北京建筑大学学报
北京建築大學學報
북경건축대학학보
Journal of Beijing University of Civil Engineering and Architecture
2015年
3期
27-32
,共6页
张进凡%戚承志%潘越峰%陈昊祥
張進凡%慼承誌%潘越峰%陳昊祥
장진범%척승지%반월봉%진호상
二维模型%非均匀土层%衰减%相对位移
二維模型%非均勻土層%衰減%相對位移
이유모형%비균균토층%쇠감%상대위이
2-D model%non-homogeneous soil stratum%attenuation%relative displacement
研究了非均匀土层自由场地震动的二维简化模型. 取非均匀土层剪切模量沿深度按幂函数变化( G=G0ΖP ,其中G0 和P为常数) . 首先,利用弹性波动理论,得到土介质的二维波动方程;再采用分离变量法来求解该方程,根据波的衰减特性确定波沿水平方向衰减系数,得到水平分量的解析解;然后,将水平分量的解析解带入原二维波动方程组中,将原二维波动方程组转化为一维形式.再利用MATLAB计算软件计算出其数值解;最后,通过具体算例,分别对研究的二维简化模型与一维剪切梁模型进行比较.
研究瞭非均勻土層自由場地震動的二維簡化模型. 取非均勻土層剪切模量沿深度按冪函數變化( G=G0ΖP ,其中G0 和P為常數) . 首先,利用彈性波動理論,得到土介質的二維波動方程;再採用分離變量法來求解該方程,根據波的衰減特性確定波沿水平方嚮衰減繫數,得到水平分量的解析解;然後,將水平分量的解析解帶入原二維波動方程組中,將原二維波動方程組轉化為一維形式.再利用MATLAB計算軟件計算齣其數值解;最後,通過具體算例,分彆對研究的二維簡化模型與一維剪切樑模型進行比較.
연구료비균균토층자유장지진동적이유간화모형. 취비균균토층전절모량연심도안멱함수변화( G=G0ΖP ,기중G0 화P위상수) . 수선,이용탄성파동이론,득도토개질적이유파동방정;재채용분리변량법래구해해방정,근거파적쇠감특성학정파연수평방향쇠감계수,득도수평분량적해석해;연후,장수평분량적해석해대입원이유파동방정조중,장원이유파동방정조전화위일유형식.재이용MATLAB계산연건계산출기수치해;최후,통과구체산례,분별대연구적이유간화모형여일유전절량모형진행비교.
In this paper the simplified 2-D model for determination of free field seismic motion of non-homogeneous soil stratum is studied. The variation of shear modulus of non-homogeneous soil along the depth is taken in a power function (G=G0ΖP, G0 and P for the constant). Firstly, the two-dimensional wave equation of the soil is obtained by using the theory of elastiodynamics. The variable separation method is used to solve the equation. According to the attenuation properties of wave propagation to infinity the wave attenuation coefficient along the horizontal direction is determined. And the analytical solution of horizontal component is obtained. Then the solution of horizontal component was substituted into the original two-dimensional motion equation and the two-dimensional motion equation is transformed into one-dimensional motion equation. The numerical solution is obtained by using MATLAB codes. Finally an numerical example is given to compare the 2-D model and 1-D model.
