1. Warunki gruntowe.
2. Współczynniki do obliczania parcia i odporu poszczególnych warstw gruntu.
Rzędna
|
γ(n) |
γ ` (n) |
φu(n) |
C |
Ka |
Kp |
2c*(Ka)(1/2) |
2c*(Kp)(1/2) |
[ m ] |
[kN/m3] |
[kN/m3] |
[ o] |
[KPa] |
1 |
1 |
kPa |
kPa |
0 ÷ 1.50 |
20 |
- |
13 |
11 |
0.633 |
1.580 |
17.503 |
27.654 |
1.50÷5.50 |
17.5 |
- |
29.5 |
- |
0.340 |
2.940 |
- |
- |
5.50÷8.50 |
- |
9 |
29.5 |
- |
0.340 |
2.940 |
- |
- |
8.50÷10.80 |
21 |
- |
19 |
16.5 |
0.509 |
1.965 |
23.544 |
46.259 |
10.80÷ ∞ |
18.5 |
- |
33 |
- |
0.295 |
3.392 |
- |
- |
Ka = tg2(45o- φ/2) Kp = tg2(45o+ φ/2)
3. Obliczenie parcia i oporu poszczególnych warstw gruntu.
Parcie gruntu z uwzględnieniem obciążenia naziomu qn = 18 kPa
ea(z) = q*Ka +γ(n) *z*Ka - 2c (Ka)(1/2)
Rzędna |
γ(n) |
γ′ (n) |
φu(n) |
Ka |
Odległość od stopnia warstwy z |
Zastępcze obciążenie naziomu qz=qn+∑γi(n)hi |
Ka*qz+γi(n)*z*Ka |
2c*(Ka)(1/2) |
ea(z) |
[m] |
[kN/m3] |
[kN/m3] |
[ o ] |
1 |
[ m ] |
[ kPa ] |
[kPa] |
[kPa] |
[kPa] |
0.00 |
20 |
- |
13 |
0.633 |
0 |
18 |
11.394 |
17.503 |
-6.109 |
1.50 |
20 |
- |
13 |
0.633 |
1.5 |
18 |
30.384 |
17.503 |
12.881 |
1.50 |
17.5 |
- |
29.5 |
0.340 |
0 |
48 |
16.320 |
0 |
16.320 |
5.50 |
17.5 |
- |
29.5 |
0.340 |
4 |
48 |
40.120 |
0 |
40.120 |
5.50 |
- |
9 |
29.5 |
0.340 |
0 |
118 |
40.120 |
0 |
40.120 |
8.00 |
- |
9 |
29.5 |
0.340 |
2.5 |
118 |
47.770 |
0 |
47.770 |
8.50 |
- |
9 |
29.5 |
0.340 |
3 |
118 |
49.300 |
0 |
49.300 |
8.50 |
21 |
- |
19 |
0.509 |
0 |
145 |
73.805 |
23.544 |
50.261 |
10.80 |
21 |
- |
19 |
0.509 |
2.3 |
145 |
98.390 |
23.544 |
74.846 |
10.80 |
18.5 |
- |
33 |
0.295 |
0 |
193.30 |
57.024 |
0 |
57.024 |
15.00 |
18.5 |
- |
33 |
0.295 |
4.2 |
193.30 |
79.945 |
0 |
79.945 |
Odpór gruntu od rzędnej 8.00 m
ep(z) = q*Ka +γ(n) *z*Kp + 2c (Kp)(1/2)
Rzędna |
γ(n) |
φu(n) |
Kp |
Odległość od stopnia warstwy z |
Zastępcze obciążenie naziomu qz = ∑γi(n)hi |
Kp*qz+γi(n)*z*Kp |
2c*(Kp)(1/2) |
ea(z) |
[m] |
[kN/m3] |
[ o ] |
1 |
[ m ] |
[ kPa ] |
[kPa] |
[kPa] |
[kPa] |
8.00
|
19 |
29.5 |
2.940 |
0 |
0 |
0 |
0 |
0 |
8.50
|
19 |
29.5 |
2.940 |
0.50 |
0 |
27.930 |
0 |
27.930 |
8.50
|
21 |
19 |
1.965 |
0 |
9.5 |
18.668 |
23.544 |
42.212 |
10.80
|
21 |
19 |
1.965 |
2.30 |
9.5 |
113.577 |
23.544 |
137.121 |
10.80
|
18.5 |
33 |
3.392 |
0 |
57.8 |
196.058 |
