   Chapter 11, Problem 11.7P Principles of Geotechnical Enginee...

9th Edition
Braja M. Das + 1 other
ISBN: 9781305970939

Solutions

Chapter
Section Principles of Geotechnical Enginee...

9th Edition
Braja M. Das + 1 other
ISBN: 9781305970939
Textbook Problem

Figure 11.46 shows a foundation with dimensions B × L supporting a column load, P. The foundation rests on a sandy soil underlain by a clay layer. Estimate the primary consolidation settlement of the clay due to the foundation load. Given: P = 350 kN, B = L = 2.5 m, Df = 2 m, H1 = 3 m, and H2 = 4.5 m. The soil properties are as follows:Sand: γd = 16.4 kN/m3; γsat = 18.8 kN/m3Clay: γsat = 17.6 kN/m3; e0 = 0.82; LL = 48; normally consolidated(Use Δ σ ′ = P B L at the middle of the clay layer.) To determine

Calculate the primary consolidation settlement of the clay due to the foundation load.

Explanation

Given information:

The foundation load (P) is 350kN.

The length of the foundation (L) is 2.5m.

The breadth of the foundation (B) is 2.5m.

The depth of foundation (Df) is 2m.

The height of the clay layer 1 (H1) is 3m.

The height of the clay layer 2 (H2) is 4.5m.

The dry unit weight of sand (γd) is 16.4kN/m3.

The saturated unit weight of sand (γsat)sand is 18.8kN/m3.

The saturated unit weight of clay (γsat)clay is 17.6kN/m3.

The void ratio (e0) is 0.82.

The liquid limit (LL) is 48.

Calculation:

Consider the unit weight of water (γw) is 9.81kN/m3.

Calculate the net applied pressure (Δσ) using the relation.

Δσ=PBL

Substitute 350kN for P, 2.5m for B, and 2.5m for L.

Δσ=3502.5×2.5=3506.25=56kN/m2

Calculate the compression index (CC) using the relation.

CC=0.009(LL10)

Substitute 48 for LL.

CC=0.009(4810)=0.342

Calculate the average effective stress at the middle of the clay layer (σo) as shown below.

σo=γdDf+((γsat)sandγw)(H1Df)+((γsat)clayγw)×H22

Substitute 16

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