Pore water pressure calculations

[db725]

Homework Statement

A cross-section of a proposed excavation for a highway corridor is to be conducted in the proximity of a house built on shallow foundation. It is expected that the original groundwater table will drop to a permanent level as shown in the figure due to the excavation. (Please refere to attachment)

The coefficient of compressibility (mv) and the coefficient of consolidation (Cv) of the normally-consolidated clay are 0.0004 m2/kN and 0.035m2/day respectively, and these values can be assumed to remain practically unchanged within the stress range of this case. The sandy gravel above and below the clay is very dense, hence it is a reasonable assumption that settlements in the upper and lower sandy gravel layers will be relatively insignificant. The saturated density of the clay is 2000 kg/m3. The dry and saturated densities of the sandy gravel are 1800 and 2100 kg/m3 respectively.

(c) Estimate the pore water pressures at points A, B, C, D and E:
(i) Prior to the excavation work.
(ii) Immediately after excavation with groundwater level dropped to its permanent level.
(iii) One year after excavation.
(iv) Long-term after excavation.

(d) Based on the results from (c) above, sketch the excess pore water pressures at points A, B, C D and E with depth (from top of clay layer):
(i) Immediately after excavation.
(ii) One year after excavation.
(Note - excess pore water pressure here refers to the water pressure difference relative to the long-term equilibrium value.)

I have managed to get through the first section of calculating the pore water pressure. However I am not aware of a formula for the calculation of pore water pressure after a long term period. I have attached the diagram to support the question. I also don't understand the sketching process. Would appreciate any help on this as I am really stuck.

Homework Equations

Uwater= γwater x height

The Attempt at a Solution

c) i- Prior to excavation workU= pore water pressure
Uwater= γwater x height

Uwater (A)=5 x 10=50 kN/m^2

Uwater (B)= 9 x 10=90 kN/m^2

Uwater (C)= 13 x 10=130 kN/m^2

Uwater (D)=17 x 10=170 kN/m^2

Uwater (E)= 21 x 10=210 kN/m^2

ii- Immediately after excavation with groundwater level dropped to its permanent level.

Uwater (A)=0 kN/m^2

Uwater (B)= 4 x 10=40 kN/m^2

Uwater (C)= 8 x 10=80 kN/m^2

Uwater (D)=12 x 10=120 kN/m^2

Uwater (E)= 16 x 10=160 kN/m^2

 

[Chestermiller]

This is a poroelasticity problem that focuses on the clay layer. When the water table is lowered, the pore pressure within the clay is not going to respond immediately, and static equilibrium will take time to become re-established. You need to solve the transient pressure equation for the pressure within the clay layer as a function of spatial position and time.