Problem $3-$ Application to civil engineering design

Walls that retain soil $($basement walls, retaining walls, etc.$)$ must resist the horizontal thrust of the

soil behind it without cracking or undergoing excessive deformation that cause structural or

operational problems. In addition, infiltration of rainwater causes soil around buildings and houses

to become saturated which can cause additional horizontal loads. This is a design situation that

gives you an opportunity to evaluate the effect of groundwater on horizontal stress.

The two sketches at right are of a

two$-$level basement for a commercial

building. A desirable design is shown

in Case $1$ where a waterproofing

membrane is placed over the exterior

wall, a perforated drainage pipe is

placed at the footing base, then a

clean, coarse$-$grained backfill soil is

placed to fill the space remaining from

excavation. The drainpipe leads to a

discharge point and any groundwater

in the backfill soil is removed before it

reaches the wall. Therefore, no

hydrostatic pressure $($u$)$ can build up

and push horizontally on the wall.

Case $2$ shows an undesirable design

where excavated CL soil is reused as

wall backfill. No drainage pipe is

installed or clean, coarse$-$grained

backfill used. Water levels can rise

behind the wall and apply additional

pressure.

In Case $1,$ assume no groundwater table develops behind the wall because of the drainage

provisions. However, in Case $2,$ assume that the groundwater level rises to the ground surface.

For each case, draw the vertical and horizontal stress diagrams and then calculate the

total horizontal force, $P[l\frac{b}{f}t]$ which acts at a distance of $\frac{H}{3}$ from the bottom of the footing.

Note that the stress diagrams should extend from the ground surface to the bottom of the wall

footing. Assume that both the moist and saturated unit weight in each case is $120$ pcf and the

coefficient of earth pressure at rest $(K_0)$ is $0\mathrm{.}5.$

Suppose that there was no engineering inspection on the project and the contractor fails to

construct the drainage system as designed for Case $1.$ Now the owner of the building actually

has Case $2.$ The exterior walls of the building are cracking, and water is infiltrating the interior

space.

Design a solution to remediate this problem and transmit your ideas using one or more

sketches, as needed.