Chapter 10, Problem 10.2CTP

### Principles of Geotechnical Enginee...

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

Chapter
Section

### Principles of Geotechnical Enginee...

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

(a)

To determine

Calculate the total vertical stress (σy) due to wheel load and the over burden pressure at each point.

Explanation

Given information:

The thickness of unpaved aggregate road (t) is 610mm.

The unit weight of aggregate layer (γagg) is 19.4kN/m3.

The radius of the wheel (R) is 150mm.

A typical single-axle wheel load (W) is 40kN.

The tire pressure (q) is 565kN/m2.

The radial distance, horizontal stress, and shear stresses at each point are given in the Table.

Calculation:

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

Calculate the increase in vertical stress (Δσz) using the relation as follows.

Δσz=q(A+B) (1)

Here, A and B are the factors and a functions of zR and rR.

Calculate the depth to radius ratio (zR) as shown below.

Substitute 305mm for z and 150mm for R.

zR=305150=2.032

For the radial distance (r) of 0.457m:

Calculate the ratio (rR) as shown below.

Substitute 0.457m for r and 0.150m for R.

rR=0.4570.150=3.053

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

Calculate the value of A as shown below.

Refer Table 10.8 “Variation of A with zR and rR” in the Text Book.

Take the value of A as 0.02221, for the values zR of 2 and rR of 3.

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

Calculate the value of B as shown below.

Refer Table 10.9 “Variation of B with zR and rR” in the Text Book.

Take the value of B as 0.00028, for the values zR of 2 and rR of 3

(b)

To determine

Calculate the maximum and minimum principal stresses for elements A, B, and C and the orientation of the principal stress with respect to the vertical using pole method.

(c)

To determine

Plot the variations of σ1 and     αi with normalized radial distance rR, from the center of loading.

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