0 |
196.058 |
15.00
|
18.5 |
33 |
3.392 |
4.20 |
57.8 |
459.616 |
0 |
459.616 |
4. Obliczeniw parcia i odporu w poszczególnych paskach
Rzędna
|
Głębokość z |
ea(z) |
z ` |
γw*z ` =10*z ` |
ea(z `) |
ep(z) |
[m] |
[m] |
[kPa] |
[m] |
[kPa] |
[kPa] |
[kPa] |
0.48 |
0 |
0 |
0 |
0 |
0 |
0 |
1.50 |
1.02 |
12.881 |
0 |
0 |
12.881 |
0 |
1.50 |
0 |
16.320 |
0 |
0 |
16.320 |
0 |
2.50 |
1.00 |
22.270 |
0 |
0 |
22.270 |
0 |
3.50 |
2.00 |
28.220 |
0 |
0 |
28.220 |
0 |
4.50 |
3.00 |
34.170 |
0 |
0 |
34.170 |
0 |
5.50 |
4.00 |
40.120 |
0 |
0 |
40.120 |
0 |
5.50 |
0 |
40.120 |
0 |
0 |
40.120 |
0 |
6.50 |
1.00 |
43.180 |
1.00 |
10 |
53.180 |
0 |
7.50 |
2.00 |
46.240 |
2.00 |
20 |
66.240 |
0 |
8.00 |
2.50 |
47.770 |
2.50 |
25 |
72.770 |
0 |
8.50 |
3.00 |
49.300 |
3.00 |
30 |
79.300 |
27.930 |
8.50 |
0 |
50.261 |
0 |
0 |
50.261 |
42.212 |
8.96 |
0.46 |
55.178 |
0 |
0 |
55.178 |
61.194 |
9.42 |
0.92 |
60.095 |
0 |
0 |
60.095 |
80.176 |
9.88 |
1.38 |
65.021 |
0 |
0 |
65.012 |
99.157 |
10.34 |
1.84 |
69.929 |
0 |
0 |
69.929 |
118.139 |
10.80 |
2.30 |
74.846 |
0 |
0 |
74.846 |
137.121 |
10.80 |
0 |
57.024 |
0 |
0 |
57.024 |
196.058 |
11.34 |
0.54 |
59.971 |
0 |
0 |
59.971 |
229.944 |
11.88 |
1.08 |
62.918 |
0 |
0 |
62.918 |
263.830 |
12.42 |
1.62 |
65.865 |
0 |
0 |
65.865 |
297.716 |
12.96 |
2.16 |
68.812 |
0 |
0 |
68.812 |
331.602 |
13.50 |
2.70 |
71.759 |
0 |
0 |
71.759 |
365.488 |
15.00 |
4.20 |
79.945 |
0 |
0 |
79.945 |
459.616 |
ea(z `) = ea(z) + γw*z `
e(z) = ep(z) - ea(z `)
5. Wypadkowa parcia i odporu
Numer paska |
hi paska |
ei
|
ei+1 |
ei + ei+1 |
0.5*hi*( ei + ei+1) [kN-1] |
|
i |
[m] |
[kPa] |
[kPa] |
[kPa] |
parcie |
odpór |
1 |
1.02 |
0 |
12.881 |
12.881 |
6.569 |
0 |
2 |
1.00 |
16.320 |
22.270 |
38.590 |
19.295 |
0 |
3 |
1.00 |
22.270 |
28.220 |
50.490 |
25.245 |
0 |
4 |
1.00 |
28.220 |
34.170 |
62.390 |
31.195 |
0 |
5 |
1.00 |
34.170 |
40.120 |
74.290 |
37.145 |
0 |
6 |
1.00 |
40.120 |
53.180 |
93.300 |
46.650 |
0 |
7 |
1.00 |
53.180 |
66.240 |
119.420 |
59.710 |
0 |
8 |
0.500 |
66.240 |
72.770 |
139.010 |
34.752 |
0 |
9 |
0.500 |
72.770 |
51.370 |
124.140 |
31.035 |
0 |
10 |
0.263 |
8.049 |
0 |
8.049 |
1.058 |
0 |
11 |
0.197 |
0 |
6.016 |
6.016 |
0 |
0.592 |
12 |
0.460 |
6.016 |
20.081 |
26.097 |
0 |
6.002 |
13 |
0.460 |
20.081 |
