MSE wall design calculation

1. PROJECT :
PREPARED BY :
DATE :
T.Z.S.K
4/11/2022
T . Z
COMPANY :
REV NO : -
DATE :
DESIGN CALCULATION REPORT
Section (1) Panels Arrangement
PREPARED BY :
11-Apr-22

2. PROJECT :
PREPARED BY :
DATE :
T.Z.S.K
4/11/2022
Design Calculation Results (SECTION 1)
SUMMARY
EXTERNAL STABILITY
Sliding
Case I F.S = 3.17 > 1.50 OK
Case II F.S = 3.82 > 1.50 OK
Case III F.S = 4.24 > 1.50 OK
Case IV F.S = 3.01 > 1.50 OK
Case V F.S = 3.82 > 1.50 OK
Overturning
Case I F.S = 7.01 > 2.00 OK
Case II F.S = 7.53 > 2.00 OK
Case III F.S = 8.48 > 2.00 OK
Case IV F.S = 3.82 > 2.00 OK
Case V F.S = 7.53 > 2.00 OK
Bearing Capacity
Case I q = 110.71 kN/m2
Case II q = 173.98 kN/m2
Control
Case III q = 118.19 kN/m2
Case IV q = 128.60 kN/m2
Case V q = 173.98 kN/m2
INTERNAL STABILITY
Pullout Resistance
Layer 1 Tmax = 9.77 kN per strip < 16.20 kN OK
Layer 2 Tmax = 13.05 kN per strip < 21.75 kN OK
Layer 3 Tmax = 16.77 kN per strip < 28.28 kN OK
Layer 4 Tmax = 18.73 kN per strip < 33.97 kN OK
Tensile Resistance
Layer 1 Tmax = 18.82 kN per strip < 33.51 kN OK
Layer 2 Tmax = 22.99 kN per strip < 33.51 kN OK
Layer 3 Tmax = 26.68 kN per strip < 33.51 kN OK
Layer 4 Tmax = 30.20 kN per strip < 33.51 kN OK
Pullout Resistance
Layer 1 Tmax = 14.56 kN per strip < 18.00 kN OK
Layer 2 Tmax = 18.17 kN per strip < 24.17 kN OK
Layer 3 Tmax = 22.58 kN per strip < 31.42 kN OK
Layer 4 Tmax = 25.22 kN per strip < 37.74 kN OK
Tensile Resistance
Layer 1 Tmax = 23.61 kN per strip < 44.67 kN OK
Layer 2 Tmax = 28.11 kN per strip < 44.67 kN OK
Layer 3 Tmax = 32.49 kN per strip < 44.67 kN OK
Layer 4 Tmax = 36.70 kN per strip < 44.67 kN OK
Pullout Resistance
Layer 1 Tmax = 12.13 kN per strip < 18.00 kN OK
Layer 2 Tmax = 16.59 kN per strip < 24.17 kN OK
Layer 3 Tmax = 20.31 kN per strip < 31.42 kN OK
Layer 4 Tmax = 22.27 kN per strip < 37.74 kN OK
Tensile Resistance
Layer 1 Tmax = 22.97 kN per strip < 44.67 kN OK
Layer 2 Tmax = 29.21 kN per strip < 44.67 kN OK
Layer 3 Tmax = 32.90 kN per strip < 44.67 kN OK
Layer 4 Tmax = 36.42 kN per strip < 44.67 kN OK
Seismic
Impact
Seismic
Impact
Static
Seismic
Impact
Static
Static
Seismic
Impact
Static

