地震作用下岩质边坡预应力锚索动力响应解析解

doi:10.12068/j.issn.1005-3026.2025.20239064

摘要/Abstract

摘要：

为明确地震作用下岩质边坡预应力锚索的动力响应，提出了一套危岩体-锚索自由段-边坡结构面-锚索锚固段-基岩协同作用的锚索动力计算模型，得到了锚索动力响应解析解.通过离心机模型试验验证了锚索动力计算模型的准确性，并根据工程案例进行了关键参数分析.结果表明：地震圆频率的增加可引发边坡共振效应，锚索自由段轴力增量峰值显著增大.随着基岩剪切模量增大，锚固界面的弹簧刚度与阻尼系数增大，锚索动力响应的轴向传递受限，锚固段顶端承担更大的剪应力增量.结构面的阻尼比和基岩的泊松比对锚索自由段的轴力增量及锚固段的内力增量分布影响较小，锚索抗震设计时可不作为重点关注对象.研究结果可为预应力锚索的动力分析与抗震设计提供理论基础.

关键词: 预应力锚索, 岩质边坡, 地震作用, 动力响应, 解析解

Abstract:

In order to clarify the dynamic response of prestressed anchor cable in rock slope under earthquake， a set of anchor cable dynamic calculation models based on the synergistic action of dangerous rock mass， free section of anchor cable， slope structural plane， anchorage section of anchor cable and bedrock is proposed， and the analytical solution of dynamic response of anchor cable is obtained. The accuracy of the anchor cable dynamic calculation model is verified by the centrifuge model test， and the key parameters are analyzed according to an engineering case. The results show that the increase of seismic circular frequency can trigger the slope resonance effect， and the peak value of axial force increment in the free segment of anchor cable increases significantly. With the increase of bedrock shear modulus， the spring stiffness and damping coefficient of the anchorage interface increase， the axial transmission of the dynamic response is limited， and the top of the anchorage segment undertakes a larger shear stress increment. The damping ratio of the structural plane and the Poisson’s ratio of the bedrock have little influence on the axial force increment of the free segment and the internal force increment distribution in anchorage segment of the anchor cable， so these parameters are not taken as the key object in seismic design of the anchor cable. The research results can provide theoretical basis for dynamic analysis and seismic design of prestressed anchor cable.

Key words: prestressed anchor cable, rock slope, earthquake, dynamic response, analytical solution

中图分类号:

TU 435

高幸, 贾金青, 张丽华, 涂兵雄. 地震作用下岩质边坡预应力锚索动力响应解析解[J]. 东北大学学报（自然科学版）, 2025, 46(5): 134-144.

Xing GAO, Jin-qing JIA, Li-hua ZHANG, Bing-xiong TU. Analytical Solution of Dynamic Response of Prestressed Anchor Cable in Rock Slope Under Earthquake[J]. Journal of Northeastern University(Natural Science), 2025, 46(5): 134-144.

图/表 14

图1 预应力锚索支护边坡示意图

Fig.1 Schematic diagram of prestressed anchor cable supporting slope

图2 锚固边坡振动体系的动力学计算模型

Fig.2 Dynamic calculation model of anchored slope vibration system

图3 预应力锚索单锚结构动力计算模型

Fig.3 Dynamic calculation model of single anchor structure of prestressed anchor cable

图4 锚固微元段受力简图

Fig.4 Force diagram of the anchoring micro-section

图5 离心机模型试验示意图(单位：mm)

Fig.5 Schematic diagram of centrifuge model test

表1 材料物理力学参数

Table 1 Physical and mechanical parameters

名称

材料

密度/

(kg·m^-3)

图6 模型计算锚索轴向应力与离心机模型试验对比（a）—30 g-8度上部；（b）—30 g-8度中部；（c）—30 g-8度下部；（d）—30 g-9度上部；（e）—30 g-9度中部；（f）—30 g-9度下部；（g）—40 g-8度上部；（h）—40 g-8度中部；（i）—40 g-8度下部；（j）—40 g-9度上部；（k）—40 g-9度中部；（l）—40 g-9度下部.

Fig.6 Comparison of axial stress calculated by dynamic model and centrifuge model test

表2 计算参数

Table 2 Calculation parameters

锚固段

长度/m

孔径/m

自由段弹性

模量/GPa

图7 锚固段内力的动力响应（a）—轴力增量分布；（b）—剪应力增量分布.

Fig.7 Dynamic response of internal forces in anchorage segment

图8 不同圆频率对自由段轴力影响（a）—自由段轴力响应；（b）—轴力放大系数.

Fig.8 Influence of different circular frequencies on axial force in free segment

图9 不同结构面刚度对自由段轴力影响（a）—自由段轴力响应；（b）—轴力放大系数.

Fig.9 Influence of different structural plane stiffness on axial force in free segment

图10 不同结构面阻尼比对自由段轴力影响（a）—自由段轴力响应；（b）—轴力放大系数.

Fig.10 Influence of different structural plane damping ratios on axial force in free segment

图11 不同剪切模量下锚固段内力增量峰值及影响系数（a）—轴力增量峰值；（b）—剪应力增量峰值；（c）—影响系数.

Fig.11 Peak increment of internal forces and influence coefficient in anchorage segment under different shear modulus

图12 不同泊松比下锚固段内力增量峰值及影响系数（a）—轴力增量峰值；（b）—剪应力增量峰值；（c）—影响系数.

Fig.12 Peak increment of internal forces and influence coefficient in anchorage segment under different Poisson’s ratios

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