34.145 |
54.226 |
0 |
12.472 |
14 |
0.460 |
34.145 |
48.210 |
82.355 |
0 |
18.942 |
15 |
0.460 |
48.210 |
62.275 |
110.485 |
0 |
25.412 |
16 |
0.540 |
139.034 |
169.973 |
309.007 |
0 |
83.432 |
17 |
0.540 |
169.973 |
200.912 |
370.885 |
0 |
100.139 |
18 |
0.540 |
200.912 |
231.851 |
432.763 |
0 |
116.846 |
19 |
0.540 |
231.851 |
262.790 |
494.641 |
0 |
133.553 |
20 |
0.540 |
262.790 |
293.729 |
556.519 |
0 |
150.260 |
6. Obliczenie sił fikcyjnych do wyznaczenia wykresu ugięć
Numer |
mi |
mi+1 |
mi+mi+1 |
hi |
0.5*hi*(mi+mi+1) |
|
pola |
|
|
|
|
+ |
- |
i |
[m] |
[m2] |
||||
1 |
0 |
0.27 |
0.27 |
0.250 |
0.034 |
- |
2 |
0.27 |
1.48 |
1.75 |
1.000 |
0.875 |
- |
3 |
1.48 |
2.24 |
3.72 |
1.000 |
1.860 |
- |
4 |
2.24 |
2.45 |
4.69 |
1.000 |
2.345 |
- |
5 |
2.45 |
1.92 |
4.37 |
1.000 |
2.185 |
- |
6 |
1.92 |
1.08 |
3.00 |
0.750 |
1.125 |
- |
7 |
1.08 |
0.32 |
1.40 |
0.500 |
0.350 |
- |
8 |
0.32 |
0 |
0.32 |
0.250 |
0.04 |
- |
9 |
0 |
0.17 |
0.17 |
0.089 |
- |
0.008 |
10 |
0.17 |
0.6 |
0.77 |
0.285 |
- |
0.111 |
11 |
0.6 |
1.05 |
1.65 |
0.325 |
- |
0.268 |
12 |
1.05 |
1.65 |
2.70 |
0.460 |
- |
0.621 |
13 |
1.65 |
2.07 |
3.72 |
0.460 |
- |
0.856 |
14 |
2.07 |
2.37 |
4.44 |
0.460 |
- |
1.021 |
15 |
2.37 |
2.26 |
4.63 |
0.540 |
- |
1.250 |
16 |
2.26 |
1.47 |
3.73 |
0.540 |
- |
1.007 |
17 |
1.47 |
0 |
1.47 |
0.540 |
- |
0.397 |
odczytano : x = 3.65 m , t = u + 1.2*x = 0.76+1.2*3.65 = 5.14 m
przyjęto : 5.15 m
7. Przyjęcie przekroju ścianki (z profili typu Larsena ze stali St3S)
A ) przy założeniu przegubowego zamocowania ścianki w gruncie
Mmax = mmax*H = 3.46*82.5 = 285.45 kNm
potrzebny wskażnik wytrzymałości na 1 mb ( dla stali St3S kd = 150 MPa )
Wx = ( Mmax / kd ) = (285.45 / 150*103) = 0.001903 m3 = 1903 cm3
przyjeto profile IVn o Wx = 2200 cm3 , szerokość B = 400 mm , długość całkowita brusów Hs + t = 8 + 3.25 = 11.25 m
B ) przy założeniu utwierdzenia ścianki w gruncie :
Mmax = mmax*H1 = 2.65*82.5 = 218.62 kNm
potrzebny wskażnik wytrzymałości ścianki na 1mb :
Wx = ( 218.62 / 150*103 ) = 0.001457 m3 = 1457 cm3
przyjęto profil IIIn o Wx = 1600 cm3 , szerokość B = 400 mm , długość całkowita brusów : Hs + t = 8.00 + 5.15 = 13.15 m
8. Obliczenie kotwy
A ) przy założeniu przegubowego zamocowania ścianki w gruncie
RA = 206 kN