3. PROJECT :
PREPARED BY :
DATE :
T.Z.S.K
4/11/2022
Wall Information
Section name = SECTION 1
Wall Height H = 4.52 m
Reinforcing fill length L = 4.50 m
B = 4.64 m
Reinforced Soil Unit Weight ϒsoil = 21.00 kN/m3
Reinforcement fill φ = 34.00 Degree
Retained Soil Unit Weight ϒsoil = 21.00 kN/m3
Retained fill φ = 34.00 Degree
Foundation Soil Unit Weight ϒfoundation = 19.00 kN/m3
Foundation internal friction angle φ = 30.00 Degree
Foundation cohesion c = 0.00 kN/m2
Nr = 22.40
Traffic surcharge q = 13.00 kN/m2
Panel
First strip location = 1.88 m
Location of slab bottom = 1.10 m
Vertical sapcing of strip Sv = 0.75 m
Panel width b = 1.50 m
Panel height h = 1.50 m
Panel thickness t = 0.14 m
Strip width b = 50.00 mm
Stritp thickness t = 4.00 mm
Horizontal spacing of strip (1st
Layer) Sh = 0.50 m
Horizontal spacing of strip Sh = 0.75 m
Steel reinforcement strength fy = 448.00 Mpa
Load Factor, ϒ (LRFD 11.5.5)
Typical application
Bearing Resistance
Vertical ϒEV = 1.35
Horizontal ϒEH = 1.5
Sliding and Eccentricity
Vertical ϒEV = 1
Horizontal ϒEH = 1.5
Live Load Surcharge on MSE Wall
Bearing and reinforcement tensile Resistance ϒLS = 1.75
Sliding, eccentricity and reinforcement pullout resistance
ϒLS = 1.75
Resistance Factor, φ (LRFD Table 11.5.6-1)
Mechanically Stabilized Earth Walls
Pullout resistance of tensile reinforcement
Static loading = 0.9
MSE WALL DESIGN CALCULATION REPORT

4. PROJECT :
PREPARED BY :
DATE :
T.Z.S.K
4/11/2022
Load Cases
Vertical
Load
Horizontal
Load
Live
Load
Load Factor ϒ (LRFD 11.5.5) ϒEV ϒEH ϒLS
Case I Strength I 1.00 1.50 -
Case II Strength II 1.35 1.50 1.75
Case III Service I 1.00 1.00 1.00
Resistance Factor φP φT
Case IV Static loading 0.90 0.75
Case V Combined static and impact loading 1.00 1.00
I. External Stability
Static Mass Stability
Vertical loads
Reinforced Soil
V1 = ϒsoil H L
= 21.00 x 4.52 x 4.50
= 427.14 kN/m
Case I V1 = 427.14 x 1
V1 = 427.14 kN/m
Case II V1 = 427.14 x 1.35
V1 = 576.64 kN/m
Case III V1 = 427.14 x 1
V1 = 427.14 kN/m
Forces acting on the MSE Wall
Forces :
V1 = ϒsoil H L
V2 = qs L
F1 = 0.5 ϒ H2 Ka
F2 = qs H Kaf

5. PROJECT :
PREPARED BY :
DATE :
T.Z.S.K
4/11/2022
Moment arm of V1 = 2.25 m
MV1 = 427.14 x 2.25
MV1 = 961.065 kN-m/m
Case I MV1 = 961.065 KN-m/m
Case II MV1 = 1297.44 KN-m/m
Case III MV1 = 961.07 KN-m/m
Traffic surcharge
V2 = q L
V2 = 13.00 x 4.5
V2 = 58.50 kN/m
Factored V2 = 58.50 x 1.75
Factored V2 = 102.38 kN/m
Moment arm of V2 = 2.25 m
MV2 = 58.50 x 2.25
MV2 = 131.63 kN-m/m
Factored MV2 = 102.38 x 2.25
Factored MV2 = 230.34 kN-m/m
Case I ∑V = 427.14 kN/m
Case II ∑V = 679.01 kN/m
Case III ∑V = 485.64 kN/m
Case I ∑Mv = 961.07 kN-m/m
Case II ∑Mv = 1527.78 kN-m/m
Case III ∑Mv = 1092.69 kN-m/m
Horizontal loads
ka = tan(45 - φ/2)2
For retained ka = 0.28
For surcharge kaf = 0.28
Retained Soil
F1 = 0.5 ϒsoil H2
Ka
= 60.65 kN/m
Case I F1 = 90.97 kN/m
Case II F1 = 90.97 kN/m
Case III F1 = 60.65 kN/m
Moment arm of F1 = 1.51 m
Case I MF1 = 137.07 kN-m/m
Case II MF1 = 137.07 kN-m/m
Case III MF1 = 91.38 kN-m/m

