土压力计算
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本工程场地平坦,经过与类似工程的比较,土体上部底面超载20kPa;假定支护墙面垂直光滑,故采用郎肯土压力理论计算,计算土压力时首先要确定土压力系数,主动土压力系数和被土压力系数的计算分式分别如下[2]:
主动土压力系数:
o 2a tan (45/2)K ϕ=- 被动土压力系数:
2p (tan 45/2)K ϕ=︒+ 其中:
a K ——主动土压力系数; p K ——被动土压力系数;
ϕ——土的摩擦角。
()12210111011222222
218tan 45tan
450.756
2220
20.756202015.12
2200 1.50.75620
15.1210tan 45tan 450.704
222K kPa
P K c kPa P K z c kPa
K P K z c ϕσσγϕγ︒⎛⎫⎛
⎫=︒-=︒-= ⎪ ⎪⎝⎭⎝
⎭==-=⨯-⨯==-=+⨯⨯-⨯=︒⎛⎫⎛
⎫=︒-=︒-= ⎪ ⎪⎝⎭⎝⎭
=-()()()222
3223
331332
200.70421511.09
2200 1.5
00.60.704215
11.0921.5tan 45tan 450.463
222200 1.500.60.463211 5.722kPa
P K z c kPa
K P K z c kPa P K z γϕγγ+⨯-⨯=-=-=+⨯+⨯⨯-⨯=-︒⎛⎫⎛
⎫=︒-=︒-= ⎪ ⎪⎝⎭⎝⎭
=-=+⨯+⨯⨯-⨯-=-4224441442223.082118.09825tan 45tan 450.406
22249.850.406227.514.796288.610.406227.50.94c kPa
K P K z c kPa P K z c kPa
ϕγγ=-⨯=︒⎛⎫⎛
⎫=︒-=︒-= ⎪ ⎪⎝⎭⎝⎭
=-=⨯-⨯=-=-=⨯-⨯=
5225551552622666130tan 45tan 450.333
22288.610.3332029.507288.610.5142029.5079tan 45tan 450.729
22288.6K P K z c kPa P K z c kPa
K P K z c ϕγγϕγ︒⎛⎫⎛
⎫=︒-=︒-= ⎪ ⎪⎝⎭⎝
⎭=-=⨯-⨯==-=⨯-⨯⨯=︒⎛⎫⎛
⎫=︒-=︒-= ⎪ ⎪⎝⎭⎝
⎭=-
=662722777177210.72923013.352146.030.72923055.2112tan 45tan 450.656
222146.030.65623539.1652192.720.656235
kPa P K z c kPa
K P K z c kPa P K z c γϕγγ⨯-⨯==-=⨯-⨯=︒⎛⎫⎛
⎫=︒-=︒-= ⎪ ⎪⎝⎭⎝
⎭=-=⨯-⨯⨯==-=⨯-⨯69.794kPa
=
828881882929991992tan 450.583
22192.720.58323558.8752252.420.58323593.68tan 450.295
22252.420.2952074.46K P K z c kPa P K z c kPa
K P K z c kPa P K ϕγγϕγγ⎛
⎫=︒-= ⎪⎝
⎭=-=⨯-⨯⨯==-=⨯-⨯⨯=⎛
⎫=︒-= ⎪⎝
⎭=-=⨯-⨯⨯=
=102101010110102112112252.420.2952074.46tan 450.361
22252.420.361229.855.3042820.820.361229.8260tan 450.472
2z c kPa
K P K z c kPa P K z c kPa
K ϕγγϕ-=⨯-⨯⨯=⎛
⎫=︒-= ⎪⎝⎭
=-=⨯-⨯==-=⨯-⨯=⎛
⎫=︒-= ⎪⎝
⎭1111111112122121212111222820.820.472253.5313.91821238.720.472253.5511.167tan 450.523
221238.720.523263556.752P K z c kPa P K z c kPa
K P K z c kPa P K γγϕγ=-=⨯-⨯⨯==-=⨯-⨯=⎛
⎫=︒-= ⎪⎝
⎭=-=⨯-⨯=
=213213131311313221581.820.5232631327.063tan 450.361
221581.820.361229.8535.21722150.220.361229.81275.962z c kPa
K P K z c kPa P K z c kPa γϕγγ-=⨯-⨯=⎛
⎫=︒-= ⎪⎝⎭
=-=⨯-⨯⨯==-=⨯-⨯=
被动土压力
,2,2tan 452a i pk i p i P K z c K γϕ=+⎛
⎫=︒+ ⎪
⎝
⎭
()(),—kPa ()pk p i i i P i K i c i kPa ϕ︒式中:
支护结构内侧,第层土中计算点的被动土压力强度标准值;
—第层土的被动土压力系数;
、—第层土的粘聚力、内摩擦角;
8228881882922999199221015.25tan 45tan 45 1.7138
222421.912524.22733tan 45tan 45 3.392
222856.22856.2tan 45K P K z c kPa P K z c kPa
K P K z c kPa P K z c kPa
K ϕγγϕγγ︒⎛⎫⎛
⎫=︒+=︒+= ⎪ ⎪⎝⎭⎝⎭=+==+=︒⎛⎫⎛
⎫=︒+=︒+= ⎪ ⎪⎝⎭⎝⎭=+==+==
︒1021010110102112211111111111228tan 45 2.7698222798.3222372.6821tan 45tan 45 2.1172221893.3622778.05P K z c kPa
P K z c kPa
K P K z c kPa P K z c kPa
K ϕγγϕγγ︒⎛⎫⎛⎫+=︒+= ⎪ ⎪⎝⎭⎝⎭=+==+=︒⎛⎫⎛⎫=︒+=︒+= ⎪ ⎪⎝⎭⎝⎭=+==+
=12221212121121221322131313113
13218.25tan 45tan 45 1.91192222542.5323198.5028tan 45tan 45 2.76982224480.502P K z c kPa P K z c kPa
K P K z c kPa P K z c ϕγγϕγγ︒⎛⎫⎛⎫=︒+=︒+= ⎪ ⎪⎝⎭⎝⎭=+==+=︒⎛⎫⎛⎫=︒+=︒+= ⎪ ⎪⎝⎭⎝⎭=+==+6054.85kPa
=