Free-Boundary Seepage from Asymmetric Soil Channels
We present an inverse method for the study of the seepage from soil channels without lining. We give integral representations of the complex potential, velocity field, stream lines, free phreatic lines, and contour of the channel by means of Levi-Civita's function 𝜔. For different values of the Taylor coefficients of 𝜔, we calculate numerically the contour of the channel, the phreatic lines, the seepage loss, the velocity field, the stream lines, and the equipotential lines. Examples are given for various symmetric or asymmetric channels, with smooth contours or with angular points.
Analytical determination of seeping soil slopes of a constant exit gradient
Soil slopes satisfying the condition of a constant exit gradient (constant Darcian velocity) and the seepage face (isobaricity) condition are found by complex analysis. For an empty drainage trench, soil is infinitely deep and the flow domain is bounded by two branches of a phreatic surface and the trench contour. The problem is solved by conformal mapping of the Zhukovskii domain (half-plane) onto the hodograph domain (lune). The ultimately stable seepage face and the inflow rate are determined as functions of a specified exit gradient. With decreasing of the gradient the trench flattens. If the gradient is 1, the depth-width aspect ratio of the trench reaches 0.21. Similar conformal mapping of a lune in the hodograph plane on a half-strip in the complex potential plane is used to solve the problem of a phreatic surface flow from a soil channel, whose equipotential contour satisfies the condition of constant entrance gradient. For a dam slope, the flow domain is underlain by an impermeable bottom and the hodograph is a circular triangle with a unit-gradient circle as the slope image. The Polubarinova-Kochina method of analytical differential equations is modified to reconstruct the complex coordinate and the complex potential as a function of an auxiliary variable. The resulting slope of unit exit gradient has a depth-width ratio of 1.22.
Centrifuge modelling of effects of shield tunnels on existing tunnels in soft clay
With the rapid development of the subway network,the phenomena of shield tunnels going across the adjacent tunnels are becoming more and more common.The interaction between shield tunneling and nearby tunnels is more complicated than the ordinary shield tunneling in intact soil strata.Based on the project of Shanghai Bund Passage crossing Metro Line 2,the method of centrifuge modeling together with the field measurement is employed to study the effects shield tunneling on nearby strata and existing tunnels.In centrifugal model tests,the effects simulation techniques considering the unloading of excavation,ground loss and grouting are developed to analyze the longitudinal settlement of the shield tunnel and the existing tunnel induced by the shield tunneling.Besides,the deformation distribution and settlement curves of the existing tunnels during shield construction are studied by using the monitoring data.