6. PROJECT :
PREPARED BY :
DATE :
T.Z.S.K
4/11/2022
Traffic surcharge
F2 = q H Kaf
F2 = 16.61 kN/m
Factored F2 = 29.07 kN/m
Moment arm of F2 = 2.26 m
MF2 = 37.54 kN-m/m
Factored MF2 = 65.70 kN-m/m
Case I ∑F = 90.97 kN/m
Case II ∑F = 120.04 kN/m
Case III ∑F = 77.26 kN/m
Case I ∑MF = 137.07 kN-m/m
Case II ∑MF = 202.77 kN-m/m
Case III ∑MF = 128.92 kN-m/m
Sliding (LRFD 11.10.5.3)
Sliding F.S = ∑V x tanφ
∑F
Case I F.S = 3.17 > 1.5 OK
Case II F.S = 3.82 > 1.5 OK
Case III F.S = 4.24 > 1.5 OK
Overturning (LRFD 11.10.5.3)
Overturning F.S = ∑Mv
∑MF
Case I = 7.01 ≥ 2 OK
Case II = 7.53 ≥ 2 OK
Case III = 8.48 ≥ 2 OK
Bearing Capacity at Base
Eccentricity e = L - ∑Mv-∑Mf
2 ∑V
Case I e = 0.32 m ≤ 0.77 m OK
Case II e = 0.30 m ≤ 0.75 m OK
Case III e = 0.27 m ≤ 0.75 m OK

7. PROJECT :
PREPARED BY :
DATE :
T.Z.S.K
4/11/2022
σv = ∑V
L-2e
Case I σv = 110.71 kN/m2
Case II σv = 173.98 kN/m2
Case III σv = 118.19 kN/m2
11.4.2 (f) qult = cf Nc + 0.5 (L-2e) ϒf Nr
qult = 844.62 kN/m2
F.S = qult
σv
= 7.63 > 1.5 OK
Sliding at base of first grid
F1 at first grid F1 = 0.5 ϒb d2
Ka
= 50.12 kN/m
F2 = q d ka
= 15.88 kN/m
∑F = 66.00 kN/m
F.S = ϒb d L tanφ C
∑F
= 4.17 > 1.5 OK

8. PROJECT :
PREPARED BY :
DATE :
T.Z.S.K
4/11/2022
II. Internal Stability
Distance from Top Steel Strip Tributary Spacing
d1 = 1.88 m V1 = 1.18 m
d2 = 2.63 m V2 = 0.75 m
d3 = 3.38 m V3 = 0.75 m
d4 = 4.13 m V4 = 0.77 m
Force developed in the reinforcement
Static Load
Compute Kr (LRFD Figure 11.10.6.2.1-3)
At Z = 0 Kr = 0.48
Under Z = 6 m Kr = 0.34
MSE Wall Panel Arrangement for Section 1
LRFD 11.4.3.Fig 29
Variation of stress ratio with depth in MSE Wall
Friction

9. PROJECT :
PREPARED BY :
DATE :
T.Z.S.K
4/11/2022
Layer 1
Vertical Stress
1 Reinforced Soil
Kr = 0.44
σv = ϒsoil H
= 39.48 kN/m2
Case I σv = 39.48 kN/m2
Case II σv = 53.30 kN/m2
Case III σv = 39.48 kN/m2
=
2 Traffic Surcharge
σv = 13.00 kN/m2
σv = 22.75 kN/m2
Case I ∑σv = 39.48 kN/m2
Case II ∑σv = 76.05 kN/m2
Case III ∑σv = 52.48 kN/m2
Horizontal Stress
σh = ϒp (σv kr + Δσh)
σh = σv kr
Case I σh = 26.06 kN/m2
Case II σh = 50.19 kN/m2
Case III σh = 23.09 kN/m2
At per strip At = 0.38 m2
Traffic Load are NEGLECTED in pullout calculation as per AASHTO LRFD 11.10.6.3.2.
Tmax = σh Sv
For Pullout Tmax = 9.77 kN per strip < 16.20 kN OK
For Tensile Tmax = 18.82 kN per strip < 33.51 kN OK
Layer 2
Vertical Stress
1 Reinforced Soil
Kr = 0.42
σv = ϒsoil H
= 55.23 kN/m2
Case I σv = 55.23 kN/m2
Case II σv = 74.56 kN/m2
Case III σv = 55.23 kN/m2
2 Traffic Surcharge
σv = 13.00 kN/m2
σv = 22.75 kN/m2
BP 5

