soil nail wall des ign wall geometry and design parameters

7/27/2017

Design Example - 15 ft Launched Soil Nail Wall with 2-5/8 to 1 (20.8 deg) backslope. 8 psi allowable bond stress

Project:

Wall Geometry and Design Parameters1

123456789101112131415161718

150

20.80

10010032.532.511015205

1.533

161.5...

Design Life:(1) Wall Height (ft), H(2) Slope rise to bench (if present) (ft), H(3) Backslope angle (deg), Backslope condition:(4) Face batter angle (deg), (5) Soil cohesion strength along base (psf), cb(6) Effective soil cohesion (psf), c` Number of nail rows:(7) Effective friction angle of soil along base (deg), `b(8) Effective friction angle of reinforced soil (deg), `(9) Total unit weight of soil mass (pcf), (10) Nail inclination from horizontal (deg), ωi Lnail

20

20

20

20

20

ft ω

15

15

15

15

15

deg(11) Nail length (ft), Lnail,i(12) Number of nail rows, n(13) Vertical distance from wall crest to top row (ft),sv1(14) Vertical spacing (ft), sv(15) Horizontal spacing (ft), sh Active earth pressure method: (16) Ultimate bond stress (psi), ult(17) Bond diameter (in), dhole(18) Bar diameter (in), db

Facing thickness:

Inner:

Soil Nail Wall Nomenclature (Lazarte, et al, 2003)Outer:

Soil Nail Wall Des ign

Concrete or Shotcrete Compressive Strength:

Soil Reinforcement Type:

Soil Reinforcement Size:

Soil Reinforcement Grade:

Wall Geometry and Design Parameters

These calculations are the intellectual property of Steven C. Devin and constitute instruments of service for use by Client only for this specific project. Any use by other parties or for projects not identified herein is strictly forbiden.

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Loads and ASD Load Combinations

Earth Pressure and Surcharge Loads

Area Loads Distances x and y from toe of outside wall face

1 2 3 4 5 6

1

2

3

4

5

6

7

8

9

10

11

12

13

14

"Type" "Dead Load" "Live Load" "Impact" "Earth" "Seismic"

"Symbol" "D" "L" "I" "E" "EQ"

"Start Mag 1 (psf)" 0 0 0 0 0

"End Mag 1 (psf)" 0 0 0 0 0

"Begin 1, x (ft)" 0 0 0 0 0

"Begin 1, y (ft)" 0 0 0 0 0

"End 1, x (ft)" 0 0 0 0 0

"End 1, y (ft)" 0 0 0 0 0

"Start Mag 2 (psf)" 0 0 0 0 0

"End Mag 2 (psf)" 0 0 0 0 0

"Begin 2, x (ft)" 0 0 0 0 0

"Begin 2, y (ft)" 0 0 0 0 0

"End 2, x (ft)" 0 0 0 0 0

"End 2, y (ft)" 0 0 0 0 ...

Line Loads Distances x and y from toe of outside wall face

1 2 3 4 5 6

1

2

3

4

5

6

7

"Type" "D" "L" "I" "E" "EQ"

"Magnitude 1 (lb/ft)" 0 0 0 0 0

"Dist 1, x (ft)" 0 0 0 0 0

"Dist 1, y (ft)" 0 0 0 0 0

"Magnitude 2 (lb/ft)" 0 0 0 0 0

"Dist 2, x (ft)" 0 0 0 0 0

"Dist 2, y (ft)" 0 0 0 0 0

AASHTO Allowable Stress Design (ASD) Load Combinations

1 2 3

12

3

4

5

"Group" "Load Combination" "% Allowable Stress""I" "D+(L+I)+CF+E+B+SF" 100

"II" "D+E+B+SF+W" 125

"V" "D+E+B+SF+W+(R+S+T)" 140

"VII" "D+E+B+SF+EQ" 133


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Length of horizontal sliding surface, BL BL H sv1 tan α( ) Lnail1cos ω1 19.32 ft

Effective height over which earth pressure acts, H1 H1 H BL H tan α( ) tan β( ) 22.34 ft