projektuje kotwy co czwarty brus , a = 4*0.4 = 1.6 m , potrzebny przekrój As kotwy ze stali 18G2 o kd = 200 MPa
As = ( RA*a ) / kd = (206*1.6) / 200*103 = 0.001648 m2 = 16.48 cm2
przyjęto pręty stlaowe 50 mm
B ) przy założeniu utwierdzenia ścianki w gruncie
RA = 188 kN
projektuje kotwy co czwarty brus a = 1.6 m
As = ( RA*a ) / kd = (188*1.6) / 200*103 = 0.001504 m2 = 15.04 cm2
przyjęto pręty stlaowe 45 mm
9. Obliczenie płyt kotwiących
9.1 Przy założeniu przegubowego zamocowania ścianki w gruncie
Parcie gruntu
Rzędna [m] |
γ(n) [kN/m3] |
(n)u [0] |
Ka |
z [m] |
qz=qn+γihi [kPa] |
Ka*qz+γi*z*Ka [kPa] |
2*c*(Ka)(1/2) [kPa] |
ea(z) [kPa] |
0.00 |
20 |
13 |
0.633 |
0 |
18 |
11.394 |
17.503 |
-6.109 |
1.00 |
20 |
13 |
0.633 |
1.00 |
18 |
24.054 |
17.503 |
6.551 |
1.50 |
20 |
13 |
0.633 |
1.50 |
18 |
30.384 |
17.503 |
12.881 |
1.50 |
17.5 |
29.5 |
0.340 |
0 |
48 |
16.320 |
0 |
16.320 |
4.00 |
17.5 |
29.5 |
0.340 |
2.50 |
48 |
31.195 |
0 |
31.195 |
q = 18 kPa D = 1.00 m h = 3.00 m h / D = 3 < 5
Odpór gruntu
Rzędna [m] |
γ(n) [kN/m3] |
(n)u [0] |
Kp |
z [m] |
qz= γihi [kPa] |
Kp*qz+γi*z*Kp [kPa] |
2*c*(Kp)(1/2) [kPa] |
ep(z) [kPa] |
0.00 |
20 |
13 |
1.580 |
0 |
0 |
0 |
27.654 |
27.654 |
1.00 |
20 |
13 |
1.580 |
1.00 |
0 |
31.600 |
27.654 |
59.254 |
1.50 |
20 |
13 |
1.580 |
1.50 |
0 |
47.400 |
27.654 |
75.054 |
1.50 |
17.5 |
29.5 |
2.940 |
0 |
30 |
47.400 |
0 |
47.400 |
4.00 |
17.5 |
29.5 |
2.940 |
2.50 |
30 |
216.825 |
0 |
216.825 |
Rzędna [m] |
0.5*ep(z) [kPa] |
0.00 |
13.827 |
1.00 |
29.627 |
1.50 |
37.527 |
1.50 |
23.700 |
4.00 |
108.412 |
Parcie wypadkowe
Rzędna
[m] |
Głębokość z [m] |
ea(z)
[kPa] |
0.5*ep(z)
[kPa] |
e(z)
[kPa] |
0.00 |
0 |
-6.109 |
13.827 |
19.936 |
1.00 |
1.00 |
6.551 |
29.627 |
23.076 |
1.50 |
1.50 |
12.881 |
37.527 |
24.646 |
1.50 |
0 |
16.320 |
23.700 |
7.38 |
4.00 |
2.50 |
31.195 |
108.412 |
77.217 |
Odległość od poziomu gruntu zw = 1.00+1.5 = 2.5 m
Wartość wypadkowej parć i odporów :
W = 11.930 + 126.896 = 138.825 kN/m
Długość kotwy lK = 12.50 m
Sprawdzenie zdolności kotwiącej płyty :
W ≥ RA*0.4
138.825 kN/m > 206*0.4
138.825 kN/m > 82.4 kN/m
9.2 Przy założeniu utwierdzenia ścianki w gruncie :
W = 138.825 kN/m
Długość kotwy lk = 10.70 m
Sprawdzenie zdolności kotwiącej płyty
W ≥ RA*0.4
138.825 kN/m > 188*0.4
138.825 kN/m > 75.2 kN/m