10. PROJECT :
PREPARED BY :
DATE :
T.Z.S.K
4/11/2022
Case I ∑σv = 55.23 kN/m2
Case II ∑σv = 97.31 kN/m2
Case III ∑σv = 68.23 kN/m2
Horizontal Stress
σh = ϒp (σv kr + Δσh)
σh = σv kr
Case I σh = 23.20 kN/m2
Case II σh = 40.87 kN/m2
Case III σh = 28.66 kN/m2
At per strip At = 0.56 m2
Traffic Load are NEGLECTED in pullout calculation as per AASHTO LRFD 11.10.6.3.2.
Tmax = σh Sv
For Pullout Tmax = 13.05 kN per strip < 21.75 kN OK
For Tensile Tmax = 22.99 kN per strip < 33.51 kN OK
Layer 3
Vertical Stress
1 Reinforced Soil
Kr = 0.40
σv = ϒsoil H
= 70.98 kN/m2
Case I σv = 70.98 kN/m2
Case II σv = 95.82 kN/m2
Case III σv = 70.98 kN/m2
2 Traffic Surcharge
σv = 13.00 kN/m2
σv = 22.75 kN/m2
Case I ∑σv = 70.98 kN/m2
Case II ∑σv = 118.57 kN/m2
Case III ∑σv = 83.98 kN/m2
Horizontal Stress
σh = ϒp (σv kr + Δσh)
σh = σv kr
Case I σh = 29.81 kN/m2
Case II σh = 47.43 kN/m2
Case III σh = 33.59 kN/m2
At per strip At = 0.56 m2
BP 5

11. PROJECT :
PREPARED BY :
DATE :
T.Z.S.K
4/11/2022
Traffic Load are NEGLECTED in pullout calculation as per AASHTO LRFD 11.10.6.3.2.
Tmax = σh Sv
For Pullout Tmax = 16.77 kN per strip < 28.28 kN OK
For Tensile Tmax = 26.68 kN per strip < 33.51 kN OK
Layer 4
Vertical Stress
1 Reinforced Soil
Kr = 0.38
σv = ϒsoil H
= 86.73 kN/m2
Case I = 86.73 kN/m2
Case II = 117.09 kN/m2
Case III = 86.73 kN/m2
2 Traffic Surcharge
σv = 13.00 kN/m2
σv = 22.75 kN/m2
Case I ∑σv = 86.73 kN/m2
Case II ∑σv = 139.84 kN/m2
Case III ∑σv = 99.73 kN/m2
Horizontal Stress
σh = ϒp (σv kr + Δσh)
σh = σv kr
Case I σh = 33.30 kN/m2
Case II σh = 53.70 kN/m2
Case III σh = 38.30 kN/m2
At per strip At = 0.56 m2
Traffic Load are NEGLECTED in pullout calculation as per AASHTO LRFD 11.10.6.3.2.
Tmax = σh Sv
For Pullout Tmax = 18.73 kN per strip < 33.97 kN OK
For Tensile Tmax = 30.20 kN per strip < 33.51 kN OK

