6.5 Please answer parts A and B thoroughly. Been having some trouble with the to

Question

6.5 Please answer parts A and B thoroughly. Been having some trouble with the topic so good, explanations help ALOT.

6.5 a saturated clay layer of thickness with an existing effective overburden pres. Consider layer construction of a building above it causes an at midheight of the The increase pressure, Ap. It is necessary to calculate the settlement S associated with the con. in struction. Considering only the primary settlement, s can be calculated as Po where ce is the compression index, eo is the initial void ratio, and the other parameters were discussed earlier. suppose H, po Ay, and eo are known constants of value 4 m, 98 kNVm 13 kN/m2, and 1.0, respectively. For the given void ratio, the compression index is normally distributed with a mean of 0.27 and a standard deviation of 0.04. (a) What is the distribution of the settlement S? Calculate the parameters of the distribution. (b) If the allowable settlement is 40 mm, what is the probability that the building will suf fer damage due to excessive settlement?

Explanation / Answer

S= CH/(1+e0)*log((p0+dp)/p0)

given values

we get

S = C * (4/(1+1) *log (98+13)/98)

S =C*0.041741

now C -N(0.27,0.04^2)

we know if X has normal distribution with mean m and sd s

then aX has normal distribution with mean a*m and sd a*s

so

S follow N(0.041741*0.27, 0.041741^2*0.04^2)

=N(0.0112700 ,0.001669^2)

b) P(S > 40 mm )

P(S>0.04)

P(Z>(0.04 - 0.0112700)/0.001669)

P(Z> 17.21 )

=0

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