Analysis of deformation of linear viscoelastic two layered laminated rocks

Abstract

Underground excavations in laminated rocks pose interesting challenges in terms of stress analysis considering the long-term viscoelastic (VE) response. While the VE response of such rocks are well understood, long term response of such structures are normally not carried out considering the computational complexity. This research work attempts to relook at this classical problem from the perspective of elastic-viscoelastic correspondence principle. A laminated roof with two horizontal rock laminae has been considered in this study. Four different VE models such as Maxwell, Kelvin, standard linear solid and Burgers’ models have been used for these two layers and closed form solutions for mid-point deflections for all the cases (single and double) have been derived.Using realistic material properties, simulations have been carried out for deflections for all the possible cases. The interesting possibilities of attachment and detachment amongst the two roof layers have been identified. For the case of relative placement of beams represented by Maxwell and standard linear solid model, the results showed either the attachment or the detachment of the beams throughout the simulation period. However, when both the beams have been represented by the Kelvin models with distinct parameters, till time about 20.7 years, the upper beam has been found to deflect more than the lower beam and beyond this, the trend gets reverse.