﻿ 基于位移与应变场的滑坡体时空形变特征研究
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 大地测量与地球动力学  2023, Vol. 43 Issue (5): 498-504  DOI: 10.14075/j.jgg.2023.05.011

引用本文

CAO Dongdong. Spatial and Temporal Characteristics of the Deformation Field of Landslide Mass Based on Displacements and Strain Fields[J]. Journal of Geodesy and Geodynamics, 2023, 43(5): 498-504.

第一作者简介

CAO Dongdong, senior engineer, majors in dynamic deformation monitoring of high-risk deformed bodies, E-mail: 153101080@qq.com.

文章历史

1. 中煤西安设计工程有限责任公司，西安市雁塔路北段66号，710054

1 应变模型 1.1 小变形条件下的应变模型

 $\left\{\begin{array}{l} u_x^0=u_x+\frac{\partial u_x}{\partial x} \Delta x+\frac{\partial u_x}{\partial y} \Delta y \\ v_y^0=v_y+\frac{\partial v_x}{\partial x} \Delta x+\frac{\partial v_x}{\partial y} \Delta y \end{array}\right.$ (1)

1.2 有限变形条件下的应变模型

 $\overrightarrow {OP} = \mathit{\boldsymbol{r}}(\Delta x, \Delta y)$ (2)

 $\left\{\begin{array}{l} u(P)=u(O)+\frac{\partial u_x}{\partial x} l|\boldsymbol{r}|+\frac{\partial u_x}{\partial y} m|\boldsymbol{r}| \\ v(P)=v(O)+\frac{\partial v_x}{\partial x} l|\boldsymbol{r}|+\frac{\partial v_x}{\partial y} m|\boldsymbol{r}| \end{array}\right.$ (3)

$\overrightarrow {OP'}$为变形后的$\overrightarrow {OP}$，则有：

 $\begin{gathered} \left|\overrightarrow{O P^{\prime}}\right|=[\Delta x+u(P)-u(O)]^2+ \\ {[\Delta y+v(P)-v(O)]^2} \end{gathered}$ (4)

 $\begin{gathered} (1+e)^2=\left[\left(1+\frac{\partial u}{\partial x}\right) l+\frac{\partial u}{\partial y} m\right]^2+ \\ {\left[\frac{\partial v}{\partial x} l+\left(1+\frac{\partial v}{\partial y}\right) m\right]^2} \end{gathered}$ (5)

 $\begin{gathered} e+\frac{1}{2} e^2=\left\{\frac{\partial u}{\partial x}+\frac{1}{2}\left[\left(\frac{\partial u}{\partial x}\right)^2+\left(\frac{\partial v}{\partial x}\right)^2\right]\right\} l^2+ \\ {\left[\frac{\partial u}{\partial y}+\frac{\partial v}{\partial x}+\left(\frac{\partial u}{\partial x} \frac{\partial u}{\partial y}+\frac{\partial v}{\partial x} \frac{\partial v}{\partial y}\right)\right] l m+} \\ \left\{\frac{\partial v}{\partial y}+\frac{1}{2}\left[\left(\frac{\partial u}{\partial y}\right)^2+\left(\frac{\partial v}{\partial y}\right)^2\right]\right\} m^2 \end{gathered}$ (6)

 $\left\{\begin{array}{l} \varepsilon_x=\frac{\partial u}{\partial x}+\frac{1}{2}\left[\left(\frac{\partial u}{\partial x}\right)^2+\left(\frac{\partial v}{\partial x}\right)^2\right] \\ \varepsilon_y=\frac{\partial v}{\partial y}+\frac{1}{2}\left[\left(\frac{\partial u}{\partial y}\right)^2+\left(\frac{\partial v}{\partial y}\right)^2\right] \\ \gamma_{x y}=\frac{\partial u}{\partial y}+\frac{\partial v}{\partial x}+\left(\frac{\partial u}{\partial x} \frac{\partial u}{\partial y}+\frac{\partial v}{\partial x} \frac{\partial v}{\partial y}\right) \end{array}\right.$ (7)

 $e+\frac{1}{2} e^2=\varepsilon_x l^2+\gamma_{x y} l m+\varepsilon_y m^2$ (8)
2 滑坡体时空变形特征分析 2.1 区域概况

 红色矢量为滑坡的主滑动轴方向; 黑色折线为支挡墙; 红色三角形标记为在滑坡上设置的变形监测点 图 1 坡体位移监测点位置分布 Fig. 1 Spatial distribution of displacement monitoring points on the slope

 图 2 位移速率时间序列 Fig. 2 Time series of displacement rate

 图 3 滑坡体滑动前的旋转应变与水平速度场 Fig. 3 Rotation strain rate and horizontal velocity field before the slide

 图 4 滑坡体滑动前最大、最小主应变分布 Fig. 4 Distribution of the maximum and minimum principle strain before the slide

 图 5 滑坡体失稳阶段位移速率分布 Fig. 5 Displacement rates in the stage of sliding

 图 6 滑坡失稳阶段最大、最小主应变分布 Fig. 6 Maximum and minimum principle strain in the stage of sliding

 图 7 滑坡体滑动后的旋转应变与水平速度场 Fig. 7 Rotation strain rate and horizontal velocity field on the slope after the slide

 图 8 滑后调整阶段的最大、最小主应变分布 Fig. 8 Distribution of the maximum and minimum principle strain after the slide
2.2 滑前演化阶段

2.3 滑动失稳阶段

2.4 滑后调整阶段

3 讨论

4 结语

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Spatial and Temporal Characteristics of the Deformation Field of Landslide Mass Based on Displacements and Strain Fields
CAO Dongdong1
1. China Coal Xi'an Design Engineering Co Ltd, 66 North-Yanta Road, Xi'an 710054, China
Abstract: We take a landslide near Libi coal mine in Qinshui county, Shanxi province as an example to carry out high-precision deformation monitoring for almost one year. By constructing strain models under small deformation conditions and finite deformation conditions, we study the spatial and temporal characteristics of the deformation field of the target landslide at different stages before, during and after sliding. Through analysis of the maximum and minimum principal strain fields, we find that the retaining wall of Libi coal mine before anchor cable reinforcement still has about 40% inhibitory effect on the accelerated sliding of the early landslide front. The compressive impact between the landslide front and the retaining wall has obvious spatiotemporal inhomogeneity, that is, the direction and strength of principal compressive strain between them have obvious spatiotemporal variations. The local strong strain anomaly of the landslide may be a significant indicator of the structural failure of the monitoring target. The local strong tensile deformation at 830 m contour in the study area on December 13, 2020, has good correspondence with a transverse 10-20 cm wide cracking on the slope. Under the steady-state background where the overall migration and relative deformation of the landslide are small, the occurrence and development of cracks on the slope surface indicate that the failure and development of the landslide are still continuous. In the post-sliding adjustment stage, the deformation mode of the whole landslide, especially the trailing edge where sliding occurs, is quite complex, and it also experiences compression deformation and tension deformation with similar strength. The landslide, after 3 months, was not completely stable, and only a local sliding trend like the direction of the original main sliding axis was initially formed in the middle part of the trailing edge.
Key words: landslide; small deformation; finite deformation; maximum and minimum principal strain; spatial and temporal characteristics