HOMEWORK SOLUTION

HW #4

GEOTECHNICAL ENGINEERING I

(Question no. 4.3-, 4.6, 4.11……Al-Khafaji textbook)

4.3 a. Estimate optimum g_d corresponding to optimum w (water content)

b. What is the range of w if % compaction = 95%

Solution:

See graph 1. :

a. Optimum g_d = 125 pcf

Optimum w = 16%...ans

b. 95% = g_df = 95% x 125 pcf = 118.75 pcf

plot the graph we get the range of w = 9.5% - 21.5% ……….ans.

4.4 Vs = 2,000,000 yards³ = 54 x 10⁶ ft3 (for embankment) note: 1 yd³=27ft³

g_m for embankment = 125 pcf

w for embankment = 15.8 %

Select one of the pit (borrowing soil) which is the minimum cost.

pit	gm	w	cost/yd^3
A	110.5	12.2	6.2
B	107.4	15.0	5.0
C	90	27.4	3.5

Solution:

Soil mass need for embankment Ws = g_d x Vs =

Ws =

= 5.83 x 10⁶ lb

Pit A.

Vs_A =

=

cost_A = V_sA x $6.2 = $ 13.578 million.

Pit B.

Vs_A =

=

cost_B = V_sB x $5.0 = $ 11.55 million.

Pit C.

Vs_A =

=

cost_C = V_sC x $3.5 = $ 10.57 million.

The minimum cost is Pit C…………………..ans.

4.11 Volume soil field = 1162 cm³

Weight of soil in the field (wet) = 2253 gr

Weight of soil in the field (dry) = 1910 gr

See graph 2:

Question:

(a) g_df ?

(b) w_f ?

(c) % compaction ?

Solution:

(a) g_df =…ans

(b) w_f =……………….ans

(c) % compaction =

g_do from graph 2. we obtain

g_do = 119.5 pcf

g_df = 102.38 pcf

% compaction = …..ans