   Chapter 11, Problem 11.3P 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

Following are the results of a laboratory consolidation test on a sample of undisturbed clay obtained from the field. The height of the specimen at the beginning of the test was 1.9 cm, and the diameter was 6.35 cm. The mass of the dry specimen was 91 g. Estimate the compression index and the preconsolidation pressure from the e – log σ′ curve. Given: Gs = 2.72.

To determine

Calculate the compression index and the preconsolidation pressure from the elogσ curve.

Explanation

Given information:

The diameter of the specimen (d) is 6.35cm.

The dry mass of the specimen (Ms) is 91g.

The specific gravity of soil solids (Gs) is 2.72.

The pressure and final height of specimen are given in the table.

Calculation:

Consider the density of water as (ρw) is 1g/cm3.

Calculate the area of the specimen (A) using the relation.

A=πd24

Substitute 6.35cm for d.

A=π×6.3524=31.67cm2

Calculate the height of solids (Hs) in the soil specimen using the relation.

Hs=MsAGsρw

Substitute 91g for Ms, 31.67cm2 for A, 2.72 for Gs, and 1g/cm3 for ρw.

Hs=9131.67×2.72×1=9186.1424=1.056cm

Calculate the initial height of voids (Hv) using the relation.

Hv=HHs

Here, H is the initial height of the specimen.

Substitute 1.9cm for H and 1.056cm for Hs.

Hv=1.91.056=0.844cm

Similarly calculate the height of voids for remaining values and tabulated as in Table 1.

Calculate the initial void ratio (e0) of the specimen using the relation.

e0=HvHs

Substitute 0.844cm for Hv and 1.056cm for Hs.

e0=0.8441.056=0.799

Similarly calculate the void ratio for remaining values and tabulated as in Table 1.

Show the height of voids and initial void ratio as in Table 1.

 Pressure, σ′ (kg/cm2) Final height of the specimen, (cm) Hs (cm) Hv=H−Hs (cm) e=HvHs 0 1.9 1.056 0.844 0.799 0.25 1.763 1.056 0.707 0.670 0.5 1.742 1.056 0.686 0.650 1 1.702 1.056 0.646 0.612 2 1.656 1

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