B1 BL

tface_in tface_out in

cos α( ) 20.32 ft

Weight of soil nailed block, W

Wsoil_sliding 39.67 kipWsoil_sliding

H2

2tan α( )

H1 H BL H tan α( )

2 BL H tan α( ) H

γ ft

Active earth pressure coefficient, KA

KA cos βeq cos βeq cos βeq 2 cos ϕ'( )( )

2

cos βeq cos βeq 2 cos ϕ'( )( )2

EP_Method 1=if

sin θ ϕ'( )( )2

sin θ( )( )2

sin θ δ'( ) 1sin ϕ' δ'( ) sin ϕ' βeq

sin θ δ'( ) sin θ βeq

2

EP_Method 2=if

"Under Construction" otherwise

0.371

KA 0.371

Links: Wall Geometry and Design Parameters Earth pressure loads:

PAx1

2KA γ H1

2 cos βeq ft 9.529 kip PAx 9.529 kip

PAy1

2KA γ H1

2 sin βeq ft 3.620 kip PAy 3.620 kip

Surcharge Wall Loads

PsurchargeDx 0.00 kip

PsurchargeLx 0.00 kip

PsurchargeDy 0.000 kip

PsurchargeLy 0.000 kip

Seismic Loads

Pseudo-static Method: Tolerable Displacement: GEC No. 7

Site Class:Table 3.10.3.1-1: 2010 AASHTO LRFD Bridge Design Specifications

Peak Ground Acceleration (g): 7 percent probability of exceedance in 75 years (approx. 1000 yr R.P.)


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Site Factor: Fpga 1.00 Table 3.10.3.2-1: 2010 AASHTO LRFD Bridge Design Specifications

Horizontal Seismic Coefficient:

kh

Fpga PGA 2

return SM 1=if

0.74 PGA 1.45 PGA PGA 1.45 PGA

de

0.25

return SM 2= PGA 0.3 H 45 ft 1 de 8 if

0.5 1.45 PGA PGAreturn SM 2= PGA 0.3if

"Under Construction" otherwise

kh 0.130

Vertical Seismic Coefficient: kv 0

Reinforced Soil Inertial Force:Finertial_x kh Wsoil_sliding 5.157 kip Finertial_x 5.157 kip

Finertial_y kv Wsoil_sliding 0.000 kipFinertial_y 0.000 kip

Mononobe-Okabe Active Earth Pressure Coefficient:

ψ atankh

1 kv

7.41 °ψ 7.41 °

α' 0 °

KAEcos ϕ' ψ α'( )( )

2

cos ψ( ) cos α'( )( )2 cos δ' α' ψ( )

1sin ϕ' δ'( ) sin ϕ' ψ βeq

cos δ' α' ψ( ) cos βeq α'

2

ϕ' βeq ψ if

"Undefined" otherwise

0.582

KAE 0.582ΔKAE 0.75 kh Backslope 1=if

KAE KA otherwise

0.211ΔKAE 0.211

ΔPAEx1

2ΔKAE γ H1

2 cos βeq α' ft 5.402 kip ΔPAEx 5.402 kip

ΔPAEy1

2ΔKAE γ H1

2 sin βeq α' ft 2.052 kip ΔPAEy 2.052 kip

Aξ tan ϕ' ψ βeq Bξ tan δ' ψ βeq

Angle of failure surface wedge with horizontal

ξ ϕ' ψ atanAξ Aξ

21

Aξ Bξ Aξ

2

1 Bξ Aξ2

1

ϕ' βeq ψif

"Undefned" otherwise

ξ 32.97 °


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Mononobe-Okabe Earth Pressure Schematic

(Lazarte, et al, 2003)

External Failure Modes

(Lazarte, et al, 2003)Sliding

Static Loading: Group I D+(L+I)+CF+E+B+SF simplified to > D+L+E

FSI_SL

cb BL ft Wsoil_sliding PAy PsurchargeDy PsurchargeLy tan ϕ'b PAx PsurchargeDx PsurchargeLx 3.10


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"Check Static Sliding"

"Static Sliding o.k."return FSI_SL SP_FSSL Design_Life 1=if

"Static Sliding o.k."return FSI_SL ST_FSSL Design_Life 2=if

"Static Sliding No Good"" otherwise

"Static Sliding o.k."

