地下结构平面问题简化人工边界侧向宽度设置研究

Determination of the width of simplified lateral boundaries in the plane problem of underground structures

地下结构抗震分析中一个重要问题就是人工边界的处理。为了简化计算,从理论上分析了平面问题侧向边界采用竖向约束、水平自由的合理性,并且为了研究侧向边界宽度的影响因素及其影响程度,通过典型案例,采用动力时程法分析了在地震荷载下土体阻尼比、结构尺度、地震波特性、土体非线性等对边界宽度的影响程度。结果表明:土体阻尼比和土体非线性对边界宽度具有类似的影响,土体阻尼比越大、非线性程度越高所需的侧向边界宽度越小,但阻尼比超过一定值、非线性达到一定程度后,对侧向边界宽度的影响并不明显;结构尺度对边界宽度有影响,结构尺度越大所需边界宽度越宽;地震波的频谱特性和持续时间影响较大。

The fictionally truncated boundary must be treated properly in the seismic analysis of underground structures.In order to simplify the calculation,simplified lateral boundary,with vertical constraints and horizontal freedom,is a good choice.Based on the plane problem,a simplified lateral boundary was derived as if it was subjected to a far field shear stress state,and the rationality of the simplified lateral boundary was analyzed theoretically.Then the performance and width of the lateral boundary were evaluated through several selected benchmark numerical examples,namely the homogeneous soil layer,general thickness layered soil and thick layered soil.There are many factors influencing the width of the lateral boundary,such as the soil damping ratio,structure's scale,seismic characteristics and soil nonlinearity,whose influential degrees were studied through the dynamic time history method.It is shown that in general,the soil damping ratio and soil nonlinearity have similar effects on the width of the boundary,that is,the larger the damping ratio or the soil nonlinearity,the smaller the needed lateral boundary width,while the trend will be not too obvious when the large soil damping ratio and strong soil nonlinearity exceed a certain degree.It is also found that the structure's scale has some influence on the width of the boundary,that is,larger size structure requires wider boundary width.The spectrum characteristics and the duration of seismic wave have great ereffect on the width of lateral boundary.