Przykład obliczenia obudowy wykopu z zakotwieniami
1. Geometria układu i profil geotechniczny
±0.00
-3.00
-8.00
-11.50
-3.00
-6.80
-8.90
-10.20
-15.00
Pg, I
L
= 0.30, (B)
φ = 16.5°, c=27kPa
γ = 20.6kN/m
3
E
0
= 24 MPa
Gp (+H), I
L
= 0.35, (C)
φ =12° , c = 8 kPa
γ = 20.0 kN/m
3
E
0
= 7 MPa
Pd, I
D
= 0.45,
φ = 30°
γ = 17.2 kN/m
3
E
0
= 50 MPa
Ps, I
D
= 0.65,
φ = 33°
γ = 18.5 kN/m
3
E
0
= 100 MPa
q = 10 kPa
zwg
1
2
3
4
5
6
zwg
-12.50
±0.0
-5.0
-10.0
-15.0
ściana szczelinowa
gr. 0.60 m
ćięgno 1 - 6 lin
φ12mm
co 2.0 m
ćięgno 2 - 6 lin
φ12mm
co 2.0 m
α = 30°
2. Etap „0” (wykres parcia gruntu i układ podpór sprężystych )
21600
16200
6300
45000
90000
Przekrój i profil
geotechniczny
Moduły reakcji
poziomej gruntu
Kx [kPa]
Podpory sprężyste
wzdłuż obudowy
kx
i
[kN/m]
Wykres parcia
granicznego
gruntu
e
a
[kPa]
±0.00
-3.00
-6.80
-10.20
-15.00
Pg, I
L
= 0.30
Gp (+H), I
L
= 0.35
Pd, I
D
= 0.45
Ps, I
D
= 0.65
q = 10 kPa
zwg
1
2
3
4
5
6
-12.5
28.9
72.3
41.2
51.3
55.1
50.6
-8.9
64.1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
4.8
6.0
7.2
12.9
20.2
23.0
25.9
28.7
31.5
34.4
37.2
29.5
31.2
32.8
34.5
36.1
37.1
38.1
35.7
36.7
37.7
38.7
39.6
40.6
41.6
42.6
43.5
22.3
340
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
1350
2700
4050
5400
6750
5625
3150
3150
3150
3150
3150
3150
3150
22500
22500
22500
22500
22500
22500
22500
45000
45000
45000
45000
45000
45000
45000
45000
45000
22500
Parcie
Siły skupione
E
i
[kN]
0.0
40.4
83.2
73.9
92.0
98.8
89.9
113.9
Wykres parcia
spoczynkowego
gruntu
e
0
[kPa]
4.7
33.8
34.7
77.8
57.6
71.7
77.0
70.3
89.0
Wykres parcia
pośredniego guntu
e=0.5(e
0
+e
a
) [kPa]
2.4
16.9
36.0
0.6
2.4
3.6
Parcie wody
e
w
[kPa]
0.2
3.0
5.5
8.0
10.5
13.0
15.5
18.0
14.4
10.8
7.2
3.6
0.5
19
20
21
22
23
24
25
26
27
28
29
30
31
E
wi
[kN]
3. Etap I
Stan realizacji
i profil geotechniczny
Schemat statyczny
i obciążenia
±0.00
-3.00
-6.80
-10.20
-15.00
Pg, I
L
= 0.30
Gp (+H), I
L
= 0.35
Pd, I
D
= 0.45
Ps, I
D
= 0.65
q = 10 kPa
zwg
1
2
3
4
5
6
-8.9
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
3150
3150
3150
22500
22500
22500
22500
22500
22500
22500
45000
45000
45000
45000
45000
45000
45000
45000
45000
22500
-3.5
20.4
128.2
567.6
321.8
501.0
2a
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
5.1
18.4
26.5
34.7
42.9
51.0
59.2
169.3
190.2
211.2
254.7
253.5
268.7
283.8
Wykres odporu
gruntu
e
I
p
[kPa]
Odpór
Siły skupione
E
I
pi
[kN]
4.8
6.0
7.2
12.9
15.1
4.6
11.4
16.6
22.0
139.8
159.0
178.4
220.2
217.4
231.6
245.7
Reakcje
graniczne
R
gri
= E
I
pi
- E
i
[kN]
Podpory
sprężyste
k
xi
[kN/m]
P
I
xi
= E
i
- E
I
pi
[kN]
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
4.8
6.0
7.2
12.9
20.2
23.0
25.9
28.7