Seismic Loading: Group VII D+E+B+SF+EQ simplified to > D+E+EQ

FSVII_SL

cb BL ft Wsoil_sliding PAy ΔPAEy PsurchargeDy Finertial_y PsurchargeEQy tan ϕ'b PAx ΔPAEx PsurchargeDx Finertial_x PsurchargeEQx 1.53

"Check Seismic Sliding "

"Seismic Sliding o.k." FSVII_SL EQ_FSSLif

"Seismic Sliding No Good"" otherwise

"Seismic Sliding o.k."

NOTESearch limits for Spencer's Method and the GLE Method are set between 0.3H and 4Hbehind the wall for an infinite slope with slipsurfaces emerging at, or in front of, the toe of the wall.

Internal Failure Modes

Limit Equilibrium Analysis

Pullout Resistance

Length of nails into resisting zone:

RP

π dhole τult 12 in ft

904.78lbf

ft

LB_Static

5.103

8.75

12.544

16.498

0.01

ft LB_Seismic

4.19

7.893

11.744

15.756

19.943

ft

Tallow

RP

ST_FSP452.39

lbf

ft

Nail Force Calculations

Tensile force in nails: Tmax_s_Static 7.46 kip

FST ST_FST Design_Life 2=if

SP_FST Design_Life 1=if

1.80

Tmax_s_Seismic 16.00 kip

Tensile Resistance of Bar

Ab 0.44 in2

RT TBar_Yield 33.00 kip Tmax

RT

FST18.33 kip

RT_Seismic TBar_Yield 1.33 43.89 kip Tmax_EQ

RT_Seismic

EQ_FST32.51 kip


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Tensile_FSRT

Tnail_StaticMAX

14.29

8.34

5.82

4.42

7294.60

Tensile_FS_EQRT_Seismic

Tnail_SeismicMAX

13.06

6.93

4.66

3.47

2.74

"Check Soil Reinforcement Strength"

"Soil Reinforcement Steel o.k." Tmax Tmax_s_Static Tmax_EQ Tmax_s_Seismicif

"Higher Grade of Steel Required" otherwise

"Soil Reinforcement Steel o.k."

Design Nail Head Force:

To_Static Tmax_s_Static 0.6 0.057 max sv sh 1ft 3

To_Static 4.48 kip

To_Seismic Tmax_s_Seismic 0.6 0.057 max sv sh 1ft 3

To_Seismic 9.60 kip

Facing Flexural Capacity

Welded Wire Fabric: Vertical Rebar Size and Grade: Horizontal Spacing of Vertical Bars:

@ Nail Head @ midspan

Horizontal Rebar Size and Grade: Vertical Spacing of Horizontal Bars:

@ Nail Head @ midspan

CF 1.00

hFF tface_in in tface_out 0=if

tface_out in otherwise

8.00 in avn 0.193in

2

ft avm 0.193

in2

ft

hFF 8.00 in ahn 0.193in

2

ft ahm 0.193

in2

ft

RFF1 3.8 CF avn avm sh hFF

sv

Rebar_Gradev psi ksi

1000 psi

39.18 kip

RFF2 3.8 CF ahn ahm sv hFF

sh

Rebar_Gradeh psi ksi

1000 psi

39.18 kip

RFF min RFF1 RFF2 39.18 kip


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Check_RFF "Permanent Facing Flexure o.k."RFF

To_StaticSP_FSFF

RFF 1.33

To_SeismicEQ_FSFFif

"No Good" otherwise

Check_RFF "Permanent Facing Flexure o.k."

