chapter  5
56 Pages

## Water Flow in Slopes

I. Water Balance on Slopes............................................ 164 II. Moisture Conditions in Slopes ................................... 165

A. Topographical Effects on Moisture Condition .... 165 B. Slope Failures and Moisture Conditions ............ 168

III. Infiltration into Slopes ............................................... 172 A. Potential Profiles During Infiltration

into Slopes............................................................ 172 B. Flux During Infiltration into Slopes................... 175 C. Equation of Flow ................................................. 178 D. Infiltration into Layered Slopes ......................... 183

1. Behavior of Wetting Front in a Layered Slope................................................ 183

2. Cessation of Wetting Front at Inclined Interface ........................................................ 183

IV. Causes of Surface Runoff............................................ 187 A. Infiltration Capacity and Horton Overland

Flow on a Slope.................................................... 187 B. Return Flow......................................................... 189 C. Crust Formation.................................................. 191 D. Ponding Time on Slopes...................................... 196

V. Subsurface Flow of Water in Slopes ............................ 198 A. One-Dimensional Steady Flow in Slopes ............. 198

1. Water Flow in Uniform Slopes ....................... 198 2. Water Flow in Layered Slopes........................ 201

B. Two-Dimensional Behavior of Water in Slopes .... 204 1. Distribution of Flux ........................................ 204 2. Refraction in Layered Slopes ......................... 206 3. Mathematical Models ..................................... 209

C. Subsurface Flow During Long-Term Drainage in Slopes ................................................ 214

References............................................................................ 216

I. WATER BALANCE ON SLOPES

Water balance is defined as the quantitative relation among integrated input (Qin), output (Qout), and storage (DS) in a given space and a given time, and is described by

Qin Â¼ Qout Ã¾S (5:1) The required space for defining a water balance is generally called the representative element volume (REV). When the REV is given along a slope, as shown in Figure 5.1, the water balance is

P Ã¾ Ir Ã¾ Rin Ã¾ Lin Â¼ (E Ã¾ T Ã¾ Rout Ã¾ Lout Ã¾Qd) Ã¾ (S1 Ã¾S2) (5:2)

where the input is composed of the precipitation, P, the quantity of irrigation, Ir, the inflow of surface water, Rin, and the lateral inflow of soil water, Lin; the output is composed of evaporation, E, transpiration, T, surface runoff, Rout, lateral outflow of soil water, Lout, and downward drainage, Qd. The change of storage is composed of two terms, surface storage, DS1, and subsurface storage, DS2.