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PRZYKŁAD
ANALIZA STATECZNOŚCI SKARPY METODĄ FELLENIUSA
x 0 = 3.0 m
B = 6.0 m
p = 20 kN/m 2
α i
0.00
R = 10 m
x i
1
Nasyp budowlany
- 3.00
2
Piasek gliniasty
3
- 5.00
b i =R/10
4
- 6.00
17
5
16
15
6
14
7
13
8
12
9
Glina pylasta
11
10
Dane:
Nasyp budowlany: Ps , I D = 0.6, φ = 32°, γ = 18 kN/m 3
Piasek gliniasty: Pg , I L = 0.2, φ = 20°, c = 15 kPa, γ = 19 kN/m 3
Glina pylasta: G π, I L = 0.40, φ = 15°, c = 10 kPa, γ = 19.5 kN/m 3
Ciężary poszczególnych bloków:
W 1 = 1.25⋅1.0⋅18.0 + 1.0⋅20 = 42.5 kN/mb
W 2 = (2.5⋅1.0 + 0.5⋅0.87)⋅18.0 + 0.5⋅1.1⋅0.75⋅19.0 + 1.0⋅20 = 80.67 kN/mb
W 3 = 3.0⋅1.0⋅18.0 + 1.7⋅1.0⋅19.0 + 1.0⋅20 = 106.3 kN/mb
W 4 = 3.0⋅1.0⋅18.0 + 2.7⋅1.0⋅19.0 + 1.0⋅20 = 125.3 kN/mb
W 5 = 3.0⋅1.0⋅18.0 + 3.0⋅1.0⋅19.0 + 0.4⋅1.0⋅19.5 + 1.0⋅20 = 138.8 kN/mb
W 6 = 3.0⋅1.0⋅18.0 + 3.0⋅1.0⋅19.0 + 1.0⋅1.0⋅19.5 + 1.0⋅20 = 150.5 kN/mb
W 7 = 3.0⋅1.0⋅18.0 + 3.0⋅1.0⋅19.0 + 1.4⋅1.0⋅19.5 + 1.0⋅20 = 158.3 kN/mb
W 8 = 2.6⋅1.0⋅18.0 + 3.0⋅1.0⋅19.0 + 1.75⋅1.0⋅19.5 = 137.93 kN/mb
W 9 = 1.75⋅1.0⋅18.0 + 3.0⋅1.0⋅19.0 + 1.95⋅1.0⋅19.5 = 126.53 kN/mb
W 10 = 0.9⋅1.0⋅18.0 + 3.0⋅1.0⋅19.0 + 2.0⋅1.0⋅19.5 = 112.2 kN/mb
W 11 = 0.5⋅0.5⋅0.6⋅18.0 + 0.4⋅0.8⋅19.0 + 2.6⋅1.0⋅19.0 + 2.0⋅1.0⋅19.5 = 97.18 kN/mb
W 12 = 2.25⋅1.0⋅19.0 + 1.95⋅1.0⋅19.5 = 80.78 kN/mb
W 13 = 1.4⋅1.0⋅19.0 + 1.75⋅1.0⋅19.5 = 60.73 kN/mb
W 14 = 1.0⋅1.0⋅19.0 + 1.4⋅1.0⋅19.5 = 46.3 kN/mb
W 15 = 1.0⋅1.0⋅19.0 + 1.0⋅1.0⋅19.5 = 38.5 kN/mb
W 16 = 1.0⋅1.0⋅19.0 + 0.45⋅1.0⋅19.5 = 27.78 kN/mb
W 17 = 0.55⋅1.15⋅19.0 = 12.02 kN/mb
32880917.002.png 32880917.003.png 32880917.004.png 32880917.005.png
Tablica: Obliczenia stateczności skarpy
Nr bloku
W i
x i
sin α i = x i / R
cos α i φ i
i ⋅ cos α i ⋅ tg α i
c i
c i ⋅ b i /cos α i W i ⋅ sin α i
[kN/m]
[m]
[°]
[kN/mb]
[kPa]
[kN/mb] [kN/mb]
1
42.50
9.4
0.94 0.3412
32
9.06
0
0.00
39.95
2
80.67
8.5
0.85 0.5268 23 (śr.)
18.04 11.25 (śr.)
21.36
68.57
3
106.30
7.5
0.75 0.6614
20
25.59
15
22.68
79.73
4
125.30
6.5
0.65 0.7599
20
34.66
15
19.74
81.45
5
138.80
5.5
0.55 0.8352
15
31.06
10
11.97
76.34
6
150.50
4.5
0.45 0.8930
15
36.01
10
11.20
67.73
7
158.30
3.5
0.35 0.9367
15
39.73
10
10.68
55.41
8
137.93
2.5
0.25 0.9682
15
35.78
10
10.33
34.48
9
126.53
1.5
0.15 0.9887
15
33.52
10
10.11
18.98
10
112.20
0.5
0.05 0.9987
15
30.03
10
10.01
5.61
11
97.18
-0.5
-0.05 0.9987
15
26.01
10
10.01
-4.86
12
80.78
-1.5
-0.15 0.9887
15
21.40
10
10.11
-12.12
13
60.73
-2.5
-0.25 0.9682
15
15.76
10
10.33
-15.18
14
46.30
-3.5
-0.35 0.9367
15
11.62
10
10.68
-16.21
15
38.50
-4.5
-0.45 0.8930
15
9.21
10
11.20
-17.33
16
27.78
-5.5
-0.55 0.8352
15
6.22
10
11.97
-15.28
17
12.02
-6.6
-0.65 0.7513
20
3.29
15
19.97
-7.93
SUMA
386.98
212.34
439.33
Współczynnik stateczności:
F = (386.98 + 212.34)/439.33 = 1.36 > F min = 1.3
Skarpa jest stateczna
32880917.001.png

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