The pressure sensitivity of rock elastic properties and seismic velocities is dependent upon pore space, grain size, grain sorting and cementation. An increasing effective pressure gradually reduces the throats between pore. It forces closure of compliant pores with low aspect ratio and reduces porosity. It also changes contact configuration that brings more cement in load bearing network. Present study models stress dependent velocity changes through this mechanical rearrangement of pore and contact system.
Although a granular rock is likely to have pore with a spectrum of aspect ratio, we put forward the concept of an ‘effective aspect ratio’ that simulates the rock elastic behavior. Such ratio can be inverted through effective medium solution. It is observed that the effective aspect ratio increases with increasing pressure due to gradual closure of compliant pores having low aspect ratio. This inturn reflects into stress sensitivity of velocities. Using dry core measurements of shear and compression velocities on variety of sandstone under multi-pressure conditions, the validity of proposal is demonstrated.
The present work also suggests a stress dependent matrix shear modulus. It accounts for the changing inter-granular frictional force and grain slippage/rotation tendencies, and varying cement contacts in matrix network. It is concluded that matrix shear modulus is significantly affected under low to moderate stress conditions, while changes are small in well cemented granular rocks. The varying aspect ratio and matrix shear modulus can be represented by uniform power laws and govern the changing velocities. It provides a rock intrinsic view to explain the stress dependent elastic behavior and is found applicable to sandstone with different cementation and porosity.