31.5
34.4
37.2
29.5
31.2
32.8
34.5
36.1
37.1
38.1
35.7
36.7
37.7
38.7
39.6
40.6
41.6
42.6
43.5
22.3
Parcie
Siły skupione
E
i
[kN]
0.6
2.4
3.6
0.6
2.4
3.6
3150
3150
0.6
6.0
Wyniki obliczeń
M
15
=
-207.0
M [kNm/m]
δ
x1
=14.0
δ [kNm/m]
10.7
8.4
6.3
32.5
22.0
13.6
7.1
2.4
0.6
6.0
706.4
1028.6
363.3
380.1
396.8
413.6
430.4
447.2
464.0
480.7
497.5
257.2
327.6
343.4
359.1
374.9
390.8
406.6
422.4
438.1
454.0
234.9
0.8
2.8
7.8
8.5
8.3
7.5
6.3
4.9
3.5
2.0
0.5
0.5
Reakcje w
podporach
R
i
[kN]
4. Etap Ia
Wyniki obliczeń
M
16
=81
M [kNm/m]
R [kNm/m]
δ
x1
=-4.4
δ [kNm/m]
Stan realizacji
i profil geotechniczny
Schemat statyczny
i obciążenia
±0.00
-3.00
-6.80
-10.20
-15.00
Pg, I
L
= 0.30
Gp (+H), I
L
= 0.35
Pd, I
D
= 0.45
Ps, I
D
= 0.65
q = 10 kPa
zwg
1
2
3
4
5
6
-8.9
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
3150
3150
3150
22500
22500
22500
22500
22500
22500
22500
45000
45000
45000
45000
45000
45000
45000
45000
45000
22500
-3.5
1.5
5.6
10.7
15.3
19.4
22.7
17.6
9.0
R
i
(Ia) [kN]
Podpory
sprężyste
k
xi
[kN/m]
S
h
= S
⋅cosα =
=160.0 kN
340
1350
2700
4050
5400
6750
5625
3150
3150
3150
3150
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
R
7
= S = 184.8
8.0
7.0
6.0
5.0
4.0
3.2
17.0
12.1
8.2
5.0
2.6
0.8
0.4
2.2
3.0
3.2
3.1
2.8
2.3
1.8
1.2
0.7
0.0
Reakcje
w podporach
sprężystych
S = 184.8 kN/m
M
7
=
-94.0
α = 30°
5. Etap II
142.6
451.8
148.8
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
2.6
21.0
41.9
62.9
88.5
112.1
135.6
159.1
182.7
191.3
200.0
208.6
217.3
113.0
365.3
Wykres odporu
gruntu
e
II
p
[kPa]
Odpór
Siły skupione
E
II
pi
[kN]
19.3
4a
44.8
64.9
84.9
104.9
125.1
Schemat statyczny
i obciążenia
Reakcje graniczne
R
gri
= E
II
pi
- E
i
- E
wi
[kN]
Obciążenie
P
II
xi
= E
i
+E
wi
- P
I
xi
- E
II
pi
[kN]
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
4.8
6.0
7.2
12.9
20.2
23.0
25.9
28.7
31.5
34.4
37.2
29.5
31.2
32.8
34.5
36.1
37.1
38.1
35.7
36.7
37.7
38.7
39.6
40.6
41.6
42.6
43.5
22.3
Parcie
Siły skupione
E
i
[kN]
0.6
2.4
3.6
0.2
3.0
5.5
8.0
10.5
13.0
15.5
18.0
14.4
10.8
7.2
3.6
0.5
19
20
21
22
23
24
25
26
27
28
29
30
31
1.8
Wyniki obliczeń
M [kNm/m]
R [kN/m]
δ [kNm/m]
R
7
= 20
M
13
= 274
M
24
=
-169
δ
x1
= 1.1
±0.00
-3.00
-6.80
-10.20
-15.00
Pg, I
L
= 0.30
Gp (+H), I
L
= 0.35
Pd, I
D
= 0.45
Ps, I
D
= 0.65
q = 10 kPa
zwg
1
2
3
4
5
6
-8.9
-8.5
-12.5
Stan realizacji
i profil geotechniczny
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
21
22
23
24
25
26
27
28
29
30
31
22500
45000
45000
45000
45000
45000
45000
45000
45000
45000
22500
5.1
18.4
25.9
28.7
31.5
34.4
37.2
29.5
31.2
32.8
31.9
15.3
1.5
5.6
10.7
15.3
19.4
22.7
17.6
9.0
8.0
7.0
6.0
5.0
4.0
3.2
17.0
12.1
8.2
5.0
2.6
0.8
Reakcje gran.
