Compressibility of Soils

​Compressibility of Soils

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

• ​Compressed soil caused its volume to decrease.

• Decrease in volume leads to reduction of void ratio of the soil.

• Structurally loaded saturated soil ​can cause undue building settlement.

• ​Cohesionless soils, compresses relatively quickly and settlement will undergo during the construction phase.

• ​Cohesive soil, much more slower compression due to slow expulsion of water from the small soil pores.

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

• ​Soil deformation may occur by change in:

  • Stress

  • Water content

  • Soil mass

  • Temperature​

• The compression is caused by

  • Deformation of soil particles

  • Relocation of soil particles

  • Expulsion of water or air from the voids

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

• ​Types of settlement:

  • Immediate Elastic Settlement, S_e

  • Primary Consolidation Settlement, S_c

  • Secondary Consolidation Settlement, S_s

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​A. Immediate Elastic Settlement

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​A. Immediate Elastic Settlement

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​A. Immediate Elastic Settlement

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​A. Immediate Elastic Settlement

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

• Especially in low permeability soils (silts and clays) settlement is delayed by the need to squeeze the water out if the soil.

• Consolidation is the process of gradual transfer if an applied load from the pore water to the soil structure as pore water is squeezed out of the voids.

• The amount of water that escapes depends on the size of the load and compressibility of the soil.

• The rate at which it escapes depends on the coefficient of permeability, thickness, and compressibility of the soil.​

​B. Primary Consolidation Settlement

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

1. Normally Consolidated Clays:

​

When P_o​ = P_c

the clay is normally consolidated​

​

P_o = average effective stress at the mid-height of clay layer or sometimes it is called as geostatic pressure.

P_c = pre-consolidation pressure, that is the maximum effective pressure that the soil is subjected to in the past.​

​

​B. Primary Consolidation Settlement

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

1. Normally Consolidated Clays:

​

The primary settlement caused by consolidation is due to the slow extrusion of water from the pores of the fine particles of clay.

​B. Primary Consolidation Settlement

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

1. Normally Consolidated Clays:

​

​B. Primary Consolidation Settlement

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

1. Normally Consolidated Clays:

​

​B. Primary Consolidation Settlement

​P_o = average effective stress at mid - height of clay layer sometimes called as geostatic pressure.

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

1. Normally Consolidated Clays:

​

​B. Primary Consolidation Settlement

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

2. Over Consolidated Clays:

​

​B. Primary Consolidation Settlement

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

2. Over Consolidated Clays:

​

​B. Primary Consolidation Settlement

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

Secondary Settlement is the additional settlement that occurs at a constant value of effective stress after excess pore water pressure has been dissipated.​

Secondary Settlement is usually small compared to primary consolidation settlement.​

​

​C. Secondary Consolidation Settlement

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​C. Secondary Consolidation Settlement

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​C. Secondary Consolidation Settlement

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Effective stress at mid-height of clay layer

​a) Case (1) with uniform surcharge of 100 kPa.

​

Average increase of effective stress on clay

layer Δ​P = 100 kPa (surcharge)

​

Effective stress at mid-height of clay layer (P_o​)

P_o​ = 18(6) + (20 - 9.81)(4) + (22 - 9.81)(3)

P_o​ = 185.33 kPa

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Effective stress at mid-height of clay layer

​b) Case (2) with foundation (footing) carrying

a load 'P'​

​

​

Effective stress at mid-height of clay layer (P_o​)

P_o​ = 198() + (19 - 9.81)(3) + (20- 9.81)(4)

P_o​ = 192.33 kPa

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Average increase of effective stress on clay layer

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Average increase of effective stress on clay layer

​

​ΔP_t = the increase in the effective pressure at the top of clay layer.

Δ​P_m = the increase in the effective pressure at the middle of clay layer.

Δ​P_b = the increase in the effective pressure at the bottom of clay layer.

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Average increase of effective stress on clay layer

​For stability analysis of footings, the pressure under a footing maybe assumed to be spread out on slope at 2 vertical to 1 horizontal.

​

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Average increase of effective stress on clay layer

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Average increase of effective stress on clay layer

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Average increase of effective stress on clay layer

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Sample Problems

​1.) A normally consolidated clay layer is 8 m. thick and has an in situ void ratio of 0.862. Consolidation tests and subsequent computations indicate that the void ratio of the clay layer corresponding to the total pressure acting at the mid height of the consolidating clay layer after construction of a commercial building is 0.836. Compute the expected primary consolidation settlement.