Reinforcement Ratio (initial check):

ρvn

avn

0.5 hFF0.0040 ρvm

avn

0.5 hFF0.0040

ρhn

ahn

0.5 hFF0.0040 ρhm

avn

0.5 hFF0.0040

ρmin 0.0024f'c

min fy_WWF Rebar_Gradev Rebar_Gradeh 1

1000

0.0038

ρmax 0.0005f'c


1000

90

90 min fy_WWF Rebar_Gradev Rebar_Gradeh 1

1000

ρmax 0.0346

Rho "Reinforcement Ratio o.k." ρmin ρvn ρmax ρmin ρvm ρmax ρmin ρhn ρmax ρmin ρhm ρmax if

"Over-Reinforced" ρvn ρmax ρvm ρmax ρhn ρmax ρhm ρmaxif

"Under-Reinforced" ρvn ρmin ρvm ρmin ρhn ρmin ρhm ρminif

Rho "Reinforcement Ratio o.k."


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Facing Reinforcement Dimensions (Lazarte, et al, 2003)

Punching Shear Capacity

Headed Studs:

Face Plate Width:

Face Plate Thickness:Stud Dimensions(Lazarte, et al, 2003)

Stud Dimensions: Face Plate Dimensions: Inner Face Punching Shear Dimensions:

Ls 4.0000 in LBP in 8.00 in D'c_inner LBP in tface_in in 1.00 ft

DH 0.7500 in Outer Face Punching Shear Dimensions:

Ds 0.3750 intp_min

6 wLBP in

2

2

12 in 1.2 Fy_plate0.4082 in

tSH 0.2810 in hc Ls tSH tp in Design_Life 1=if

"Outer Facing Not Used" otherwise

fy_stud 36 ksi tp_min 0.4082 in

tp in 0.500 in hc 4.219 in

SHS LBP in Ds 1 in 6.625 in D'c_outer min SHS hc 2 hc 8.438 in


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Required Minimum Outer Face Thickness:

tface_outer_min ceil max tface_out tp

Ls

in 2

tface_outer_min in 8.00 in

RFP_inner 0.58 f'c π D'c_innertface_in

12 ft

kip 38.41 kip

RFP_inner_Allow

RFP_inner

ST_FSFP28.45 kip RFP_inner_Allow 28.45 kip

"Inner Facing o.k." RFP_inner_Allow To_Static RFP_inner_Allow 1.33 To_Seismicif

"No Good" otherwise

"Inner Facing o.k."

RFP_outer 0.58 f'c πD'c_outer hc

ft2

kip 28.49 kip

RFP_outer_Allow

RFP_outer

SP_FSFP18.99 kip RFP_outer_Allow 18.99 kip

"Outer Facing o.k." RFP_outer_Allow To_Static RFP_outer_Allow 1.33 To_Seismicif

"No Good" otherwise

"Outer Facing o.k."

Headed Stud Tensile Capacity:

RHT 4 πDs

2

4

fy_stud 15.90 kip

RHT_Allow

RHT

ST_FSHT8.84 kip RHT_Allow 8.84 kip

"Headed Stud Capacity o.k." RHT_Allow To_Static RHT_Allow 1.33 To_Seismicif

"Headed Stud Capacity No Good" RHT_Allow To_Static RHT_Allow 1.33 To_Seismicif

"Headed Studs Not Used" otherwise

"Headed Stud Capacity o.k."

Headed Stud Concrete Bearing:

"Headed Stud Bearing o.k." πDH

2

4

2.5 πDs

2

4

tSH 0.5 DH Ds if

"Headed Stud Bearing No Good" otherwise

"Headed Stud Bearing o.k."


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h'FF tface_in in tface_out 0=if

max tface_outer_min in tface_out in otherwise

8.00 in

Reinforcement Ratio:

ρ'vn

avn

0.5 h'FF0.0040 ρ'vm

avn

0.5 h'FF0.0040

ρ'hn

ahn

0.5 h'FF0.0040 ρ'hm

avn

0.5 h'FF0.0040

ρmin 0.0024f'c


1000

0.0038

ρmax 0.0005f'c


1000

90

90 min fy_WWF Rebar_Gradev Rebar_Gradeh 1

1000

ρmax 0.0346

Rho "Reinforcement Ratio o.k." ρmin ρ'vn ρmax ρmin ρ'vm ρmax ρmin ρ'hn ρmax ρmin ρ'hm ρmaxif

"Over-Reinforced" ρ'vn ρmax ρ'vm ρmax ρ'hn ρmax ρ'hm ρmaxif

"Under-Reinforced" ρ'vn ρmin ρ'vm ρmin ρ'hn ρmin ρ'hm ρminif

Rho "Reinforcement Ratio o.k."


