Schematy obliczeniowe dla metody Falleniusa (przy braku wypełnienia zbiornika).
1).Linia położenia najniebezpieczniejszych środków obrotu
H = 10 [m.]
4,5H = 45 [m.]
α = 26034`
δ1 = 250
δ2 = 350 (wartości odczytano z tabl.10-2 Z. Wiłun, Zarys geotechniki, 1987, W-wa)
2).Wyznaczenie najniebezpieczniejszego środka obrotu : F = Fmin
Równanie paraboli : F(x) = ax2 + bx + c
F(3,369) =0,9 a = 0,039
F(4,280) =0,78 b = -0,389
F(6,426) =0,7 c = 1,829
Równanie paraboli : F(x) = 0,039x2 -0,389x +1,829
F'(x) =0,078x -0,389 = 0 ⇒ x = 5,721
Fmin= F(5,721) = 0,716
Najniebezpieczniejszy środek obrotu wypada pomiędzy punktami O2, i O3. Płaszczyzna poślizgu wypada więc pomiędzy płaszczyzną 2 i 3. Wskaźnik stateczności „F” wynosi 0,716.
I |
bi[m] |
Φ`[°] |
Ui[kPa] |
li[m] |
hi[m] |
α [°] |
sinα |
cosα |
tgΦ` |
G[kN] |
W[kN] |
|
|
1 |
1.2 |
33,0 |
9.81 |
2.11 |
1.00 |
58 |
0.8480 |
0.5299 |
0.6494 |
44.43 |
43.51 |
0.8633 |
37.6783 |
2 |
1.2 |
37,0 |
27.96 |
3.21 |
2.85 |
52 |
0.7880 |
0.6157 |
0.7536 |
111.71 |
229.02 |
10.7620 |
88.0295 |
3 |
1.2 |
37,0 |
42.67 |
2.38 |
4.35 |
48 |
0.7431 |
0.6691 |
0.7536 |
156.88 |
285.20 |
21.4347 |
116.586 |
4 |
2.1 |
40,0 |
57.88 |
2.46 |
5.90 |
40 |
0.6428 |
0.7660 |
0.8391 |
333.18 |
395.46 |
81.0294 |
214.167 |
5 |
2.1 |
33,0 |
68.67 |
2.22 |
7.00 |
33 |
0.5446 |
0.8387 |
0.6249 |
343.89 |
410.34 |
72.7766 |
187.298 |
6 |
2.1 |
33,0 |
71.12 |
2.08 |
7.25 |
27 |
0.4540 |
0.8910 |
0.6249 |
335.26 |
432.26 |
81.9122 |
152.203 |
7 |
2.1 |
33,0 |
70.14 |
1.97 |
7.15 |
20 |
0.3420 |
0.9397 |
0.6249 |
313.50 |
429.11 |
86.1345 |
107.224 |
8 |
2.1 |
33,0 |
66.22 |
1.89 |
6.75 |
15 |
0.2588 |
0.9659 |
0.6249 |
287.92 |
406.61 |
83.8271 |
74.5203 |
9 |
2.1 |
33,0 |
60.33 |
1.85 |
6.15 |
8 |
0.1392 |
0.9903 |
0.6249 |
255.88 |
380.57 |
78.3905 |
35.612 |
10 |
2.1 |
33,0 |
52.48 |
1.81 |
5.35 |
3 |
0.0523 |
0.9986 |
0.6249 |
220.73 |
354.03 |
68.7757 |
11.5523 |
11 |
1.8 |
33,0 |
42.67 |
1.80 |
4.35 |
-2 |
-0.0349 |
0.9994 |
0.6249 |
153.72 |
325.11 |
47.9684 |
-5.3647 |
12 |
1.8 |
33,0 |
31.88 |
2.20 |
3.25 |
-7 |