R
gri
= -R
Ia
i
[kN]
22500
δ
x7
= 4.2
δ
x13
= 5.9
E
wi
[kN]
136.3
147.6
158.8
170.2
90.2
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
22.7
17.6
9.0
8.0
7.0
6.0
5.0
4.0
3.2
17.0
12.1
8.2
5.0
2.6
0.8
19.3
44.8
62.1
41.8
24.9
11.1
1.8
0.0
9.3
17.3
24.8
16.0
0.4
2.1
5.7
10.8
17.2
Reakcje w podporach
sprężystych
R
II
i
[kN]
6. Etap IIa
Wyniki obliczeń
M
23
= 37
M [kNm/m]
R [kNm/m]
δ
x1
= 0.2
δ [kNm/m]
Schemat statyczny
i obciążenia
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
3150
3150
3150
22500
22500
22500
22500
22500
22500
22500
45000
45000
45000
45000
45000
45000
45000
45000
45000
22500
0.1
0.2
0.1
0.3
0.9
1.8
2.1
1.5
R
i
(IIa) [kN]
Podpory
sprężyste
k
xi
[kN/m]
S
h
= S
⋅cosα =
180.0 kN/m
340
1350
2700
4050
5400
6750
5625
3150
3150
3150
3150
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
R
7
= -2
1.8
2.1
2.4
2.6
2.9
3.0
22.2
22.2
21.5
19.6
17.1
14.2
11.3
17.1
12.2
8.0
4.6
1.8
0.4
2.2
3.7
5.1
3.3
Reakcje w podporach
sprężystych
M
17
=
-113
Stan realizacji
i profil geotechniczny
±0.00
-3.00
-6.80
-10.20
-15.00
Pg, I
L
= 0.30
Gp (+H), I
L
= 0.35
Pd, I
D
= 0.45
Ps, I
D
= 0.65
q = 10 kPa
zwg
1
2
3
4
5
6
-8.9
-8.5
S=207.8 kN/m
R
17
= S
=207.8
δ
x17
= 1.0
7. Etap III
Wyniki obliczeń
M [kNm/m]
R [kN/m]
δ [kNm/m]
δ
x1
=-1.6
94.1
180.6
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
2.9
23.5
47.1
55.7
64.4
73.0
81.7
45.2
Wykres odporu
gruntu
e
III
p
[kPa]
Odpór
Siły skupione
E
III
pi
[kN]
0.7
12.0
23.2
34.6
44.8
Schemat statyczny
i obciążenia
Obciążenie
P
III
xi
= E
i
+ E
wi
– P
I
xi
- P
II
xi
- E
III
pi
[kN]
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
4.8
6.0
7.2
12.9
20.2
23.0
25.9
28.7
31.5
34.4
37.2
29.5
31.2
32.8
34.5
36.1
37.1
38.1
35.7
36.7
37.7
38.7
39.6
40.6
41.6
42.6
43.5
22.3
Parcie
Siły skupione
E
i
[kN]
0.6
2.4
3.6
0.2
3.0
5.5
8.0
10.5
13.0
15.5
18.0
14.4
10.8
7.2
3.6
0.5
19
20
21
22
23
24
25
26
27
28
29
30
31
R
7
≈ 0.0
R
7
= 15
M
23
=249
δ
x22
= 4.2
Reakcje graniczne
R
gri
= E
III
pi
- E
i
- E
wi
[kN]
±0.00
-3.00
-6.80
-10.20
-15.00
Pg, I
L
= 0.30
Gp (+H), I
L
= 0.35
Pd, I
D
= 0.45
Ps, I
D
= 0.65
q = 10 kPa
zwg
1
2
3
4
5
6
-8.9
-11.5
-12.5
Stan realizacji
i profil geotechniczny
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
45000
45000
45000
45000
45000
2.6
21.0
40.1
43.6
43.7
47.2
47.8
30.7
10.5
0.3
0.9
1.8
2.1
1.5
1.8
2.1
2.4
2.6
2.9
3.0
22.2
22.2
21.5
19.6
17.1
14.2
11.3
Reakcje gran.
