[探讨]Question 1: why the displacements in 2D analysis are a little bigger than that in 3D analysis? [复制链接]

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Question 1: why the lateral displacements in 2D(plain strain) analysis are a little bigger than that in 3D analysis based on static analysis in general? 1m:XR0P  
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Who can explain that in theory? Welcome to discuss and comment! :y%/u%L  
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I will set up the question series in numerical analysis. T`\x
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Prize:flower

2D(平面应变)忽略了两个侧面上的剪应力的作用，故计算出的位移要比3D的大，在边坡中，即算的安全系数要比3D的偏小，因而2D分析是偏保守的。至于从理论上讨论，估计得从弹塑性理论上去考虑，我没有研究过，呵呵。

简单来说,２Ｄ没有空间效应。 {*0<T|<n  
就拿基坑来说，如果变长很长一般就可以不考虑空间效应；当然也可以分块开挖，分块浇筑底板，以利用空间效应。 xLNtIzx  
至于理论上，同意楼上的看法，就是３Ｄ分析考虑了相邻ｓｌｉｃｅ之间的剪切，减应力一直传递到截面变化处。

我现在做两个算例比较. \W1,F6&
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算例一:平面应变问题的稳定性; R7$:@<:g  
算例二:采用相同平面,在轴线方向拉伸后的稳定性,其中两个端面固定;

平面计算,Fs=2.2

3D计算结果,Fs=2.3

实际上当沿着轴线足够长的话,3D的稳定系数越来越接近2D问题,这在某方面说明了3D的边界效应. Ntrn("!  
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上面分析中,取分析精度Fs=0.1

geofem 兄，有个小小的问题，从你的途上可以看出潜在的滑体了，不知道在你这个软件中如何把这个滑体的地面给勾勒出来，如果能把滑体勾勒出来，进行一下3D极限平衡分析与3D有限元强度折减法计算结果的比较可能更有意义，呵呵。以前我在FLAC3D中想这么做，难度太大，没有做下去 。

用强度折减法分析边坡稳定性确实存在滑裂面难以确定的问题。一般计算结果与其说是滑裂面还不如说是滑动带比较合适。 Z28@yD+  
一般可以用J2应变，或者位移云彩图大致判断出滑裂面的位置。但是，有的土结构相互作用的例子，判断的时候就有些困难了。

Thank for "geofem" and "benjackxu" pDfF'jt9  
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In 2D plain strain analysis, it is assumed that strain in z direction is zero and shear sigma zx , sigma zy are zero. 
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How's the shear affect?  As "geofem" said  that is "three-dimensional effect'. How is the "three-dimensional effect'?  D1a2|^zt  
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For a certain work, the energy release is governed by force and displacements in three-dimensional space in reality.  In Z direction, it should be have energy AU2Nmf?]%  
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release(0.5*stress*strain^2), since strain in z direction is zero , the energy release will be zero in this direction, in other word, all the external work will be taken by the other two directions, c6.|; 4  
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which cause bigger displacements.  Is this one of  three-dimensional effects? hNfL /^w  
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Welcome more discussion!

Thanks for your explanation. Your explanation focuses on energy dissipation.Could you explain it  from  the other aspect such as analytic demonstration through plasto elasticity? 6zSN?0c  
My english is poor , could you understand what i write above? .v'8G)6g  
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The study of "three-dimensional effect" often focuses on the geometrical effect of the geologic model.

You may try to take a look Mindlin theory that explains the shear effect. There are terms(negative) from shear stresses in the displacements calculation if the strain in Z direction is not equal zero.  i[swOYz]X  
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Hope some help!