Calculate the vertical stress increase expected 20 m under

Question

Problem 1:

Calculate the vertical stress increase expected 2.0 m under the ground surface, under the centre of a rigid 2m by 2m footing resting on the soil surface if the total contact load the footing places on the soil is 80kN.

Problem 2:

A rigid square 2m by 2m footing rests on the soil surface, the total contact load the footing places on the soil is 40kN. Calculate the vertical stress increase expected:

(a) 2m below the soil surface and under the centre of the footing

(b) 4m below the soil surface and 6m horizontally from the centre of the footing

(c) 7m below the soil surface and 6m horizontally from the centre of the footing.

Problem 3:

A 2m x 2m footing on the ground surface applies a total contact load of 40kPa to the soil beneath. Find the increase in soil pressure such a footing causes:-

(a) Under the centre of the footing (Ans: Ds_Z = 3.4kPa)

(b) Under the middle of one side of the footing (Ans: Ds_Z = 2.46kPa)

(c) At a point 2m away from the footing and in line with one edge of the footing. (Ans: Ds_Z = 20Pa)

Problem 4:

A concrete pad footing is 2.5m x 2.5m in plan. It sits on the ground surface. The soil below is a 1.5m layer of dense well graded gravely sand (g_S =18kN/m³) overlying a uniform layer of normally consolidated clay 3m thick (g_Csat =20kN/m³). Under the clay layer is bedrock. The watertable is 1.5m below the ground surface, that is, at the top of the clay layer.

A test trench was excavated and samples were taken from the mid-height of the clay layer to conduct the oedometer test. The test was carried out and data analysed to prepare an e-logp' graph and the slope of the Normal Consolidation Line (NCL). The slope of the NCL is the Compression Index, C_C = -0.36 in this case.

Determine the amount of footing settlement expected when:

(a) the contact pressure under the footing is 200kPa

(b) the contact pressure under the footing is 400kPa

Problem 5:

A square footing has sides of 1.5m, the embedment depth D_f is 1.20m.

The foundation soil is a stiff clay with unit weight g₁=g₂ =18.9kN/m³

Tests on the soil were conducted to determine cohesion. The unconfined compression strength of the soil obtained from tests was  s₁ =144kN/m²

The water table is more than 2B below the footing contact surface.

Find the ultimate bearing capacity on the foundation soil and the allowable footing contact pressure using a Factor of Safety of 3.

Problem 6:

A circular footing has a diameter of 1.52m, the embedment depth D_f is 1.22m.

The foundation soil is a dense soil with unit weight g₁=g₂ =20.1kN/m³

Tests on the soil were conducted to strength parameters. These gave ∅= 25° and cohension c=48.0 kPa.

The water table is more than 2B below the footing contact surface.

Find the ultimate bearing capacity on the foundation soil and the allowable footing contact pressure using a Factor of Safety of 3. Calculate the allowable footing contact force.

Answer 1

For the following numerical problem discussion, solve each part of the question by applying the appropriate principles and concepts to comprehend the solution. Problem 1: Compute the vertical stress increase expected 2.0 m in the ground surface, under the centre of a rigid 2m by 2m footing resting on the soil surface if the net contact loads the footing places on the soil will be 80kN. Problem 2: A stiff square 2m by 2m footing rests on the soil surface, the net contact load the footing places on the soil is 40kN. Compute the vertical stress increase anticipated: a) 2m beneath the soil surface and in the centre of the footing. b) 4m beneath the soil surface and 6m horizontally from the centre of the footing. c) 7m beneath the soil surface and 6m horizontally from the centre of the footing.