Slope Stability (Internal & Global) and Bearing Capacity Analysis & Design of Geogrid Reinforced Earth

1. Geodomisi Ltd.
Prof. Dr. Costas Sachpazis
University of Western Macedonia
Analysis of Geogrid Reinforced Eatrh Slope Stability & Capacity
Last Cheak
www.uowm.gr
Geodomisi Ltd., URL: http://www.geodomisi.com, E-mail: costas@sachpazis.info 1
[GeoStructural Analysis - www.geodomisi.com
Analysis of reinforced slopes
Input data
Project
Task
Part
Description
Customer
Author
Date
Project ID
Project number
:
:
:
:
:
:
:
:
Analysis of Geogrid Reinforced Eatrh Slope Stability & Capacity
Last Cheak
Slope Staibily (Internal & Global) and Bearing Capacity Analysis & Design of Geogrid Reinforced Eatrh
UOWM
Prof. Dr. Costas Sachpazis
14-Feb-20
UOWM-R.E.S.-Edu
Edu200214-7
Name : Project Stage - analysis : 1 - 0
+z+z
1: 5.00
0.1600
0.0800
7.927.92
2.742.74
Fortrac 3D-150
5.46 m
+x
+y
+x
+z
Settings
Standard - safety factors
Materials and standards
Concrete structures :
Coefficients EN 1992-1-1 :
EN 1992-1-1 (EC2)
standard
Wall analysis
Active earth pressure calculation :
Passive earth pressure calculation :
Earthquake analysis :
Shape of earth wedge :
Allowable eccentricity :
Internal stability :
Verification methodology :
Coulomb
Caquot-Kerisel
Mononobe-Okabe
Calculate as skew
0.333
Standard - straight slip surface
Safety factors (ASD)
Safety factors
Permanent design situation
Safety factor for overturning :
Safety factor for sliding resistance :
SFo =
SFs =
1.50
1.50
[–]
[–]

2. Geodomisi Ltd.
Prof. Dr. Costas Sachpazis
University of Western Macedonia
Analysis of Geogrid Reinforced Eatrh Slope Stability & Capacity
Last Cheak
www.uowm.gr
Geodomisi Ltd., URL: http://www.geodomisi.com, E-mail: costas@sachpazis.info 2
[GeoStructural Analysis - www.geodomisi.com
Safety factors
Permanent design situation
Safety factor for bearing capacity :
Safety factor for sliding along geo-reinforcement :
Safety factor for geo-reinforcement strength :
Safety factor for pull out resistance of geo-reinf. :
Safety factor for connection strength :
SFb =
SFsr =
SFst =
SFpo =
SFcon =
1.50
1.50
1.50
1.50
1.50
[–]
[–]
[–]
[–]
[–]
Stability analysis
Verification methodology : Safety factors (ASD)
Safety factors
Permanent design situation
Safety factor : SFs = 1.50 [–]
Geometry of structure
Embankment height
Embankment length
Cover thickness
hn
ln
tc
=
=
=
7.92
2.74
0.20
m
m
m
Material
Cover material
Unit weight
Shear resistance
g
Rs
=
=
23.00
0.00
kN/m3
kPa
Types of reinforcements
No.
Name
Type of
reinforcement
Line type Reinforcement strength
Tult[kN/m] Rt[kN/m]
Coefficient
Cds[–] Ci[–]
1 Fortrac 3D-150
Fortrac
3D-150
150.00 58.91 0.60 0.70
Reinforcement details
1. Fortrac 3D-150
Short-term char. strength
Long-term design strength
Overall coeff. of model uncertainty
Tult
Rt
FSUNC
=
=
=
150.00
58.91
1.50
kN/m
kN/m
Calculate reduction factors
Life time :
Creep red. factor
Chemistry :
Durability red. factor
Partical size :
Installation damage red. factor
120 years
pH 4.0-9.0
D90 £ 32 mm
RFCR
RFD
RFID
=
=
=
1.60
1.03
1.03
Reinforcement
No.
Number
of
reinforcements
Type of reinforcement
Spacing of
reinforcements
hr[m]
Height of
first
reinforcement
h[m]
Reinforcements geometry
1 6 Fortrac 3D-150 0.91 0.91 identical ending of reinforcements
Reinforcement details
Reinforcement No. 1
Reinforcement type : Fortrac 3D-150