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Nail Head Dimensions (Lazarte, et al, 2003)


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Cantilever at Top of Wall for Permanent Facing Applicable Load Factors

xx = Load Factor H 15.00 ft

γDC_max 1.25H2 H

0.5H tan βeq

1 0.5 tan βeq

γDC_min 0.90H2 18.52 ft

γEH_Active_max 1.50

γEH_Active_min 0.90

γEV_Walls_max 1.35

γEV_Walls_min 1.00

γES_max 1.50

γES_min 0.75

γLL_StrI 1.75

γLL_ExtI 0.00

γLS_StrI 1.75

γLS_ExtI 0.00

γCT_ExtII 1.00

γEQ_ExtI 1.00

KA 0.371 βeq 20.80 °

γ 110.00 pcfqsD

qsurD11 qsurD12

2

γconcrete 150 pcf

tface_outer_min in 8.00 in

qsL

qsurL11 qsurL12

2

sv1 1.50 ft

AASHTO LRFD Load Combinations

Strength I:

γWcant z( ) γDC_max tface_outer_min in z γconcrete ft

γRface z( ) γEH_Active_min 0.5KA γ z2

ft γES_min KA qsL z ft

VuStrI z( ) γES_max KA qsD z cos βeq ft γEH_Active_max 0.5 KA γ z2 cos βeq

ft

PuStrI z( ) γWcant z( ) γRface z( ) γEV_Walls_max 0.5 KA γ z2 sin βeq

ft

MuStrI z( ) γES_max KA qsD z cos βeq z

2 γEH_Active_max 0.5 KA γ z( )

2 cos βeq

z

3


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Extreme Event I - Loads:

zis z( ) z ft1

4H2 tan βeq EQface z( ) γEQ_ExtI PGA γWcant z( )

γPis

γEQ_ExtI

8PGA γ ft H2

2 tan βeq

zir' z( )z ft

2

γPir' z( )γEQ_ExtI

2PGA γ H2 z ft

2

Extreme Event I (Seismic):

VuExtI z( ) γES_max KA qsD z ft cos βeq ft γEH_Active_max 0.5KA γ z ft( )2 cos βeq

ft EQface z( ) ft

PuExtI z( ) γWcant z( ) γRface z( ) γEV_Walls_max 0.5 KA γ z2 sin βeq

ft

MuExtI z( ) γES_max KA qsD z ft cos βeq ftz ft

2

γEH_Active_max 0.5 KA γ z ft( )2 cos βeq

ft

z ft

3

EQface z( ) ftz ft

2

γPis zis z( ) γPir' z( ) zir' z( )

Shear, Moment, and Axial Force Diagrams - Strength I and Extreme I Load Combinations

0.00 0.25 0.50 0.75 1.00 1.25 1.50

0.100

0.050

0.000

0.050

VuStrI z( )

kip

VuExtI z( )

kip

z

ft

0.00 0.25 0.50 0.75 1.00 1.25 1.500.060

0.045

0.030

0.015

0.000

3.00

2.25

1.50

0.75

0.00

MuStrI z( )

kip ft

MuExtI z( )

kip ft

z

ft


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0.00 0.25 0.50 0.75 1.00 1.25 1.500.000

0.050

0.100

0.150

0.200

PuStrI z( )

kip

PuExtI z( )

kip

z

ft


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Permanent Facing - Upper Cantilever Structural Design

Welded Wire Fabric: Vertical Rebar Size and Grade: Horizontal Spacing of Vertical Bars:

Horizontal Rebar Size and Grade: Vertical Spacing of Horizontal Bars:

As_cant_v 0.20001

ftin

2ds_cant

tface_outer_min in

24.00 in

εc_cant 0.003 As_cant_h 0.20001

ftin

2

εs_cant 0.005 Check Shear:

ϕv 0.90cface

εc_cant

εc_cant εs_cant

ds_cant 1.5000 inbv 12 in

aface β1 cface 1.2750 indv

tface_outer_min in

20.33 ft

Mn_cant As_cant_v ft Rebar_Gradev_up psi ds_cant

aface

2

Vc 0.06 f'c psi ksi bv dv

Mn_cant 2.24 kip ft Vr ϕv Vc 5.18 kip

Flexural Resistance Factor ϕƒ 0.90

ϕƒ Mn_cant 2.02 kip ft

Check_Up "Upper Cantilever Design - o.k."