R
gri
= -R
i
(IIa)
[kN]
17.1
12.2
8.0
4.6
1.8
32
22500
M
11
= -18
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
1.6
0.7
12.0
23.2
34.6
23.4
1.6
3.2
2.8
Reakcje w podporach
spręzystych
R
II
i
[kN]
32
wydłużenie obudowy
o 0.5 m
2.1
1.5
1.8
2.1
2.4
2.6
2.9
3.0
22.2
22.2
21.5
19.6
17.1
14.2
11.3
17.1
12.2
8.0
4.6
1.8
8. Superpozycja wyników obliczeń
OBUDOWA WYKOPU KOTWIONA - SUPERPOZYCJA MOMENTÓW ZGINAJĄCYCH
Nr
zagłęb.
Wartości momentów zginających
Superpozycja
Obwiednia
Obwiednia x 1.25
węzła
z
Etap I Etap Ia Etap II Etap IIa Etap III
E I+Ia
E I+Ia+II EI+Ia+II+IIa
EI+Ia+II+IIa+III
Mmin
Mmax
Mmin
Mmax
[m ppt] [kNm/m]
[kNm/m]
[kNm/m]
[kNm/m]
[kNm/m]
[kNm/m] [kNm/m]
[kNm/m]
[kNm/m]
[kNm/m]
[kNm/m]
[kNm/m]
[kNm/m]
1
0,0
0,0
0,0
0,0
0,0
0,0
0,0
0,0
0,0
0,0
0,0
0,0
0,0
0,0
2
0,5
0,0
-1,0
0,0
0,0
0,0
-1,0
-1,0
-1,0
-1,0
-1,0
0,0
-1,3
0,0
3
1,0
-2,0
-4,0
1,0
0,0
0,0
-6,0
-5,0
-5,0
-5,0
-6,0
-2,0
-7,5
-2,5
4
1,5
-5,0
-13,0
6,0
0,0
0,0
-18,0
-12,0
-12,0
-12,0
-18,0
-5,0
-22,5
-6,3
5
2,0
-11,0
-30,0
15,0
0,0
-2,0
-41,0
-26,0
-26,0
-28,0
-41,0
-11,0
-51,3
-13,8
6
2,5
-20,0
-56,0
33,0
0,0
-5,0
-76,0
-43,0
-43,0
-48,0
-76,0
-20,0
-95,0
-25,0
7
3,0
-32,0
-94,0
63,0
-1,0
-8,0 -126,0
-63,0
-64,0
-72,0
-126,0
-32,0
-157,5
-40,0
8
3,5
-51,0
-60,0
110,0
-5,0
-12,0 -111,0
-1,0
-6,0
-18,0
-111,0
-1,0
-138,8
-1,3
9
4,0
-77,0
-31,0
160,0
-9,0
-15,0 -108,0
52,0
43,0
28,0
-108,0
52,0
-135,0
65,0
10
4,5 -105,0
-6,0
205,0
-14,0
-17,0 -111,0
94,0
80,0
63,0
-111,0
94,0
-138,8
117,5
11
5,0 -134,0
16,0
240,0
-20,0
-18,0 -118,0 122,0
102,0
84,0
-134,0
122,0
-167,5
152,5
12
5,5 -159,0
34,0
264,0
-27,0
-18,0 -125,0 139,0
112,0
94,0
-159,0
139,0
-198,8
173,8
13
6,0 -179,0
50,0
274,0
-35,0
-17,0 -129,0 145,0
110,0
93,0
-179,0
145,0
-223,8
181,3
14
6,5 -195,0
64,0
269,0
-45,0
-14,0 -131,0 138,0
93,0
79,0
-195,0
138,0
-243,8
172,5
15
7,0 -207,0