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Sample Problems

​1.) Solution

​

​

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Sample Problems

​2.) A 2.1 m. layer of clay is buried beneath a 3 m. stratum of very compact granular soil. Compact sand underlies the clay. The layer of granular soil is composed of material having a unit weight of 20.46 kN/m³. The clay unit weight is 16.52 kN/m³. A laboratory compression test on a sample of the clay indicates a compression index of 0.40 and a natural void ratio of 1.30. A planned building loading will cause a 26.38 kPa stress increase at the middle of the clay layer.

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Sample Problems

​2.)

a. What amoun​t of primary compression occurs in the clay for the indicated conditions?

​b. How much primary compression of the clay layer would result if the groundwater table was at the ground surface (all other conditions remain the same)?

c. How much clay layer compression would occur if the clay was an over-consolidated material, the past maximum pressure was 95.94 kPa and the C_s​ value was 0.10? Assume a deep water table.

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Sample Problems

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Sample Problems

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Sample Problems

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Sample Problems

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Sample Problems

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Sample Problems

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Sample Problems

​3.) A buried clay layer has the following condition:

• The ground is very deep.

• The thickness of buried clay layer is 1.8m.

• A 2.4 m thick layer of compact sand overlies the clay layer and

  extends to the ground surface.

• A deep zone of compact sand underlies the clay layer.​

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Sample Problems

​3.) A buried clay layer has the following condition:

• The unit weight of the compact sand is 21.24 kN/m³, and the unit weight of clay is 15.74 kN/m³.

• The foundation size and loading causes a stress increase of 33.58 kPa at the center of the clay layer.

• Laboratory testing of the clay indicates the clay is normally consolidated, the soil void ratio is 1.28.

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Sample Problems

​3.) Solution:

a.​ Compute the compression index if the clay has a liquid limit of 46.66.

b. Compute the average effective stress at the mid-height of clay layer.

c. Compute the foundation​ settlement due to primary compression.

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Sample Problems

​3.a Solution:

Compression index:

C_c​ = 0.009(LL - 10)

C_c​ = 0.009(46.66 - 10)

C_c​ = 0.33

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Sample Problems

​3.b Solution:

Average effective stress at the mid-height

of clay layer.

​

P_o​ = 21.21(2.4) + 15.74(0.9)

P_o​ = 65.14 kPa

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Sample Problems

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Sample Problems

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Sample Problems

​4.) Assume a buried stratum of clay 1.83 m. thick will be subjected to a stress increase of 33.6 kPa at the center of clay. The magnitude of the pre-construction soil overburden pressure P = 48kPa at the center of the clay layer. A laboratory compression test indicates that the clay has a pre-consolidation pressure of 72 kPa. Compression index is 0.30 and the value of swell index is 0.05. Void ratio of clay is 1.50.

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Sample Problems

​4.) Solution:

a. Compute the settlement due to primary compression of clay.

b. If full consolidation settlement (primary compression settlement) will require approximately 8 years, compute the settlement due to secondary compression of clay over a period of 20 year time span. Assume secondary compression index = 0.008.

c. Estimate the total settlement to be expected over a 20 year time span considering the effects of secondary compression.​

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Sample Problems

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Sample Problems

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Sample Problems

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Sample Problems

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Sample Problems

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Sample Problems

​5.) Two footings rest in a layer of sand 2.7 m thick. The bottom of the footings are 0.90 m. below the ground surface. Beneath the sand layer is a 1.8 m clay layer. Beneath the clay layer is hard pan. The water table is at a deoph of 1.8 m. below the ground surface

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Sample Problems

​5.)

a. Compute the stress in​crease at the center of clay layer assume that the pressure beneath the footing is spread at an angle of 1 vertical to 1 horizontal.

b. Determine the size of footing B so that the settlement in the clay layer is the same beneath A and B. Footing A is 1.5 m. square​.

c. Determine the settlement beneath footing A.​

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Sample Problems

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Sample Problems

CE 52/ 421 (GEOTECHNICAL ENGINEERING I) - 1S, 2022-2023 Compressibility of Soils

​Sample Problems