3. Geodomisi Ltd.
Prof. Dr. Costas Sachpazis
University of Western Macedonia
Analysis of Geogrid Reinforced Eatrh Slope Stability & Capacity
Last Cheak
www.uowm.gr
Geodomisi Ltd., URL: http://www.geodomisi.com, E-mail: costas@sachpazis.info 3
[GeoStructural Analysis - www.geodomisi.com
Number of reinforcements 6
Reinforcement geometry : identical ending of reinforcements
End point coordinate : 11.00 m
Reinforcement
No.
Origin
l1[m]
End
l2[m]
Height from bottom
h[m]
Length
l[m]
1
2
3
4
5
6
-2.43
-2.11
-1.80
-1.48
-1.17
-0.85
8.26
8.26
8.26
8.26
8.26
8.26
0.91
1.82
2.73
3.64
4.55
5.46
10.68
10.37
10.06
9.74
9.43
9.11
Name : Reinforcement Stage - analysis : 1 - 0
Fortrac 3D-150
5.46 m
+x
+y
Soil parameters
Soil No. 1
Unit weight :
Angle of internal friction :
Cohesion of soil :
Angle of friction struc.-soil :
Saturated unit weight :
g
jef
cef
d
gsat
=
=
=
=
=
19.00
29.00
18.00
15.00
19.00
kN/m3
°
kPa
°
kN/m3
Geological profile and assigned soils
No.
Layer
[m]
Assigned soil Pattern
1 - Soil No. 1

4. Geodomisi Ltd.
Prof. Dr. Costas Sachpazis
University of Western Macedonia
Analysis of Geogrid Reinforced Eatrh Slope Stability & Capacity
Last Cheak
www.uowm.gr
Geodomisi Ltd., URL: http://www.geodomisi.com, E-mail: costas@sachpazis.info 4
[GeoStructural Analysis - www.geodomisi.com
Name : Profile and assignment Stage - analysis : 1 - 0
+z+z
Terrain profile
Terrain behind construction has the slope 1: 5.00 (slope angle is 11.31 °).
Water influence
Ground water table is not considered.
Resistance on front face of the structure
Resistance on front face of the structure is not considered.
Earthquake
Factor of horizontal acceleration
Factor of vertical acceleration
Kh
Kv
=
=
0.1600
0.0800
Water below the GWT is restricted.

5. Geodomisi Ltd.
Prof. Dr. Costas Sachpazis
University of Western Macedonia
Analysis of Geogrid Reinforced Eatrh Slope Stability & Capacity
Last Cheak
www.uowm.gr
Geodomisi Ltd., URL: http://www.geodomisi.com, E-mail: costas@sachpazis.info 5
[GeoStructural Analysis - www.geodomisi.com
Name : Earthquake Stage - analysis : 1 - 0
0.1600
0.0800
Settings of the stage of construction
Design situation : permanent
Verification No. 1
Active pressure behind the structure - partial results
Layer
No.
Thickness
[m]
a
[°]
jd
[°]
cd
[kPa]
g
[kN/m3]
dd
[°]
Ka Comment
1
2
3
4
5
6
7
8
9
2.46
0.11
0.80
0.91
0.91
0.91
0.91
0.91
1.65
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
29.00
29.00
29.00
29.00
29.00
29.00
29.00
29.00
29.00
18.00
18.00
18.00
18.00
18.00
18.00
18.00
18.00
18.00
19.00
19.00
19.00
19.00
19.00
19.00
19.00
19.00
19.00
29.00
29.00
29.00
29.00
29.00
29.00
29.00
29.00
29.00
0.365
0.365
0.365
0.365
0.365
0.365
0.365
0.365
0.365
Active pressure distribution behind the structure (without surcharge)
Layer
No.
Start [m]
End [m]
sZ
[kPa]
sW
[kPa]
Pressure
[kPa]
Hor. comp.
[kPa]
Vert. comp.
[kPa]
1
2
3
4
0.00
2.46
2.46
2.58
2.58
3.37
3.37
4.28
0.00
46.83
46.83
48.98
48.98
64.12
64.12
81.41
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
5.53
5.53
11.84
0.00
0.00
0.00
0.00
0.00
4.83
4.83
10.35
0.00
0.00
0.00
0.00
0.00
2.68
2.68
5.74

