-

    sure-grouted soil nails. Moreover, the load–displacement

    behavior with different length of pressure-grouted soil nail is

    well predicted by the proposed 2D FE model.

    2. The pressure-grouted soil nails exhibits obvious reinforcing

    effects for the slope stability with increasing the safety factor

    by around fifty and eleven percent compared with safety factors

    for natural slope and gravity-grouted reinforced slope, respec-

    tively. The slope reinforced with pressure-grouted soil nails

    exhibits expanded failure surface from the slope surface com-

    pared with that for the gravity-grouted reinforced slope. The

    expanded failure surface can be explained by the increased

    stiffness of the reinforced slope system due to grouting

    pressure.

    3. Higher pullout resistance distribution is observed for the pres-

    sure-grouted soil nail than the gravity-grouted soil nail. The

    shear resistance developed along both types of soil nails are

    very low and can be ignored. The distribution of pullout resis-

    tance increases with increase in the slope angle while the neg-

    ligibly low shear resistance is developed along the soil nail

    without reference to the slope angle. These analysis results con-

    firm the fact that the pullout resistance of a soil nail is the main

    factor for stabilizing slopes.

     Acknowledgments

    This work was supported by the National Research Foundation

    of Korea (NRF) grant funded by the Korea government (MEST) (No.

    2011-0030842).

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