VuStrI sv1 0.06 kip MuStrI sv1 ft 0.03 kip ft

VuExtI

sv1

ft

0.11 kip MuExtI

sv1

ft

1.88 kip ft


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Estimated Typical Wall Displacements (Lazarte, et al, 2003)

Soil Type:

(δ/H)1

1000return Soil_Type 1= Soil_Type 2=if

1

500return Soil_Type 3=if

1

333return Soil_Type 4=if

δh (δ/H) H 0.36 in

δv δh

δh 0.36 in

δv 0.36 in

C 1.25return Soil_Type 1= Soil_Type 2=if

0.8return Soil_Type 3=if

0.7return Soil_Type 4=if

DDEF C 1 tan α( ) H 12.00 ft

DDEF 12.00 ft


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Wall Design Summary

Design Example - 15 ft Launched Soil Nail Wall with 2-5/8 to 1 (20.8 deg) backslope. 8 psi allowable bond stress

Height: H 15.0 ft

Face Batter: α 0 °

Backslope Angle: βeq 20.8 °

Number of Nail Rows: n 5

Nail Lengths: Nail Inclination:

Lnail

20.0

20.0

20.0

20.0

20.0

ft ω

15

15

15

15

15

deg

Nail Bar Size: SR_Size 6 ASTM A615 or Manufacturer Designation

Nail Steel Yield Strength: fy_SR psi 75 ksi Allowable Bond Stress: τallow 8.0 psi

Nail Hole Diameter: dhole 1.50 in

Vertical Distance from Crest to Top Row: sv1 1.50 ft

Vertical Nail Spacing: sv 3.00 ft

Horizontal Nail Spacing: sh 3.00 ft

Inner Face Thickness: tface_in in 4.00 in

Outer Face Thickness: tface_outer_min in 8.00 in

Shotcrete Compressive Strength: f'c psi 4000 psi

Inner Face Face Reinforcement Welded_Wire_Fabric "4 x 4-W2.0 x W2.0"

Walers: Rebarv 4 ASTM A615 Designation

Rebar_Gradev psi 40 ksi

Nail Face Plate Size: LBP in 8.00 in

Nail Plate Thickness: tp in 0.500 in

Headed Studs: Headed_Studs "3/8 x 4-1/8"

Permanent Facing - Upper Cantilever:

Vertical Rebar Size and Spacing: Welded_Wire_Fabricup "Not Used"

Rebarv_up 4 ASTM A615 or Manufacturer Designation

svn_rebar_up in 12 in

Horizontal Rebar Size and Spacing: Rebarh_up 4 ASTM A615 or Manufacturer Designation

shn_rebar_up in 12 in


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References: AASHTO LRFD Bridge Design Specifications - Fifth Edition with 2010 Revisions

Anderson, D.G., Martin, G.R., Lam, I., and Wang, J.N., (2008) Seismic Analysis and Design ofRetaining Walls, Buried Structures, Slopes, and Embankments. NCHRP Report 611.Transportation Research Board

Byrne, R.J., Cotton, D., Porterfield, J., Wolschag, C., and Ueblacker, (1998) Manual for Designand Construction Monitoring of Soil Nail Walls. FHWA-SA-96-069R

Concrete Reinforcing Steel Institute (CRSI), (1997) Manual of Standard Practice, MSP-1-97

Geotechnical Design Manual M 46 with Revisions through 2010 - Washington Department ofTransportation

Lazarte, C.A., Elias, V., Espinoza, R.D., and Sabatini, P.J., (2003) Geotechnical EngineeringReport No. FHWA0-IF-03-017 (GEC No. 7)


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soil nail wall des ign wall geometry and design parameters

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