-0.1219 |
0.9925 |
0.6249 |
115.64 |
354.16 |
35.5910 |
-14.093 |
13 |
1.8 |
33,0 |
20.60 |
2.23 |
2.10 |
-12 |
-0.2079 |
0.9781 |
0.6249 |
75.82 |
299.36 |
22.6536 |
-15.764 |
14 |
1.8 |
33,0 |
7.36 |
2.28 |
0.75 |
-17 |
-0.2924 |
0.9563 |
0.6249 |
27.70 |
234.60 |
7.8973 |
-8.0979 |
Zestawienie obliczeń dla O3 Σ = 700.0162 Σ = 1019.504
Σ = -37.9555
= 0.72
I |
bi[m] |
Φ`[°] |
Ui[kPa] |
li[m] |
hi[m] |
α [°] |
sinα |
cosα |
tgΦ` |
G[kN] |
W[kN] |
|
|
1 |
1.0 |
33.0 |
10.30 |
2.18 |
1.05 |
63 |
0.8910 |
0.4540 |
0.6494 |
44.92 |
44.92 |
-1.3423 |
40.0274 |
2 |
1.9 |
37.0 |
34.83 |
3.23 |
3.55 |
54 |
0.8090 |
0.5878 |
0.7536 |
230.77 |
230.77 |
17.3841 |
186.695 |
3 |
1.7 |
37.0 |
58.37 |
2.45 |
5.95 |
46 |
0.7193 |
0.6947 |
0.7536 |
292.82 |
292.82 |
45.6414 |
210.64 |
4 |
1.7 |
40.0 |
76.52 |
2.19 |
7.80 |
39 |
0.6293 |
0.7771 |
0.8391 |
351.49 |
351.49 |
88.7545 |
221.197 |
5 |
1.7 |
32.0 |
75.05 |
2.05 |
7.65 |
34 |
0.5592 |
0.8290 |
0.6249 |
307.78 |
307.78 |
63.2805 |
172.106 |
6 |
2.1 |
32.0 |
87.80 |
2.36 |
8.95 |
27 |
0.4540 |
0.8910 |
0.6249 |
413.87 |
413.87 |
101.119 |
187.892 |
7 |
2.1 |
32.0 |
93.69 |
2.23 |
9.55 |
20 |
0.3420 |
0.9397 |
0.6249 |
418.73 |
418.73 |
115.047 |
143.215 |
8 |
2.1 |
32.0 |
93.20 |
2.16 |
9.50 |
14 |
0.2419 |
0.9703 |
0.6249 |
403.40 |
403.40 |
118.549 |
97.5917 |
9 |
2.1 |
32.0 |
89.76 |
2.13 |
9.15 |
9 |
0.1564 |
0.9877 |
0.6249 |
381.70 |
381.70 |
116.319 |
59.7107 |
10 |
2.1 |
32.0 |
83.88 |
2.10 |
8.55 |
3 |
0.0523 |
0.9986 |
0.6249 |
352.76 |
352.76 |
109.913 |
18.4621 |
11 |
1.9 |
32.0 |
75.54 |
1.90 |
7.70 |
-2 |
-0.0349 |
0.9994 |
0.6249 |
287.22 |
287.22 |
89.6268 |
-10.024 |
12 |
1.9 |
32.0 |
65.73 |
1.92 |
6.70 |
-8 |
-0.1392 |
0.9903 |
0.6249 |
252.22 |
252.22 |
77.2676 |
-35.102 |
13 |
1.9 |
32.0 |
54.94 |
1.95 |
5.60 |
-13 |
-0.2250 |
0.9744 |
0.6249 |
214.25 |
214.25 |
63.5072 |
-48.195 |
14 |
1.9 |
32.0 |
33.84 |
2.00 |
3.45 |
-18 |
-0.3090 |
0.9511 |
0.6249 |
135.23 |
135.23 |
38.1141 |
-41.788 |
15 |
1.9 |
32.0 |
9.32 |
2.08 |
0.95 |
-24 |
-0.4067 |
0.9135 |
0.6249 |
38.77 |
