Prediction of water flow into rock tunnels: an analytical solution assuming an hydraulic conductivity gradient

A solution is obtained for predicting tunnel water inflows for the commonly observed case of an exponential decrease of hydraulic conductivity with depth. The analytical solution is applicable to the prediction of ubiquitous inflows from a jointed rock mass, and the risk of major isolated inflows from singular conductors such as faults must be separately evaluated.The predictions are verified by finite-element modelling and compared with published inflows for tunnels in a variety of rock conditions. The new solution predicts the commonly observed trend that inflows at first increase then decrease as a tunnel goes deeper, rather than continue to increase as predicted by Goodman's solution where the hydraulic conductivity is assumed constant. Goodman's solution can underestimated inflow by 30% or overestimate it by an order of magnitude, depending on the depth at which hydraulic conductivity is measured.Upper and lower bound predictions corresponding to extreme values of stress-independent factors such as an increase of joint spacing with depth are examined for a range of typical tunnel characteristics. The differences are found to be insignificant when the hydraulic conductivity gradient A is small, but increase to 30% A = 0.01. An]estimate mid-way between upper an lower bound values gives a maximum prediction error of about ±15% which is likely to be adequate in most practical applications.The analytical and finite element models of both predict that inflows are insensitive to tunnel diameter (maximum 2% increase in flowrate per metre increase in diameter). This agrees with the observation that inflows during the driving of a full-bore tunnel can be similar to those from a pilot tunnel or exploratory drillhole ahead of the face.