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3 分析原理
Janbu法是一种既满足力和力矩平衡条件,又可用于任何形状的滑动面的较精确的方法,其特点是假定条块间水平作用力的位置。因而每个条块都满足全部静力平衡条件和极限平衡条件,滑动体的整体力矩平衡条件也得到满足。
计算中考虑最复杂的情况。即计算块体为多地层,同时有地震力和地下水作用,从而比一般的计算公式考虑更为全面。从滑体中取出任意条块i进行分析,Janbu法条块作用力分析见图1。
![img](https://epubservercos.yuewen.com/809E9A/21277078701910206/epubprivate/OEBPS/Images/txt014_1.jpg?sign=1739522448-68dwIxjCrrQAthhq0Vwb4nnUivWlLLf8-0-6291264229f8691a474ea0cf67db9dcd)
图1 Janbu法条块作用力分析图
图中,条块的侧面分别有法向力Pi、Pi+1和切向力Hi、Hi+1,hi、hi+1为法向力到滑面底的距离。则根据图1有以下推导:
![img](https://epubservercos.yuewen.com/809E9A/21277078701910206/epubprivate/OEBPS/Images/txt014_2.jpg?sign=1739522448-KwiIRantpX1mZ5WKmcmEVdHWuZYFnsiX-0-df72bd6986f6b06074471039ff68fecf)
其中
![img](https://epubservercos.yuewen.com/809E9A/21277078701910206/epubprivate/OEBPS/Images/txt014_3.jpg?sign=1739522448-B5PSHCAPWqch4ovxZ2EYqwn1IxpLiyvE-0-5a511462f6e8dfe13dab5e17c7039d92)
由∑Fy=0,得:
![img](https://epubservercos.yuewen.com/809E9A/21277078701910206/epubprivate/OEBPS/Images/txt014_4.jpg?sign=1739522448-C4MBSN5p6aLoRaGfTfe6BwIxSa1iITCv-0-13e07d80a6c668a193c7ef2503196548)
由极限平衡条件,设稳定系数为Fs,则有:
![img](https://epubservercos.yuewen.com/809E9A/21277078701910206/epubprivate/OEBPS/Images/txt014_5.jpg?sign=1739522448-cpPm9KkWK0KVAb1srpxy54cAl0wJrERb-0-14144924638e456cd0f8ee33d7b74a81)
从而可得到
![img](https://epubservercos.yuewen.com/809E9A/21277078701910206/epubprivate/OEBPS/Images/txt014_6.jpg?sign=1739522448-PyOMZvDtzBPsA2PEZ7gOh5aJbvDV5uhM-0-018b9f53f07fa7e299a71ab709bb3da3)
对条块侧面的法向力P,显然P1=ΔP1,P2=ΔP2+P1=ΔP1+ΔP2,以此类推,若有n条块,则
![img](https://epubservercos.yuewen.com/809E9A/21277078701910206/epubprivate/OEBPS/Images/txt014_7.jpg?sign=1739522448-QEY8mlwzKPygYjxpx7H6623d9A8l5RB4-0-15ebeac11446e8a7c139bb754f068ef6)
式(6)代入式(5)得到
![img](https://epubservercos.yuewen.com/809E9A/21277078701910206/epubprivate/OEBPS/Images/txt014_8.jpg?sign=1739522448-ZHYMkLJBd79j6askkJnKyIsipQbquvWs-0-b7fc360fdc2590a97d0347c985aa5926)
其中。
由于ΔH未知,对滑面中点取矩∑Mi=0,则得到
![img](https://epubservercos.yuewen.com/809E9A/21277078701910206/epubprivate/OEBPS/Images/txt014_10.jpg?sign=1739522448-rzTLT0cnCYnYWW0yX1XQvWdL7xsnqwUO-0-c96839e9629464f7abf292022fe177c9)