6. Geodomisi Ltd.
Prof. Dr. Costas Sachpazis
University of Western Macedonia
Analysis of Geogrid Reinforced Eatrh Slope Stability & Capacity
Last Cheak
www.uowm.gr
Geodomisi Ltd., URL: http://www.geodomisi.com, E-mail: costas@sachpazis.info 6
[GeoStructural Analysis - www.geodomisi.com
Layer
No.
Start [m]
End [m]
sZ
[kPa]
sW
[kPa]
Pressure
[kPa]
Hor. comp.
[kPa]
Vert. comp.
[kPa]
5
6
7
8
9
4.28
5.19
5.19
6.10
6.10
7.01
7.01
7.92
7.92
9.58
81.41
98.70
98.70
115.99
115.99
133.28
133.28
150.57
150.57
181.95
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
11.84
18.15
18.15
24.45
24.45
30.76
30.76
37.07
37.07
48.52
10.35
15.87
15.87
21.39
21.39
26.91
26.91
32.42
32.42
42.44
5.74
8.80
8.80
11.86
11.86
14.91
14.91
17.97
17.97
23.52
Earthquake effects (active earth pressure) - partial results
Layer
No.
Thickness
[m]
jd
[°]
b
[°]
y
[°]
Ka Kae Kae-Ka Comment
1
2
3
4
5
6
7
8
9
2.46
0.11
0.80
0.91
0.91
0.91
0.91
0.91
1.65
29.00
29.00
29.00
29.00
29.00
29.00
29.00
29.00
29.00
11.31
11.31
11.31
11.31
11.31
11.31
11.31
11.31
11.31
9.87
9.87
9.87
9.87
9.87
9.87
9.87
9.87
9.87
0.365
0.365
0.365
0.365
0.365
0.365
0.365
0.365
0.365
0.603
0.603
0.603
0.603
0.603
0.603
0.603
0.603
0.603
0.238
0.238
0.238
0.238
0.238
0.238
0.238
0.238
0.238
Earthquake effects (active earth pressure)
Layer
No.
Start [m]
End [m]
sZ
[kPa]
sD
[kPa]
Pressure
[kPa]
Hor. comp.
[kPa]
Vertical comp.
[kPa]
1
2
3
4
5
6
7
8
9
0.00
2.46
2.46
2.58
2.58
3.37
3.37
4.28
4.28
5.19
5.19
6.10
6.10
7.01
7.01
7.92
7.92
9.58
0.00
43.08
43.08
45.06
45.06
58.99
58.99
74.90
74.90
90.81
90.81
106.71
106.71
122.62
122.62
138.53
138.53
167.39
167.39
124.31
124.31
122.33
122.33
108.40
108.40
92.49
92.49
76.59
76.59
60.68
60.68
44.77
44.77
28.87
28.87
0.00
39.88
29.62
29.62
29.15
29.15
25.83
25.83
22.04
22.04
18.25
18.25
14.46
14.46
10.67
10.67
6.88
6.88
0.00
34.88
25.91
25.91
25.49
25.49
22.59
22.59
19.28
19.28
15.96
15.96
12.65
12.65
9.33
9.33
6.02
6.02
0.00
19.34
14.36
14.36
14.13
14.13
12.52
12.52
10.68
10.68
8.85
8.85
7.01
7.01
5.17
5.17
3.33
3.33
0.00

