CIE444 - HW1 solution - CIE 444 SOIL MECHANICS Lebanese...

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CIE 444 – SOIL MECHANICS Lebanese American University – Fall 2009 Prof. Grace Abou-Jaoude Estephan HOMEWORK#1 SOLUTION Out Tuesday Oct. 6, 2009 Due Tuesday Oct. 13, 2009, IN CLASS PROBLEM #1 (30%) Derive the following weight-volume equations by using the phase diagram and combining the definitions of void ratio, porosity, degree of saturation, water content, unit weight, and specific gravity of solids: 1- ( ) S G c w G s w s d . . 1 + = γ γ (15pts) 2- 1 = d w s G e γ γ (15pts) SOLUTION 1- ( ) S G c w G s w s d . . 1 + = γ γ By definition: V W s d = γ We start from the left hand side with the definition of dry unit weight: s v s s s v s s s s s v s s s d V V V W V V V V W V V V V W V W + = + = × + = = 1 γ Multiply the numerator by w w γ γ Multiply the term s v V V in the denominator by s s W W and w w γ γ => s s w w s v w w s s d W W V V V W × × + × = γ γ γ γ γ 1 Based on the definitions of % 100 . . × = s w W W c w , % 100 × = v w V V S , and w s s w s s V W G γ γ γ = = Page 1 of 7
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