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Unformatted text preview: Vertical
load V,
N
100
200
300 normal
effective stress
σ', kPa
27.8
55.6
83.3 ln(σ') 3.325
4.018
4.422 Shear Shear
load
stress τult,
Fult, N kPa
53
14.7
105
29.2
156
43.3 Water
content
w, % Specific
volume v 35.1
31.3
29.5 1.95
1.85
1.80 Plot graphs of τult against σ' and v against lnσ' to determine the critical state parameters, as
in main text Figure 2.28 (Example 2.2). φ'crit ≈ 28°; vo ≈ 2.43; λ ≈ 0.14
During the undrained tests, there is no overall volume change. Assuming that the specific
volume is uniform throughout the sample, it must remain constant during the test. The critical
state eventually reached therefore depends on the astested specific volume. Our model
predicts that, at the critical state, the vertical effective stress σ' is related to the specific
volume by the expression
v = vo  λ.lnσ' (main text Equation 2.11) or σ' = exp{(vov)/λ}
The normal effective stress at the critical state is related to the shear stress τult by the
expression τult = σ'.tanφ'crit (main text Equation 2.10) Hence τult = exp{(vov)/λ}.tanφ'crit
where v = 1 + w.Gs. The calculated and measured values of τult for the undrained tests are
compared below:
Vertical
load V,
N normal
effective stress
σ', kPa Shear
load
Fult, N 100
200
300 27.8
55.6
83.3 42
80
120 Measured
shear
stress τult,
kPa
11.7
22.2
33.3 Water
content
w, % Specific
volume v 36.0
32.6
20.6 1.972
1.880
1.826 Calculated
shear
stress, τult
kPa
14.0
27.0
39.8 The measured values are smaller than the theoretical values by about 16%. This is probably
due to internal drainage and discontinuous sample behaviour.
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This note was uploaded on 12/28/2011 for the course CHM 4302 taught by Professor Stuartchalk during the Fall '11 term at UNF.
 Fall '11
 StuartChalk
 Analytical Chemistry, pH

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