7. Geodomisi Ltd.
Prof. Dr. Costas Sachpazis
University of Western Macedonia
Analysis of Geogrid Reinforced Eatrh Slope Stability & Capacity
Last Cheak
www.uowm.gr
Geodomisi Ltd., URL: http://www.geodomisi.com, E-mail: costas@sachpazis.info 7
[GeoStructural Analysis - www.geodomisi.com
Forces acting on construction
Name Fhor
[kN/m]
App.Pt.
z [m]
Fvert
[kN/m]
App.Pt.
x [m]
Design
coefficient
Gravity force
Earthquake - soil wedge
Active pressure
Earthq.- act.pressure
0.00
252.69
148.50
167.03
-4.16
-4.16
-2.33
-6.38
1579.29
-126.34
82.32
92.59
6.33
6.33
11.00
11.00
1.000
1.000
1.000
1.000
Verification of complete wall
Check for overturning stability
Resisting moment
Overturning moment
Mres
Movr
=
=
11113.87
2463.90
kNm/m
kNm/m
Safety factor = 4.51 > 1.50
Wall for overturning is SATISFACTORY
Check for slip
Resisting horizontal force
Active horizontal force
Hres
Hact
=
=
1093.63
568.22
kN/m
kN/m
Safety factor = 1.92 > 1.50
Wall for slip is SATISFACTORY
Overall check - WALL is SATISFACTORY
Bearing capacity of foundation soil
Design load acting at the center of footing bottom
No.
Moment
[kNm/m]
Norm. force
[kN/m]
Shear Force
[kN/m]
Eccentricity
[–]
Stress
[kPa]
1 303.21 1627.85 568.22 0.017 153.17
Service load acting at the center of footing bottom
No.
Moment
[kNm/m]
Norm. force
[kN/m]
Shear Force
[kN/m]
1 303.21 1627.85 568.22
Verification of foundation soil
Eccentricity verification
Max. eccentricity of normal force
Maximum allowable eccentricity
e
ealw
=
=
0.017
0.333
Eccentricity of the normal force is SATISFACTORY
Verification of bearing capacity
Max. stress at footing bottom
Bearing capacity of foundation soil
s
Rd
=
=
153.17
300.00
kPa
kPa
Safety factor = 1.96 > 1.50
Bearing capacity of foundation soil is SATISFACTORY
Overall verification - bearing capacity of found. soil is SATISFACTORY

8. Geodomisi Ltd.
Prof. Dr. Costas Sachpazis
University of Western Macedonia
Analysis of Geogrid Reinforced Eatrh Slope Stability & Capacity
Last Cheak
www.uowm.gr
Geodomisi Ltd., URL: http://www.geodomisi.com, E-mail: costas@sachpazis.info 8
[GeoStructural Analysis - www.geodomisi.com
Name : Bearing cap. Stage - analysis : 1 - -1
153.17
153.17
Verification of slip on georeinforcement No. 1
Forces acting on construction (verification of most utilized reinforcement)
Name Fhor
[kN/m]
App.Pt.
z [m]
Fvert
[kN/m]
App.Pt.
x [m]
Design
coefficient
Active pressure
Earthq.- act.pressure
Gravity force
Earthquake - soil wedge
112.40
136.79
0.00
222.69
-2.03
-5.78
-3.75
-3.75
62.30
75.82
1391.83
-111.35
10.69
10.69
6.11
6.11
1.000
1.000
1.000
1.000
Check for slip along geo-reinforcement with the maximal utilization (Reinforc. No.: 1)
Inclination of slip surface
Overall normal force acting on reinforcement
Coefficient of reduction of slip along
geo-textile
Wall resistance
Overall bearing capacity of reinforcements
Resistance along geo-reinforcement
=
=
=
=
=
=
90.00
1418.61
0.60
0.00
0.00
471.81
°
kN/m
kN/m
kN/m
kN/m
Check for slip:
Resisting horizontal force
Active horiz. force
Hres
Hact
=
=
471.81
249.19
kN/m
kN/m
Factor of safety = 1.89 > 1.50
Slip along geotextile is SATISFACTORY