12. PROJECT :
PREPARED BY :
DATE :
T.Z.S.K
4/11/2022
Resistance in friction of one strip against soil (LRFD Equation 11.10.6.3.2-1)
At Z = 0 F*
= 1.80
Under Z = 6 m F*
= 0.67
LRFD Figure 11.10.6.3.2-1
Default Values for the Pullout Friction Factor, F*
α = 1
C = 2.00 for strip
Rc = 0.10 For 3 strip per panel
Rc = 0.07 For 2 strip per panel
Pullout calculation at each reinforcement level
Le ≥ Tmax ≥ 1 m
φ F* α σv C Rc
Layer 1
F*
= 1.45
Le = 1.83 m ≥ 1 m
Take Le = 1.83 m
Layer 2
F*
= 1.3
Le = 2.67 m ≥ 1 m
Take Le = 2.67 m
Layer 3
F*
= 1.16
Le = 2.70 m ≥ 1 m
Take Le = 2.70 m
Layer 4
F*
= 1.02
Le = 2.85 m ≥ 1 m
Take Le = 2.85 m

13. PROJECT :
PREPARED BY :
DATE :
T.Z.S.K
4/11/2022
Calculate L A at each layer
for H/2 from bottom LA = 0.6 (H1 - d) for inextensible reinforcement
for H/2 from top LA = 0.3 H1 for inextensible reinforcement
LA1 = 1.36 m
LA2 = 1.13 m
LA3 = 0.68 m
LA4 = 0.23 m
LRFD Figure 11.10.6.3.1-1
Location of Potential Failure Surface for Internal Stability Design of MSE Walls
Calculate L T at each layer
Layer 1 LT1 = 3.18 m < 4.50 m OK
Layer 2 LT2 = 3.80 m < 4.50 m OK
Layer 3 LT3 = 3.38 m < 4.50 m OK
Layer 4 LT4 = 3.08 m < 4.50 m OK
Allowable Tensile Strength
Design Life = 100 years
For Corrosion Losses Ec = En - Es
Loss of galvanizing = 0.015 mm/yr for first 2 year
= 0.004 mm/yr for subsequent years
Zinc coating lift = 16.00 years
Loss of carbon steel = 0.012 mm/yr after zinc depletion
Ec = 1.99 mm
Ac = 99.72 mm2

14. PROJECT :
PREPARED BY :
DATE :
T.Z.S.K
4/11/2022
Tal = AC FY
Case V φTall = 44.67 kN
Case IV φTall = 33.51 kN
Pullout Resistance Strength
C11.10.6.3.2 P = F*
α σv Le C b
Layer 1 Case V φP = 18.00 kN
Case IV φP = 16.20 kN
Layer 2 Case V φP = 24.17 kN
Case IV φP = 21.75 kN
Layer 3 Case V φP = 31.42 kN
Case IV φP = 28.28 kN
Layer 4 Case V φP = 37.74 kN
Case IV φP = 33.97 kN
Connection Strength
Strip width b = 60 mm
Stritp thickness t = 4 mm
Yield Strength Fy = 345 Mpa
C11.10.6.3.2 Tac = AC FY
Case V φTac = 63.48 kN > 44.67 kN OK
Case IV φTac = 47.61 kN > 33.51 kN OK
III. External Stability with Seismic
Peak Ground Acceleration a0/g = 0.46
11.6.5.2.1 Horizontal acceleration coefficient
kh = 0.5 Kho
= 0.23
ζ = Arc tan(Kh)
= 12.95
kae = cos2
(φ - ζ)
cos ( ζ ) cos (ζ + δ) (1 + √(sin(φ + δ) sin(φ - ζ - δ)/cos (ζ + δ) cosδ))2
kae = 0.871
0.950 x 2.114
= 0.434
11.6.5.3-2 Horizontal Seismic Thrust PAE = 0.5 KAE ϒ H2
= 93.06 kN/m