77,0
248,0
-56,0
-10,0 -130,0 118,0
62,0
52,0
-207,0
118,0
-258,8
147,5
16
7,5 -204,0
81,0
220,0
-79,0
6,0 -123,0
97,0
18,0
24,0
-204,0
97,0
-255,0
121,3
17
8,0 -189,0
79,0
182,0 -113,0
32,0 -110,0
72,0
-41,0
-9,0
-189,0
72,0
-236,3
90,0
18
8,5 -168,0
73,0
133,0
-67,0
77,0
-95,0
38,0
-29,0
48,0
-168,0
48,0
-210,0
60,0
19
9,0 -143,0
64,0
69,0
-31,0
130,0
-79,0
-10,0
-41,0
89,0
-143,0
89,0
-178,8
111,3
20
9,5 -116,0
54,0
0,0
-4,0
181,0
-62,0
-62,0
-66,0
115,0
-116,0
115,0
-145,0
143,8
21
10,0
-90,0
44,0
-69,0
16,0
219,0
-46,0 -115,0
-99,0
120,0
-115,0
120,0
-143,8
150,0
22
10,5
-66,0
33,0 -127,0
31,0
241,0
-33,0 -160,0
-129,0
112,0
-160,0
112,0
-200,0
140,0
23
11,0
-45,0
24,0 -163,0
37,0
249,0
-21,0 -184,0
-147,0
102,0
-184,0
102,0
-230,0
127,5
24
11,5
-29,0
17,0 -169,0
37,0
241,0
-12,0 -181,0
-144,0
97,0
-181,0
97,0
-226,3
121,3
25
12,0
-17,0
11,0 -153,0
33,0
212,0
-6,0 -159,0
-126,0
86,0
-159,0
86,0
-198,8
107,5
26
12,5
-9,0
6,0 -125,0
26,0
170,0
-3,0 -128,0
-102,0
68,0
-128,0
68,0
-160,0
85,0
27
13,0
-3,0
3,0
-91,0
19,0
124,0
0,0
-91,0
-72,0
52,0
-91,0
52,0
-113,8
65,0
28
13,5
-1,0
1,0
-57,0
12,0
78,0
0,0
-57,0
-45,0
33,0
-57,0
33,0
-71,3
41,3
29
14,0
0,0
2,0
-28,0
6,0
38,0
2,0
-26,0
-20,0
18,0
-26,0
18,0
-32,5
22,5
30
14,5
0,0
0,0
-8,0
2,0
10,0
0,0
-8,0
-6,0
4,0
-8,0
4,0
-10,0
5,0
31
15,0
0,0
0,0
0,0
0,0
0,0
0,0
0,0
0,0
0,0
0,0
0,0
0,0
0,0
Siły w zakotwieniach [kN/m]
7
3,0
184,8
20,0
-2,0
0,0 184,8 204,8
202,8
202,8
184,8
204,8
231,0
256,0
17
8,0
207,8
15,0
207,8
222,8
207,8
222,8
259,8
278,5
Obudowa kotwiona
Obwiednia momentów M [kNm/m]
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
-250
-200
-150
-100
-50
0
50
100
150
200
po Etapie I
po Etapie Ia
p Etapie II
po Etapie IIa
po Etapie III
R
1
=204,8 kN/m
R
2
=222,8
kN/m
Opracowanie: dr inż. Adam Krasiński
Katedra Geotechniki i Geologii Stosowanej PG