球面波加载下黄土线黏弹性本构关系

Linear viscoelastic constitutive relation of loess under spherical stress wave

采用0.125 g TNT当量的微型炸药球作为爆炸源,利用在Φ1 370 mm×1 200 mm黄土样品180～1 280 m.kt-1/3范围内实测球面波径向粒子速度数据为基础,结合强间断波相容条件及变模量本构模型假设,反演得到黄土的弹性模量E=(1.927±0.216)GPa、体积模量K=(1.284±0.144)GPa及剪切模量G=(0.771±0.086)。把黄土视为线黏弹性ZWT(朱-王-唐)材料进行数值模拟,以实测粒子速度幅值vmax、位移幅值umax及对应时刻作为数值模拟结果的对比参数,定义了误差函数,其极小值对应的松弛剪切模量GM=0.13 GPa、松弛因子θM=21μs,将GM、θM作为黄土黏弹性本构参数的描述对球面波在黄土中的传播进行了数值模拟,结果表明:模拟得到的粒子速度曲线与试验曲线吻合较好,粒子速度幅值vmax、位移幅值umax与试验结果的最大偏差分别为8%、6%;粒子速度、位移幅值对应时刻与试验结果的最大偏差分别为1%、5%;数值模拟得到不同比距离处的径向应力σr、切向应力σθ、径向应变εr、切向应变εθ与基于强间断及变模量模型假设得到的结果具有较好的一致性。

Using miniature spherical explosive of 0.125 g TNT equivalent as explosion source and based on the observed velocities of radial particles of Φ 1 370 mm×1 200 mm loess sample at 180-1 280 m·kt-1/3,the elastic modulus E=（1.927±0.216） GPa,bulk modulus K=（1.284±0.144） GPa and shear modulus G=（0.771±0.086） GPa are inverted by combining the assumption of strong discontinuous wave and variable modulus model.Assuming the loess as linear viscoelastic ZWT material for numerical simulation,the error function is defined using the particle velocity vmax,the particle displacement umax,and the corresponding time of vmax and umax obtained from the numerical simulation and experimental results respectively.When the error function gets minimum value,the relaxation shear modulus GM and the relaxation factor θM are 0.13 GPa and 21 μs respectively.Using GM and θM as the linear viscoelastic ZWT parameters,the numerical simulation of spherical stress wave propagation in loess is made.The results reveal that： the velocity curves obtained from the numerical simulation are consistent with the experimental results;the maximum deviations of vmax and umax are 8% and 6% respectively;the maximum deviations of the corresponding time of vmax and umax are 1% and 5% respectively;the radial stress σr,the tangential stress σθ,the radial strain εr,the tangential strain εθ obtained from the numerical simulation are in good agreement with the results obtained from the assumption of strong discontinuity and variable modulus model.