岩土力学
巖土力學
암토역학
ROCK AND SOIL MECHANICS
2013年
4期
1001-1008
,共8页
饱和黏弹性土%球空腔%分数导数%稳态振动%解析解
飽和黏彈性土%毬空腔%分數導數%穩態振動%解析解
포화점탄성토%구공강%분수도수%은태진동%해석해
saturated viscoelastic soil%spherical cavity%fractional derivative%steady-state vibration%analytical solution
将土骨架视为具有分数阶导数本构关系的黏弹性体,基于 Biot 两相饱和介质模型,建立具有球形空腔饱和分数导数黏弹性土体稳态振动的控制方程.通过引入势函数,得到球对称情形下具有球形空腔饱和分数导数黏弹性土体的位移、应力和孔隙流体压力等解析表达式.考察分数导数模型参数和饱和土参数等对土体振动特性的影响,结果表明,流体压缩性对饱和土体的动力特性有显著影响,而土骨架压缩性和流-固耦合系数的影响相对较小;分数导数阶数对土体动力特性的影响与材料参数比的取值有关.同时,边界不排水条件下饱和土体的动力响应大于排水条件下饱和土体的动力响应.
將土骨架視為具有分數階導數本構關繫的黏彈性體,基于 Biot 兩相飽和介質模型,建立具有毬形空腔飽和分數導數黏彈性土體穩態振動的控製方程.通過引入勢函數,得到毬對稱情形下具有毬形空腔飽和分數導數黏彈性土體的位移、應力和孔隙流體壓力等解析錶達式.攷察分數導數模型參數和飽和土參數等對土體振動特性的影響,結果錶明,流體壓縮性對飽和土體的動力特性有顯著影響,而土骨架壓縮性和流-固耦閤繫數的影響相對較小;分數導數階數對土體動力特性的影響與材料參數比的取值有關.同時,邊界不排水條件下飽和土體的動力響應大于排水條件下飽和土體的動力響應.
장토골가시위구유분수계도수본구관계적점탄성체,기우 Biot 량상포화개질모형,건립구유구형공강포화분수도수점탄성토체은태진동적공제방정.통과인입세함수,득도구대칭정형하구유구형공강포화분수도수점탄성토체적위이、응력화공극류체압력등해석표체식.고찰분수도수모형삼수화포화토삼수등대토체진동특성적영향,결과표명,류체압축성대포화토체적동력특성유현저영향,이토골가압축성화류-고우합계수적영향상대교소;분수도수계수대토체동력특성적영향여재료삼수비적취치유관.동시,변계불배수조건하포화토체적동력향응대우배수조건하포화토체적동력향응.
Regarding the soil skeleton as a viscoelastic medium with fractional derivative constitutive relation, the governing equations of the steady state vibration of the saturated fractional derivative viscoelastic soil embedded a spherical cavity are established based on the Biot’s theory. The analytical expressions of the displacements, stresses and pore water pressure of the saturated fractional derivative viscoelastic soil with a spherical cavity are obtained with the introduction help of potential functions in case of spherical symmetry. The influences of the parameters of fractional derivative model and saturated soil on the vibration characteristics of the soil are examined;and the numerical results show that the fluid compressibility has a great influence on the dynamic characteristics;while the influences of the soil skeleton compressibility and fluid-solid coupling coefficient are trivial. The influence of the fractional derivative order on the dynamic behavior of the soil depends on the values of material parameter ratio. Furthermore, the dynamic responses of the saturated soil with undrained boundary condition are greater than those with the drained boundary condition.