In Figure 1 active earth pressure for partially submerged sand and surcharge is shown. The height of the wall is Z and the position of the water table is at a depth of Z_{1} and the surcharge acting at the top of horizontal surface of the wall is q. The height of the wall below water table is Z_{2}. The unit weight of the sand above water table is Î³_{t} and that below water table is Î³_{sat.}

**CASE 1**

Consider a depth z, such that z is less than Z_{1}. Then the earth pressure at depth z is given by:

P_{Z} = K_{a}(Î³_{t}z + q)

When, z = Z_{1}, P_{Z1} = K_{a}(Î³_{t}Z_{1} + q)

**Case 2**

Consider a depth z, such that z is greater than Z_{1}. Then the earth pressure at depth z is given by:

P_{z} = K_{a}[Î³_{t}Z_{1} + Î³_{sat}(z-Z_{1}) + q]

When, z = Z_{1 } P_{Z1} = K_{a}[Î³_{t}Z_{1} + q]

When, Z = Z_{1} + Z_{2}, P_{Z} = K_{a}Î³_{t}Z_{1} + K_{a}Î³_{sat}Z_{2} + K_{a}q

P_{Z} = [K_{a}Î³_{t}Z_{1 } + K_{a}(Î³_{sub} + Î³_{W})Z_{2} + K_{a}q]

P_{Z} = [K_{a}Î³_{t}Z_{1} + K_{a}Î³_{sub}Z_{2} + K_{a}Î³_{W}Z_{2} + K_{a}q]

As shear strength of water is zero, then value of K_{a} in the third term of the above equation is unity. Hence,

P_{Z} = [K_{a}Î³_{t}Z_{1} + K_{a}Î³_{sub}Z_{2 }+ Î³_{W}Z_{2} + K_{a}q]

The following condition can exist.

**Soil is dry or moist and no surcharge**

In this case, depth Z_{2} = 0, Z_{1} = Zand q = 0. Hense,

P_{a }= K_{a}Î³_{t}Z

**Soil is completely submerged and no surcharge**

In this case, depth Z_{1} = 0, Z_{2} = Z and q = 0. Hence,

P_{a} = K_{a}Î³_{sub}Z + Î³_{W}Z_{2}

**Soil is dry or moist and carries surcharge**

In this case, depth Z_{2} = 0 and Z_{1} = Z. Hence,

P_{a} = K_{a}Î³_{t}Z+ K_{a}q

**Soil is completely submerged and no surcharge**

In this case, depth Z_{1} = 0, Z_{2} = Z and q = 0. Hence,

P_{a} = K_{a}Î³_{sub}Z + Î³_{W}Z + K_{a}q

**Effect of soil stratification**

If the backfill comprises two or more soil strata, then the top strata acts as a surcharge for the subsequent lower strata,