15. PROJECT :
PREPARED BY :
DATE :
T.Z.S.K
4/11/2022
Moment arm of PAE = 1.51 m
Moment MAE = 140.22 KN-m
Horizontal Inertia Force PIR = 0.5 Kh ϒ H2
= 49.34 kN/m
Moment arm of PIR = 2.26 m
Moment MIR = 111.51 KN-m
∑MF = 251.72 KN-m
Sliding (LRFD 11.10.5.3)
Sliding F.S = ∑V x tanφ
∑F
Rv = 427.14 kN/m
Moment arm of Pv = 2.25 m
Moment Mv = 961.07 KN-m
Rh = 95.87 kN/m
F.S = 3.01 > 1.5 OK
Overturning (LRFD 11.10.5.3)
Overturning F.S = ∑Mv
∑MF
= 3.82 > 2 OK
Bearing Capacity at Base
Eccentricity e = L - ∑Mv-∑Mf
2 ∑V
= 0.59 < 0.75 OK
σv = ∑V
L - 2e
σv = 128.60 kN/m2

16. PROJECT :
PREPARED BY :
DATE :
T.Z.S.K
4/11/2022
qult = cf Nc + 0.5 (L-2e) ϒf Nr
qult = 706.78 kN/m2
F.S = qult
σv
= 5.50 > 1.5 OK
IV. Internal Stability with Seismic
PI = Kh Wa
= 22.20 kN/m
Tmd = Pi Lei / ∑Lei
Layer 1 Tmd = 4.78 kN per strip
Layer 2 Tmd = 5.12 kN per strip
Layer 3 Tmd = 5.81 kN per strip
Layer 4 Tmd = 6.49 kN per strip
Ttotal = Tmax + Tmd
Layer 1 For Pullout Ttotal = 14.56 kN per strip < 18.00 kN OK
For Tensile Ttotal = 23.61 kN per strip < 44.67 kN OK
Layer 2 For Pullout Ttotal = 18.17 kN per strip < 24.17 kN OK
For Tensile Ttotal = 28.11 kN per strip < 44.67 kN OK
Layer 3 For Pullout Ttotal = 22.58 kN per strip < 31.42 kN OK
For Tensile Ttotal = 32.49 kN per strip < 44.67 kN OK
Layer 4 For Pullout Ttotal = 25.22 kN per strip < 37.74 kN OK
For Tensile Ttotal = 36.70 kN per strip < 44.67 kN OK

17. PROJECT :
PREPARED BY :
DATE :
T.Z.S.K
4/11/2022
V. Impact Load
Width of slab b = 2.1 m
Depth of slab h = 1.1 m
Eccetricity of traffic barrier e = 0.12 m
Slab Length L = 6 m
11.10.10.2 Static impact Load P = 44.48 kN
Earth pressure F1 = 0.5 Ka ϒ h2
Case I F1 = 3.59 kN/m
Case II F1 = 4.85 kN/m
Traffic surcharge F2 = Ka q h
Case I F2 = 4.04 kN/m
Case II F2 = 7.08 kN/m
PH1 = 7.41 kN/m
Case I ∑ F 11.01 kN/m
Case II ∑ F = 19.34 kN/m
Horizontal pressure due to traffic barrier
L1 = (cr + bf - 2e') (tan 45 + φ/2)
= 3.50 m
Δσhmax = 2 ∑F / L1
Case I Δσhmax = 6.29 kN/m2
Case II Δσhmax = 11.06 kN/m2

18. PROJECT :
PREPARED BY :
DATE :
T.Z.S.K
4/11/2022
Tmax = σh Sv
Layer 1
For Pullout Tmax = 12.13 kN per strip < 18.00 kN OK
For Tensile Tmax = 22.97 kN per strip < 44.67 kN OK
Layer 2
For Pullout Tmax = 16.59 kN per strip < 24.17 kN OK
For Tensile Tmax = 29.21 kN per strip < 44.67 kN OK
Layer 3
For Pullout Tmax = 20.31 kN per strip < 31.42 kN OK
For Tensile Tmax = 32.90 kN per strip < 44.67 kN OK
Layer 4
For Pullout Tmax = 22.27 kN per strip < 37.74 kN OK
For Tensile Tmax = 36.42 kN per strip < 44.67 kN OK