Example Problem

Example Problem: A concrete dam is built over an isotropic sand layer with a permeability of $k = 4 \times 10^{-5} \, m/s$. The water depth upstream is $12 \, m$, and downstream is $2 \, m$. A flow net is drawn with $4$ flow channels ($N_f = 4$) and $10$ equipotential drops ($N_d = 10$). Calculate the seepage loss per meter length of the dam in $m^3/day/m$.

Example Problem 2: Consider an anisotropic soil deposit under a dam. The horizontal permeability is $4.0 \times 10^{-3} \, cm/s$ and the vertical permeability is $1.0 \times 10^{-3} \, cm/s$. The total head loss across the structure is $6 \, m$. After applying the coordinate transformation for an isotropic flow net, the transformed flow net has 4 flow channels and 12 equipotential drops. Calculate the total seepage rate per meter length of the dam.

Example Problem 3: A concrete dam is constructed with a cut-off wall (sheet pile) at the heel. The total head loss across the dam is $8 \, m$. A flow net is drawn with 5 flow channels and 15 equipotential drops. A critical equipotential line passes just beneath the toe of the dam. The soil has a saturated unit weight of $20 \, kN/m^3$, and the length of the flow path at the exit element is $1.2 \, m$. Calculate the factor of safety against boiling at the toe.