**Problem Description:**A 6-meter thick clay layer is resting over an incompressible glacial till deposit of infinite thickness (assumed impermeable). From lab tests, the results shown in Table 1 were obtained for a sample from the midpoint of the clay layer. A 3-meter thick fill mainly comprising sandy soil is planned to be placed on top of the clay layer. The groundwater level is assumed to be at the top of the clay layer. The saturated unit weight of the clay layer and dry unit weight of the sandy layer are 20 KN/m³ and 17 KN/m³, respectively. The unit weight of water is 9.81 KN/m³.**Questions:**a. What is the ultimate settlement of the clay layer after the fill is placed?b. If the clay layer was resting on a sandy gravel layer of infinite thickness, how many years will it take to complete a settlement of 24.1 cm due to the fill?**Table 1: Soil Properties**| Preconsolidation Stress | Cc | Cr | Cv (m²/day) | e₀ ||-------------------------|-----|-----|-------------|-----|| Soil is found to be normally consolidated | 0.32 | 0.12 | 0.0021 | 0.7 |**Answer Options:**- a. 241 mm and 2.3 years respectively.- b. 481 mm and 9.2 years respectively.- c. 241 mm and 9.2 years respectively.- d. 481 mm and 2.3 years respectively.**Explanation of Terms in Table 1:**- **Cc (Compression Index):** It is a measure of the magnitude of the change in volume under load for normally consolidated soil. - **Cr (Recompression Index):** It indicates the change in volume occurring when a previously compressed soil is unloaded and then reloaded. - **Cv (Coefficient of Consolidation):** This parameter describes how fast consolidation can occur, and is specific to the rate at which water is expelled from the soil. - **e₀ (Initial Void Ratio):** It is the initial ratio of the volume of voids to the volume of solids in the soil.This setup will help in solving for the settlement and the time it will take for settlement to occur with the given soil properties and load conditions.

Given values: The given problem can be represented by this diagram: Saturated unit weight of clay =20kN/m3 Dry unit weight of sand =17kN/m3 Unit weight of water =9.81kN/m3 Solution:(a) Ultimate settlement of clay layer after the fill is placed- ∆H=HoCc1+eo×log(σo+∆σ)σoσo=(6×20)-(6×9.81)=61.14kN/m2∆σ=3×17=51kN/m2Putting the values in the equation-∆H=6×0.321+0.7×log(61.14+51)61.14∆H=297 mm Solution (b) Time required for the settlement of 24.1 cm- %U=∆h∆H×100%U=241mm297mm×100%U=81.14% Now, Tv=π4×%U2Tv=π4×0.81142Tv=0.517 Now, Tv=Cv×td20.517=0.0021m2/day×t32Here, d=6m2(double drainage condition)t=2215.7days=6.07years Hence, Final Answers: settlement=297mm time=6.07years Hence most appropriate answer is C

Engineering

Civil Engineering

A6 meter thick clay layer is resting over an incompressible glacial till deposit of infinite thickness (assumed impermeable). From lab tests, the results shown in table 1 were obtained for a sample from midpoint of clay layer. A 3 meter thick fill mainly comprising of sandy soil is planned to be placed on top of the clay layer. Ground water level is assumed to be at the top of clay layer. Saturated unit weight of clay layer and dry unit weight of sandy layer are 20 and 17 KN/m respectively. Unit weight of water is 9.81 KN/m3. a. What is the ultimate settlement of the clay layer after the fill is placed? b. If the clay layer was resting on a sandy gravel layer of infinite thickness, how many years will it take to complete a settlement of 24.1 cm due to the fill? Table 1 Preconsolidation Stress Сс Cr Cv eo Soil is found to be normally consolidated 0.32 0.12 0.0021 m2/day 0.7 a 241 mm and 2.3 years respectively. b. 481 mm and 9.2 years respectively. C. 241 mm and 9.2 years respectively. d. 481 mm and 2.3 years respectively.

A6 meter thick clay layer is resting over an incompressible glacial till deposit of infinite thickness (assumed impermeable). From lab tests, the results shown in table 1 were obtained for a sample from midpoint of clay layer. A 3 meter thick fill mainly comprising of sandy soil is planned to be placed on top of the clay layer. Ground water level is assumed to be at the top of clay layer. Saturated unit weight of clay layer and dry unit weight of sandy layer are 20 and 17 KN/m respectively. Unit weight of water is 9.81 KN/m3. a. What is the ultimate settlement of the clay layer after the fill is placed? b. If the clay layer was resting on a sandy gravel layer of infinite thickness, how many years will it take to complete a settlement of 24.1 cm due to the fill? Table 1 Preconsolidation Stress Сс Cr Cv eo Soil is found to be normally consolidated 0.32 0.12 0.0021 m2/day 0.7 a 241 mm and 2.3 years respectively. b. 481 mm and 9.2 years respectively. C. 241 mm and 9.2 years respectively. d. 481 mm and 2.3 years respectively.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Laboratory Determination of Hydraulic Conductivity

Hydraulic conductivity is the measure of flowability of water inside the soil in the presence of a hydraulic gradient. The hydraulic gradient is defined as the difference in the water heads in the soil, which induces a water motion. In simple terms, a hydraulic gradient is the presence of a potential that induces a flow of water.

Question

**Problem Description:**

A 6-meter thick clay layer is resting over an incompressible glacial till deposit of infinite thickness (assumed impermeable). From lab tests, the results shown in Table 1 were obtained for a sample from the midpoint of the clay layer. A 3-meter thick fill mainly comprising sandy soil is planned to be placed on top of the clay layer. The groundwater level is assumed to be at the top of the clay layer. The saturated unit weight of the clay layer and dry unit weight of the sandy layer are 20 KN/m³ and 17 KN/m³, respectively. The unit weight of water is 9.81 KN/m³.

**Questions:**

a. What is the ultimate settlement of the clay layer after the fill is placed?

b. If the clay layer was resting on a sandy gravel layer of infinite thickness, how many years will it take to complete a settlement of 24.1 cm due to the fill?

**Table 1: Soil Properties**

| Preconsolidation Stress | Cc | Cr | Cv (m²/day) | e₀ |
|-------------------------|-----|-----|-------------|-----|
| Soil is found to be normally consolidated | 0.32 | 0.12 | 0.0021 | 0.7 |

**Answer Options:**

- a. 241 mm and 2.3 years respectively.
- b. 481 mm and 9.2 years respectively.
- c. 241 mm and 9.2 years respectively.
- d. 481 mm and 2.3 years respectively.

**Explanation of Terms in Table 1:**

- **Cc (Compression Index):** It is a measure of the magnitude of the change in volume under load for normally consolidated soil.

- **Cr (Recompression Index):** It indicates the change in volume occurring when a previously compressed soil is unloaded and then reloaded.

- **Cv (Coefficient of Consolidation):** This parameter describes how fast consolidation can occur, and is specific to the rate at which water is expelled from the soil.

- **e₀ (Initial Void Ratio):** It is the initial ratio of the volume of voids to the volume of solids in the soil.

This setup will help in solving for the settlement and the time it will take for settlement to occur with the given soil properties and load conditions.

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