Experimental Study on Coefficient Value of Subgrade Reaction in Seismic Analysis of Underground Structures
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摘要: 在对地下结构进行抗震分析时，基床系数的准确性直接决定了反应位移法的计算精度. 针对基床系数相关研究的不足，提出了一种拟静力试验法，自主研发了大型拟静力模型箱，围绕砂土场地开展了有无轴压两组试验;在此基础上，提出了基床系数沿深度修正法，并进行了算例验证. 结果表明：水平基床系数随推覆水平的增大而减小，随土层深度的增大而增大；附加应力对基床系数取值存在较大影响；采用修正基床系数可显著提高反应位移法的计算精度，较规范中基床系数静力有限元法，地下结构弯矩误差最大可由16.7%降低至9.1%，顶底板相对位移的计算误差可由35.0%降低至18.8%，验证了该新型室内基床系数测试方法的可行性及基床系数沿深度修正法的合理性.Abstract: In seismic analysis of underground structures, the precision of the coefficient of subgrade reaction directly determines the accuracy of response displacement method. Considering the deficiencies of relevant research on the coefficient of subgrade reaction, a quasi-static test method was proposed, a large quasi-static model box was developed, and two groups of tests with and without axial load in sandy soil were carried out. On this basis, a correction method for the coefficient of subgrade reaction along depth is proposed and verified by an example. Results indicate that the horizontal coefficient of subgrade reaction decreases with an increase in the pushover level and increases with the soil depth. Moreover, the additional stress has great influence on the coefficient value; using modified coefficient can significantly improve the accuracy of the response displacement method. Compared with the result adopting the coefficient in terms of static finite element method in the code, the maximum bending moment error of the underground structure can be reduced from 16.7% to 9.1%, and the relative displacement error between roof and floor can be reduced from 35.0% to 18.8%. Thus, the feasibility of the new coefficient measuring method and the rationality of the coefficient modified method are validated.
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表 1 深度修正系数
Table 1. Depth correction factor
工况 埋深/mm 300 600 900 1 200 1 500 Ⅰ 0.848 0.888 1 1.183 1.457 Ⅱ 0.866 0.967 1 1.062 1.131 
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表 2 两种方法所得基床系数值
Table 2. Coefficient values of subgrade reaction by two methods
MN•m−3 反向位移法 侧边基床系数 顶部基床系数 底部基床系数 正向 切向 正向 切向 正向 切向 1 33.5 23.8 12.4 13.7 56.9 43.5 2 11.1～55.3 7.9～39.3 12.4 13.7 56.9 43.5
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表 3 地下结构地震反应计算结果
Table 3. Seismic response calculation results of underground structure
方法类型 弯矩/（kN•m） 弯矩误差/% 顶底板相对位移/mm 位移误差/% 点 A 点 B 点 A 点 B 动力时程分析 347.5 340.6 4.144 反应位移法 1 291.8 16.0 283.7 16.7 2.694 35.0 反应位移法 2 315.3 9.3 309.6 9.1 3.366 18.8
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