﻿ 深基坑开挖引起邻近地下管线位移的两阶段法
 上海理工大学学报  2019, Vol. 41 Issue (5): 479-484 PDF

Two-Stage Method on the Displacement of Underground Pipelines Caused by Excavation of Deep Foundation Pit
LIU Xiaobing, CHEN Youliang, MENG Weibo
School of Environment and Architecture, University of Shanghai for Science and Technology, Shanghai 200093, China
Abstract: Aiming at the displacement of underground pipelines caused by excavation of deep foundation pit, the algorithm for the displacement of the surrounding free soil caused by excavation was proposed based on the two-stage method. Combined with Winkler elastic foundation beam model, the equations for calculating the vertical and horizontal displacement of underground pipelines subjected to additional deformation of soil unloading are established. The displacement of underground pipeline was solved by finite difference method. Then the two-stage method was applied to an engineering example. The results show that the theoretical calculation is in good agreement with the data measured in field. Thus, the rationality and usability of the two-stage method has been verified. The method presented in this paper can be used for analysis of the influences of pipelines buried depth, distance between pipelines, and soil properties on the deformation of pipelines.
Key words: Winkler model     two-stage method     underground pipeline     displacement     finite difference method

1 基坑开挖引起周围地下管线位移的两阶段法分析

1.1 作用在管线上的竖向附加应力

 ${\omega _{\rm v}}\left(\! {x,y,0} \right) \!=\! \left\{ \begin{array}{l} {\omega _{{\rm v},\;\max }}\left( {x/H + 0.5} \right) {{\rm{e}}^{ - {\text{π}} {{\left({y/A} \right)}^2}}}\\ \quad\left( {0 \!<\! x \!\leqslant\! 0.5H} \right) \\ {\omega _{{\rm v},\;\max }}\left( { - 0.6x/H + 1.3} \right) {{\rm{e}}^{ - {\text{π}} {{\left( {y/A} \right)}^2}}}\!\!\!\\ \quad\left( {0.5H \!<\! x \!\leqslant\! 2H} \right) \\ {\omega _{{\rm v},\;\max }}\left( { - 0.05x/H + 0.2} \right) {{\rm{e}}^{ - {\text{π}} {{\left( {y/A} \right)}^2}}}\!\!\!\\ \quad\left( {2H \!<\! x \!\leqslant\! 4H} \right) \\ \end{array} \right.$ (1)

 $A = L \left( {0.069\ln (H/L) + 1.03} \right)/2$

 ${\omega _{\rm v}}\left( {x,y,z} \right) = \left\{ \begin{array}{l} {\omega _{\rm v}}\left( {x,y,0} \right)\left( {1.54{{\rm e}^{ - z/3x}} - 0.54} \right)\\ \quad\left( {0 < x \leqslant 0.5H} \right) \\ {\omega _{\rm v}}\left( {x,y,0} \right)\left( { - 0.6z/x + 1} \right)\\ \quad\left( {0.5H < x \leqslant 1.5H} \right) \\ {\omega _{\rm v}}\left( {x,y,0} \right)\left( { - 1.5z/x + 1} \right)\\ \quad\left( {x > 1.5H} \right) \\ \end{array} \right.$ (2)

 ${q_1} = {K_{\rm v}}{\omega _{\rm v}}= {K_0}D{\omega _{\rm v}}$ (3)

 ${K_0} = \frac{{0.65{E_{\rm s}}}}{{1 - {{v^2_{\rm s}}}}}{\left(\frac{{{E_{\rm s}}{D^4}}}{{EI}}\right)^{\frac{1}{12}}}$ (4)

Vesic公式是基于置于地表的弹性地基梁提出的，没有考虑埋深对地基竖向机床系数的影响。俞剑等[12]改进了Vesic的地基基床系数，可以考虑地基土埋深的影响，本文将地下管线看做埋于地下的弹性地基梁，因此俞剑等[12]提出的模型公式更为符合本文实际情况，公式如下：

 ${K_0} = \frac{{3.08{E_{\rm s}}}}{{\eta {{(1 - {v^2_{\rm s}})}}}}{\left(\frac{{{E_{\rm s}}{D^4}}}{{EI}}\right)^{\frac{1}{8}}}$ (5)

1.3 作用在管线上的水平附加应力

 $y' = a{x^2} + bx + c$ (14)

 $\left\{ \begin{array}{l} x = 0,\;y' = \delta \\ x = L,\;y' = 0 \\ x = - L,\;y' = 0 \\ \end{array} \right.$ (15)

 $y' = - \frac{\delta }{{{L^2}}}{x^2} + \delta$ (16)

 ${q_1} = {K_{\rm h}}y'$ (17)

 ${q_1} = {K_{\rm h}}\left( - \frac{\delta }{{{L^2}}}{x^2} + \delta \right)$ (18)
1.4 地下管线的水平方向变形理论

 $EI\frac{{{d^4}y}}{{d{x^4}}} + {K_{\rm h}}y - {K_{\rm h}}y' - {q_0} = 0$ (19)

2 工程实例

 图 3 管线监测点示意图 Fig. 3 Schematic diagram of pipeline monitoring points

 图 4 基坑周围管线竖向位移理论值与实测值 Fig. 4 Theoretical and measurement values for the vertical displacement of pipelines surrounding the foundation pit
3 基坑开挖引起地下管线变形的因素分析 3.1 管线埋深

 图 5 不同埋深地下管线的竖向位移情况 Fig. 5 Vertical displacements of pipelines with different depths

 图 6 埋深对地下管线的最大竖向位移的影响 Fig. 6 Influence of depth on the vertical displacement of pipelines
3.2 地下管线到基坑边缘的水平距离

 图 7 水平距离对管线最大竖向位移的影响 Fig. 7 Influence of horizontal distance on the maximum vertical distance of pipeline
3.3 地基土性质（基床系数）

 图 8 地基土基床系数对管线竖向位移的影响 Fig. 8 Influence of foundation soil coefficient of subgrade reaction on the vertical distance of pipeline
4 结　论

a. 基于Winkler弹性地基梁理论，利用两阶段法建立了受基坑开挖影响的地下管线竖向位移及水平位移方程，并通过工程实例验算，证明计算结果与现场实测的地下管线变形值基本吻合。

b. 管线竖向位移随着其埋深的增大而减小，且其减小的速度与管线埋深的增大速度不是线性关系。管线埋深越大，其最大竖向位移越小，且其随埋深的增大而减小的速率也越小。

c. 管线最大竖向位移与管线到基坑的水平距离之间的变化规律为凹槽形，即先增大后减小，当水平距离增加到一定程度后（本文为50 m），管线竖向位移趋近于零。最大竖向位移出现在水平距离0.5HH为基坑开挖深度）左右。

d. 地下管线的最大沉降值随地基土基床系数${K_{\rm{v}}}$增加而减小的，但当${K_{\rm{v}}}$增大到一定程度后(本例${K_{\rm{v}}}$=1.2×107 N/m2)，地下管线的最大沉降增加趋势趋于平稳，即${K_{\rm{v}}}$的增加对管线沉降的影响已逐渐减小。

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