Reply to the discussion by Chen et al. on “Wetting front advancing column test for measuring unsaturated hydraulic conductivity”Appears in Canadian Geotechnical Journal, 47(10): 1159–1161.

Abstract

The authors appreciate R. Chen, Z.H. Li, and J.H. Li for their interest in and valuable thoughts about the paper. Our paper presents an efficient method for measuring unsaturated hydraulic conductivity of soil. The proposed method utilizes water contents recorded at one monitoring section to calculate the hydraulic conductivity with the help of instantaneous wetting front advancing velocity. In the new method, a wetting zone (i.e., the zone between the monitoring section and the wetting front) is assumed to advance a distance of Dh in a small time step of Dt. In the wetting zone, the water content contours are assumed to be stationary. In this small time step, the water content change in the wetting zone is assumed to be very small compared with the water content change due to the advancement of the wetting zone, namely QB calculated using eq. [8] in Li et al. (2009). As mentioned in the Discussion, the water content profile advances along the soil column in a way similar to wave propagation. Such propagation is under constant boundary conditions both at the front and back of the wetting zone. In our experiments and the simulations in the Discussion, the water content at the front of the wetting zone is lower than the residual water content and the hydraulic conductivity at the front of the wetting zone is extremely low (e.g., lower than 10–13 m/s). Hence, the boundary conditions (i.e., the water content, suction, and hydraulic conductivity along the advancing path) at the front of the wetting zone are considered to be unchanged in the small time step. However, the boundary conditions at the back of the wetting zone vary during the wetting process. Consider a wetting zone with a suction equivalent to the air-entry value (AEV) at the back. If the wetting front advances a distance of Dh in Dt, the change in suction at the back of the wetting zone will be Du = gwDh where gw is the unit weight of water. The relative change of suction will then be Du/AEV. If the testing material is a coarse sand or gravel, the AEV is usually small and Du/AEV could be large. Such a large change induced by gravity in the boundary condition at the back of the wetting front will change the wetting front advancing process. For example, in the capillary experiment conducted on GW-GM with sand, the observed wetting front could only reach 113 mm above the water table. This is because the dominant pores in the GW-GM with sand are large, i.e., above 1 mm (Zhang and Li 2010). Similar problems should be considered in the numerical simulation of flow in uniform sand. Referring to Fig. D1 in the Discussion, the AEV of the uniform sand is about 3 kPa (i.e., 300 mm water head). During the capillary rise process, the final water content in a wetted section of the sand column will decrease gradually when the height is above 300 mm, approaching the water content at the hydrostatic state. Hence, the boundary condition at the back of the wetting zone changes during the capillary process. For such a soil, the wetting front advancing experiment should be carried out in a horizontal soil column, in which the effect of gravity on the boundary condition is less significant. For clays, the AEV values are likely high (say, above 100 kPa or 10 000 mm head); the change of suction, Du, at the back of the wetting zone is negligible. In this case, the boundary condition at the back of the wetting zone can be considered to be constant. Referring to Fig. D2 in the Discussion, the wetting front advancing velocities are indeed different if different water contents are used to define the wetting front. Let us consider the wetting front advancing velocities in silty clay in Fig. D2 at any instant. The slopes of the three curves may differ by 2 times at >3 104 s. That is to say, the calculated hydraulic conductivity may differ within 2 times when different definitions of the wetting front are used. The error is in reality much smaller when a consistent set of definitions is followed. Considering the high variability of soil hydraulic conductivity, such an error may be considered acceptable in engineering practice. Received 31 May 2010. Accepted 16 August 2010. Published on the NRC Research Press Web site at cgj.nrc.ca on 1 October 2010.