9. Geodomisi Ltd.
Prof. Dr. Costas Sachpazis
University of Western Macedonia
Analysis of Geogrid Reinforced Eatrh Slope Stability & Capacity
Last Cheak
www.uowm.gr
Geodomisi Ltd., URL: http://www.geodomisi.com, E-mail: costas@sachpazis.info 9
[GeoStructural Analysis - www.geodomisi.com
Name : Slip on georeinf. Stage - analysis : 1 - 1
+x
+z
128.51
+x
+z
156.40
+x
+z
1391.83
+x
+z
248.98
Calculation of internal stability No. 1
Check for bearing capacity of geo-reinforcement No.: 1
Check for tensile strength
Tensile strength
Geo-reinforcement force
Rt
Fx
=
=
58.91
16.84
kN/m
kN/m
Factor of safety = 3.50 > 1.50
Geo-reinforcement for tensile strength is SATISFACTORY
Check for pull out resistance
Pull out resistance
Geo-reinforcement force
Tp
Fx
=
=
1154.48
16.84
kN/m
kN/m
Factor of safety = 68.54 > 1.50
Geo-reinforcement for pull out resistance is SATISFACTORY
Overall verification - geo-reinforcement is SATISFACTORY

10. Geodomisi Ltd.
Prof. Dr. Costas Sachpazis
University of Western Macedonia
Analysis of Geogrid Reinforced Eatrh Slope Stability & Capacity
Last Cheak
www.uowm.gr
Geodomisi Ltd., URL: http://www.geodomisi.com, E-mail: costas@sachpazis.info 10
[GeoStructural Analysis - www.geodomisi.com
Name : Internal stability Stage - analysis : 1 - 1
+x
+z
16.84
Global stability analysis No. 1
Slip surface parameters
(slip surface after optimization)
Center
Radius
Angle
S
r
a1
a2
=
=
=
=
(-2.34;-17.99)
27.16
-17.45
59.51
m
m
°
°
Slope stability check (Bishop)
FS = 1.53 > 1.50
Slope stability is SATISFACTORY
Name : Global stability Stage - analysis : 1 - 1
+x
+z
(-2.34;-17.99)

11. Geodomisi Ltd.
Prof. Dr. Costas Sachpazis
University of Western Macedonia
Analysis of Geogrid Reinforced Eatrh Slope Stability & Capacity
Last Cheak
www.uowm.gr
Geodomisi Ltd., URL: http://www.geodomisi.com, E-mail: costas@sachpazis.info 11
[GeoStructural Analysis - www.geodomisi.com
Slope stability analysis
Input data
Project
Settings
Standard - safety factors
Stability analysis
Earthquake analysis :
Verification methodology :
Standard
Safety factors (ASD)
Safety factors
Permanent design situation
Safety factor : SFs = 1.50 [–]
Interface
No. Interface location
Coordinates of interface points [m]
x z x z x z
1
2
3
-34.32
23.77
0.00
-2.74
38.30
-7.92
4.75
0.00
-7.92
-0.07
-2.74
38.30
0.19
-2.55
-7.92
4.75
-0.07
-7.99
0.00
0.19
0.00
-0.07
Name : Interface Stage : 1

