   Chapter 11, Problem 11.8P 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

Redo Problem 11.7 using the weighted average method [Eq. (11.76)] to late the stress increase in the clay layer.11.7 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 distributed load (q) as shown below.

q=PBL

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

q=3502.5×2.5=3506.25=56kN/m2

Calculate the increase in vertical stress (Δσz) below the center of a rectangular area using the relation as follows.

Δσz=qI4 (1)

Here, I4 is the influence factor and as a function of m1 and n1.

For the depth (z) of 1m:

Calculate the width (b) as shown below.

b=B2

Substitute 2.5m for B.

b=2.52=1.25m

Calculate the ratio (m1) as shown below.

m1=LB

Substitute 2.5m for L and 2.5m for B.

m1=2.52.5=1

Calculate the ratio (n1) as shown below.

n1=zb

Substitute 1.25m for b and 1m for z.

n1=11.25=0.8

Similarly calculate the remaining values and tabulate as in Table 1.

Refer Table 10.11 “Variation of I4 with m1 and n1” in the Text Book.

Take the value of I4 as 0.800, for the values m1 of 1 and n1 of 0.80.

Similarly calculate the remaining values and tabulate as in Table 1.

Calculate the increase in vertical stress (Δσz) as shown below.

Substitute 330kN/m2 for q and 0.91 for I4 in Equation (1).

Δσz=330×0.91=300.3kN/m2

Similarly calculate the increase in vertical stress values and tabulate as in Table 1.

Show the increase in vertical stress for each depth below the center of the loaded area as in Table 1.

 m1=LB b=B2 Depth, z (m) n1=zb I4 Δσz (kN/m2) 1 1.25 1 0.8 0.8 44.8 1 1.25 3.25 2.6 0.2418 13.54 1 1.25 5.5 4.4 0.0936 5.24

Table 1

Refer to table 1.

Calculate the stress increase in the clay layer (Δσ) using the relation

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