As anisotropic granular materials

soil’s dynamic characteristics depend on the stress path. Foundation soil is in heart-shaped line rotation stress path of the maximum shear stress space under train load. Yet it is not reported that the heart-shaped line stress path is imitated in laboratory test. The simplified form of the soil’s dynamic response is proposed

which is justified by analyzing the stress path of foundation soil caused by train load. For imitating the stress characteristics produced by train load

the loading methods of three types of hollow cylindrical apparatus (HCA) are derived: (1) The two-directional vibration HCA can achieve the heart-shaped line stress path by determining the forms of axial force and torque. The variation of spherical stress p is similar to the load waveform of axial force. When the internal pressure is equal to external pressure

the variation of coefficient of intermediate principal stress b will like cosine curve. (2) When the three-directional vibration HCA imitates stress characteristics produced by train load

p can remain unchanged or b can be kept at the constant of 0.5. (3) With the control of the axial force

torque as well as the internal and external pressures

the four-directional vibration HCA can imitate stress characteristics of the foundation soil under train load. By setting a constant b

the linear relationship between p and q can be realized. Besides the constraint conditions on loading parameters are derived

under which the normal stress in soil is compressive stress and the direction of intermediate principal stress is kept at the diametrical direction all along.