12. Geodomisi Ltd.
Prof. Dr. Costas Sachpazis
University of Western Macedonia
Analysis of Geogrid Reinforced Eatrh Slope Stability & Capacity
Last Cheak
www.uowm.gr
Geodomisi Ltd., URL: http://www.geodomisi.com, E-mail: costas@sachpazis.info 12
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Soil parameters - effective stress state
No. Name Pattern
jef
[°]
cef
[kPa]
g
[kN/m3]
1 Soil No. 1 29.00 18.00 19.00
Soil parameters - uplift
No. Name Pattern
gsat
[kN/m3]
gs
[kN/m3]
n
[–]
1 Soil No. 1 19.00
Soil parameters
Soil No. 1
Unit weight :
Stress-state :
Angle of internal friction :
Cohesion of soil :
Saturated unit weight :
g
effective
jef
cef
gsat
=
=
=
=
19.00
29.00
18.00
19.00
kN/m3
°
kPa
kN/m3
Rigid bodies
No. Name Sample
g
[kN/m3]
1
2
Cover
Material of cover
23.00
23.00
Assigning and surfaces
No. Surface position
Coordinates of surface points [m]
x z x z
Assigned
soil
1
2
3
38.30
23.77
0.19
-2.55
0.00
0.19
-2.74
-34.32
38.30
-0.07
4.75
-0.07
-7.99
0.00
-0.07
-7.92
-12.99
-0.07
38.30
0.00
0.19
-2.74
-2.55
-34.32
38.30
4.75
0.00
-0.07
-7.92
-7.99
-7.92
-12.99
Soil No. 1
Cover
Soil No. 1

13. Geodomisi Ltd.
Prof. Dr. Costas Sachpazis
University of Western Macedonia
Analysis of Geogrid Reinforced Eatrh Slope Stability & Capacity
Last Cheak
www.uowm.gr
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Reinforcements
No.
Point to the left
x [m] z [m]
Point to the right
x [m] z [m]
Length
L [m]
Strength
Rt [kN/m]
Pull out resist.
End of
reinf.
1
2
3
4
5
6
-0.85
-1.17
-1.48
-1.80
-2.11
-2.43
-2.46
-3.37
-4.28
-5.19
-6.10
-7.01
8.26
8.26
8.26
8.26
8.26
8.26
-2.46
-3.37
-4.28
-5.19
-6.10
-7.01
9.11
9.43
9.74
10.06
10.37
10.69
58.91
58.91
58.91
58.91
58.91
58.91
Tp = 51.92 kN/m2
Tp = 71.09 kN/m2
Tp = 90.25 kN/m2
Tp = 109.42 kN/m2
Tp = 128.59 kN/m2
Tp = 147.76 kN/m2
Fixed
Fixed
Fixed
Fixed
Fixed
Fixed
Water
Water type : No water
Tensile crack
Tensile crack not inputted.
Earthquake
Horizontal seismic coefficient :
Vertical seismic coefficient :
Kh =
Kv =
0.16
0.08
Settings of the stage of construction
Design situation : permanent
Results (Stage of construction 1)
Analysis 1
Circular slip surface
Slip surface parameters
Center :
Radius :
x =
z =
R =
-1.73
19.10
27.96
[m]
[m]
[m]
Angles :
a1 =
a2 =
-14.90
58.30
[°]
[°]
The slip surface after optimization.
Reinforcement forces
Reinforcement
1
2
3
4
5
6
Force [kN/m]
0.00
0.00
0.00
0.00
0.00
0.00
Slope stability verification (Bishop)
Sum of active forces :
Sum of passive forces :
Sliding moment :
Resisting moment :
Fa =
Fp =
Ma =
Mp =
1398.60
2144.86
39104.91
59970.33
kN/m
kN/m
kNm/m
kNm/m
Factor of safety = 1.53 > 1.50
Slope stability ACCEPTABLE

14. Geodomisi Ltd.
Prof. Dr. Costas Sachpazis
University of Western Macedonia
Analysis of Geogrid Reinforced Eatrh Slope Stability & Capacity
Last Cheak
www.uowm.gr
Geodomisi Ltd., URL: http://www.geodomisi.com, E-mail: costas@sachpazis.info 14
[GeoStructural Analysis - www.geodomisi.com
Name : Analysis Stage - analysis : 1 - 1