NCEES Civil PE Specification Soil mechanics: Foundation settlement

Problem

For each of the two foundation options shown, find the ratio of long-term settlement \(\frac{S_{c1}}{S_{c2}}\) for the clay layers after 2 years of loading caused by normal consolidation settlement of each layer.

Assume the following:
• Both footings have the same load.
• Consider long term settlement only in the normally consolidated clay layers.
• \(p_f = 2 p_0\) (Final pressure = 2 x Initial pressure for both footings at center of clay layer).

Select an Answer:

CORRECT 😃

INCORRECT 😟

% Students Correctly Answered:

36.0%

Solution

Answer: A) 0.5

Long-term settlement of clay layer depends on the following factors from the equation of long-term settlement for consolidating layers (time-dependent).

Refer to PE Civil Reference Handbook section 3.2.3:

\[t_{v} = \frac{C_{v} t}{(H_{d})^2} \\\]

where:

\(C_{v} = Coeff.\ of\ consolidation\)

\(t= time\)

\(H_{d} = longest\ drainage\ distance\)

Given that time is the same for both options 1 and 2, we can find the relationship between \(C_v\) for each option as follows.

Relationship between drainage paths:

\[\frac{H_{d1}}{H_{d2}}\ =\ (10)/(20/2) =1 \\\]

where:

\(H_{d1}\) (drainage path for option 1) = Whole layer thickness because it has an impermeable layer of rock underneath.

\(H_{d2 }\) (drainage path for option 2) = Half layer thickness because it has permeable layers of sand above and below.

Relationship between consolidation times:

\[t_{1}\ =\ t_{2}\ =\ 2\ years \\\]

\[t_{v1}\ = t_{v2}\]

Based on the previous relationships listed:

\[\frac{C_{v1}}{C_{v2}} = 1 = C_{c}\]

Find the consolidation settlement, refer to PE Civil Reference Handbook section 3.2.1: