This paper discusses the multi-level cyclic triaxial testing of bimsoils (block-inmatrix soils), which are chaotic, mechanically and/or spatially heterogeneous geological masses in geotechnical construction. The cyclic triaxial tests simulate the behavior of bimsoil material under varying number of passing vehicle wheels. It is found that the applied confining pressure alters the stress state of the tested bimsoil and a transmission from strain softening to strain hardening occurs. The bimsoil deformation, strength, fatigue life, and stiffness are improved as the ambient pressure increases. The strain rate analysis reveals that the strong volumetric dilatancy occurs earlier for a bimsoil under relatively low confining pressure. Post-test CT scanning shows the mesoscopic structural changes inside the bimsoil, including the multiple interface cracking behaviors and crack propagation surrounding the rock blocks. It is suggested that the contact, interlocking, occlusion, and separation among the existing blocks greatly contribute to the volume dilatancy characteristics of bimsoil under high ambient pressure.