Active Earth Pressure for Partially submerged Sand with Surcharge

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What is Active Earth Pressure for Partially submerged Sand with Surcharge?

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 Z1 and the surcharge acting at the top of horizontal surface of the wall is q. The height of the wall below water table is Z2. The unit weight of the sand above water table is \gamma_t and that below water table is \gamma_{sat}.

rankine's active earth pressure in partially submerged sand

CASE 1 | Active Earth Pressure for Partially submerged Sand with Surcharge

Consider a depth z, such that z is less than Z1. Then the earth pressure at depth z is given by:

P_Z = K_a(\gamma_tz+q)

When, z = Z_1, P_{Z_1} = K_a(\gamma_tZ_1 + q)

Case 2 for Partially submerged Sand with Surcharge

Consider a depth z, such that z is greater than Z1. Then the earth pressure at depth z is given by:

P_z = K_a[\gamma_tZ_1 + \gamma_{sat}(z-Z_1)+q]

When, z = Z_1, P_{Z_1} = K_a(\gamma_tZ_1 + q)

When, Z = Z_1 + Z_2, P_Z = K_a\gamma_tZ_1 + K_a\gamma_satZ_2 + K_aq

P_Z = [K_a\gamma_tZ_1 + K_a(\gamma_{sub} + \gamma_w)Z_2 + K_aq]

P_Z = [K_a\gamma_tZ_1 + K_a\gamma_{sub}Z_2 + K_a\gamma_wZ_2 + K_aq]

As shear strength of water is zero, then value of Ka in the third term of the above equation is unity. Hence,

P_Z = [K_a\gamma_tZ_1 + K_a\gamma_{sub}Z_2 + \gamma_wZ_2 + K_aq]

The following condition can exist.

Soil is dry or moist and no surcharge

In this case, depth Z2 = 0, Z1 = Zand q = 0. Hence,

K_a\gamma_tZ

Soil is completely submerged and no surcharge

In this case, depth Z1 = 0, Z2 = Z and q = 0. Hence,

P_a = K_a\gamma_{sub}Z + \gamma_wZ_2

Soil is dry or moist and carries surcharge

In this case, depth Z2 = 0 and Z1 = Z. Hence,

P_a = K_a\gamma_tZ + K_aq

Soil is completely submerged and no surcharge

In this case, depth Z1 = 0, Z2 = Z and q = 0. Hence,

P_a = K_a\gamma_{sub}Z+\gamma_wZ + K_aq

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.

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