[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? ,\FJVS;NeJ  
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Who can explain that in theory? Welcome to discuss and comment! p6yC1\U!o  
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I will set up the question series in numerical analysis. HZ1e~IIw  
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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。 ?v>!wuiP  
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。 2<Tbd"x?  
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. )oJn@82C|  
算例一:平面应变问题的稳定性; {(@M0?  
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. 5}S~8  
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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。 YCBp]xuE  
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" {tKi8O^Rb  
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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. E]MyP=g$  
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How's the shear affect?  As "geofem" said  that is "three-dimensional effect'. How is the "three-dimensional effect'?  1r:i'cWh  
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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 Q[6<Y,}(pd  
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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, pw, <0UhV  
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which cause bigger displacements.  Is this one of  three-dimensional effects? P#j>
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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? h*lU&8)m\  
My english is poor , could you understand what i write above? dN)@/R^E;  
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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.  0(h'ZV  
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Hope some help!