38.77 |
10.0175 |
-15.767 |
Zestawienie obliczeń dla O1 Σ = 1053.198 Σ = 1327.513
Σ = -140.8522
= 0.9
I |
bi[m] |
Φ`[°] |
Ui[kPa] |
li[m] |
hi[m] |
α [°] |
sinα |
cosα |
tgΦ` |
G[kN] |
W[kN] |
|
|
1 |
1.1 |
33.0 |
10.30 |
2.20 |
1.05 |
61 |
0.8746 |
0.4848 |
0.6494 |
45.40 |
45.40 |
-0.4479 |
39.7073 |
2 |
1.0 |
37.0 |
28.45 |
1.84 |
2.90 |
56 |
0.8290 |
0.5592 |
0.7536 |
107.46 |
107.46 |
5.7799 |
89.0899 |
3 |
1.0 |
37.0 |
42.67 |
1.64 |
4.35 |
51 |
0.7771 |
0.6293 |
0.7536 |
143.23 |
143.23 |
15.2727 |
111.311 |
4 |
1.9 |
40.0 |
58.37 |
2.57 |
5.95 |
44 |
0.6947 |
0.7193 |
0.8391 |
315.40 |
315.40 |
64.3431 |
219.093 |
5 |
2.3 |
32.0 |
76.03 |
2.86 |
7.75 |
36 |
0.5878 |
0.8090 |
0.6249 |
434.92 |
434.92 |
83.9804 |
255.638 |
6 |
1.9 |
32.0 |
85.35 |
2.16 |
8.70 |
29 |
0.4848 |
0.8746 |
0.6249 |
369.39 |
369.39 |
86.469 |
179.082 |
7 |
1.9 |
32.0 |
85.84 |
2.06 |
8.75 |
23 |
0.3907 |
0.9205 |
0.6249 |
352.99 |
352.99 |
92.7519 |
137.924 |
8 |
1.9 |
32.0 |
83.88 |
1.99 |
8.55 |
18 |
0.3090 |
0.9511 |
0.6249 |
333.84 |
333.84 |
94.0937 |
103.163 |
9 |
1.9 |
32.0 |
79.95 |
1.93 |
8.15 |
12 |
0.2079 |
0.9781 |
0.6249 |
309.41 |
309.41 |
92.4454 |
64.3299 |
10 |
1.9 |
32.0 |
74.07 |
1.91 |
7.55 |
7 |
0.1219 |
0.9925 |
0.6249 |
282.47 |
282.47 |
86.9387 |
34.4248 |
11 |
1.9 |
32.0 |
66.22 |
1.89 |
6.75 |
2 |
0.0349 |
0.9994 |
0.6249 |
250.81 |
250.81 |
78.2671 |
8.75323 |
12 |
1.7 |
32.0 |
57.39 |
1.73 |
5.85 |
-2 |
-0.0349 |
0.9994 |
0.6249 |
198.51 |
198.51 |
61.9468 |
-6.928 |
13 |
1.7 |
32.0 |
47.09 |
1.74 |
4.80 |
-7 |
-0.1219 |
0.9925 |
0.6249 |
164.01 |
164.01 |
50.4772 |
-19.987 |
14 |
1.7 |
32.0 |
35.32 |
1.77 |
3.60 |
-13 |
-0.2250 |
0.9744 |
0.6249 |
125.30 |
125.30 |
37.141 |
-28.186 |
15 |
1.7 |
32.0 |
22.56 |
1.81 |
2.30 |
-17 |
-0.2924 |
0.9563 |
0.6249 |
81.56 |
81.56 |
23.2565 |
-23.847 |
16 |
1.7 |
32.0 |
7.85 |
1.86 |
0.80 |
-22 |
-0.3746 |
0.9272 |
0.6249 |
29.26 |
29.26 |
7.81082 |
-10.961 |
Zestawienie obliczeń dla O2 Σ=880.5264 Σ=1242.512
Σ= -89.9099
= 0.78
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