Calculation of erosion mass of bentonite based on fractal model for colloids

The water inflow into the deposition holes and tunnels in a repository will mainly take place through fractures in the rock and will lead to that the buffer and backfill will be wetted and eroded. If the counter pressure and strength of the buffer or backfill are insufficiently high, piping erosion will take place. An erosion model to estimate the erosion mass (m_s) of bentonite buffer in saline solution for a certain water inflow rate during a certain time based on the fractal model for bentonite colloids is proposed as $m_{\text{s}}=\beta V_{\text{w}}{}^{\alpha }$, in terms of a power law, V_w is the accumulated volume of water flow. The exponent parameter (α) is related to the fractal dimension (D) of bentonite colloids as $\alpha =D/(6-D)$. The relationship between the erosion mass (m_s) and the accumulated volume of water flow (V_w) is verified by the experiments of MX-80 bentonite piping erosion in NaCl solutions by Börgesson et al and Suzuki et al. The fractal dimension (D) of bentonite colloids is calculated according to the small-angle X-ray scattering (SAXS) of MX-80 bentonite by Svensson & Hansen (2013).