This is a question from slope stability bishop method Please Note i am not asking for the entire problem to be completed, i am simply seeking guidance on how to calculate slice 1 entire row that is highlighted in red. example  how did we derive the values of (W) in the table. formula ....W=ybz but im not getting the values see diagram attached   Question A compacted earth fill is constructed on a soft, saturated clay (figure below). The fill was compacted  to an average dry unit weight of 19 kN m3 ⁄ and water content of 15%. The shearing strength of the  fill was determined by CU tests on samples compacted to representative field conditions. The shear  strength parameters are ?? = 45 kPa, ??′ = 34°, and ???′ = 28°. The variation of undrained shear  strength of the soft clay with depth as determined by simple shear tests is shown in the figure below,  and the friction angle at the critical state is ???′ = 30°. The average water content of the soft clay is  40%. Compute the factor of safety using Bishop’s simplified method. Assume that a tension crack  will develop in the fill.

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ISBN:9781337630931
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This is a question from slope stability bishop method

Please Note i am not asking for the entire problem to be completed, i am simply seeking guidance on how to calculate slice 1 entire row that is highlighted in red.

example 

how did we derive the values of (W) in the table.

formula ....W=ybz but im not getting the values

see diagram attached

 

Question

A compacted earth fill is constructed on a soft, saturated clay (figure below). The fill was compacted 
to an average dry unit weight of 19 kN m3 ⁄ and water content of 15%. The shearing strength of the 
fill was determined by CU tests on samples compacted to representative field conditions. The shear 
strength parameters are ?? = 45 kPa, ??′ = 34°, and ???′ = 28°. The variation of undrained shear 
strength of the soft clay with depth as determined by simple shear tests is shown in the figure below, 
and the friction angle at the critical state is ???′ = 30°. The average water content of the soft clay is 
40%. Compute the factor of safety using Bishop’s simplified method. Assume that a tension crack 
will develop in the fill.

0
€ 1.0
2.5
Depth (m)
5.0
Su (kPa)
7.5 15
10 kPa
10 m
8 m
3
Compacted fill
KX KNKI NY
Soft clay
Very dense sand)
Figure 1: Cross Section of Embankment and it's Slope Failure
6 m
4 m
Clay crust
m
Transcribed Image Text:0 € 1.0 2.5 Depth (m) 5.0 Su (kPa) 7.5 15 10 kPa 10 m 8 m 3 Compacted fill KX KNKI NY Soft clay Very dense sand) Figure 1: Cross Section of Embankment and it's Slope Failure 6 m 4 m Clay crust m
Tension cracks filled with water
Two soil layers
Soil 1
10
30
9.8
17.8
Su
$
Yw
Za
L'a
2₂
R
TCM/R
FS
Slice
123456
7
8
9
2.45
b
m
3
3
3
3
3
3
2
1.8
2
Soil 2
35
28
9.8
21.9
3.20
5.79
4
14.4
21.3
assumed
Z₁
N
m
1.3
~
3
4
1799
4.1
3.8
2.6
1
0
0
kPa
deg.
kN/m³
kN/m³
m
m
m
m
KN
N
54
0.5
1.4
55
2.5 377.9
448.9
498.6
500.2
298.4
205.0
131.4
55
in in
3.5
4.5
R = 14.4m
5.5
6
5.2
3
W-ybz
KN
102.3
252.2
+
248NA-6888
0 m Wsine
deg
27
3
1.05 -59.1
1.00
7.8
14.5 0.97 124.8
1.00
1.09 183.7
1.18
147.5
1.48
114.9
38
4
61
1.49 -60.1
1.19 -94.5
5
Sum 592.1
FS
№
2₂
6
N
ESA TSA
Wtan
m₁
88.0
173.5
229.4
258.1
280.3
227.1 289.4
187.0
0.0
0.0
Soil 1
1505.8
2.45
Su
kPa
9
18
18
15
0
0
Soil 2
5m
Su
b/cose
15 55.6
18
58.2
18
54.7
18 54.0
55.8
60.6
38.1
oo
0.0
0.0
377.0
0.61
Transcribed Image Text:Tension cracks filled with water Two soil layers Soil 1 10 30 9.8 17.8 Su $ Yw Za L'a 2₂ R TCM/R FS Slice 123456 7 8 9 2.45 b m 3 3 3 3 3 3 2 1.8 2 Soil 2 35 28 9.8 21.9 3.20 5.79 4 14.4 21.3 assumed Z₁ N m 1.3 ~ 3 4 1799 4.1 3.8 2.6 1 0 0 kPa deg. kN/m³ kN/m³ m m m m KN N 54 0.5 1.4 55 2.5 377.9 448.9 498.6 500.2 298.4 205.0 131.4 55 in in 3.5 4.5 R = 14.4m 5.5 6 5.2 3 W-ybz KN 102.3 252.2 + 248NA-6888 0 m Wsine deg 27 3 1.05 -59.1 1.00 7.8 14.5 0.97 124.8 1.00 1.09 183.7 1.18 147.5 1.48 114.9 38 4 61 1.49 -60.1 1.19 -94.5 5 Sum 592.1 FS № 2₂ 6 N ESA TSA Wtan m₁ 88.0 173.5 229.4 258.1 280.3 227.1 289.4 187.0 0.0 0.0 Soil 1 1505.8 2.45 Su kPa 9 18 18 15 0 0 Soil 2 5m Su b/cose 15 55.6 18 58.2 18 54.7 18 54.0 55.8 60.6 38.1 oo 0.0 0.0 377.0 0.61
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