For purely cohesive soil, the bearing capacity is given by which of the following equation?

Question

Examoogle · Accepted Answer

The correct answer is Option A: $q_f = 5.7 c + \bar{\sigma}$. For purely cohesive soil (saturated clay, $\phi = 0$), the ultimate bearing capacity is determined using Terzaghi's bearing capacity theory. The formula is given as $q_f = c N_c + \bar{\sigma} N_q$, where for $\phi = 0$, $N_c = 5.7$ and $N_q = 1$.

Step-by-Step Solution & Concepts:
For purely cohesive soil (saturated clay, $\phi = 0$), the ultimate bearing capacity is determined using Terzaghi's bearing capacity theory. The formula is given as $q_f = c N_c + \bar{\sigma} N_q$, where for $\phi = 0$, $N_c = 5.7$ and $N_q = 1$.

Working Principle: In saturated clay, the internal angle of friction is assumed to be zero. Consequently, the term involving $\bar{\sigma} N_q$ simplifies because $N_q$ becomes unity, leading to the expression $q_f = 5.7c + \bar{\sigma}$. This represents the sum of the cohesive component and the surcharge pressure at the footing level.

Key Formulas: $q_f = c N_c + \bar{\sigma} N_q + 0.5 \gamma B N_{\gamma}$ — Terzaghi's General Bearing Capacity Equation; $q_f = 5.7 c + \bar{\sigma}$ — Simplified form for purely cohesive soil ($\phi = 0$)

Key Points: For cohesive soils, $\phi = 0$ is the defining characteristic for short-term analysis.; Terzaghi's bearing capacity factor $N_c$ is approximately $5.7$ for strip footings.; The bearing capacity of cohesive soil is independent of the width of the footing (B) when $\phi = 0$.

Advantages: Simple mathematical model for undrained clay conditions.; Standardized approach for geotechnical site investigation.

Disadvantages: Over-simplifies soil behavior by assuming perfect rigidity.; Does not account for long-term consolidation settlements.

Applications: Design of shallow foundations on saturated clay.; Initial stability assessment of clayey strata.

Additional Info: The factor $N_c = 5.7$ is strictly for a strip footing. For circular or square footings, the factor varies.. Option B incorrectly omits the bearing capacity factor $N_c$. Option C omits the surcharge component $\bar{\sigma}$, which is only valid if the foundation is placed at the surface ($\bar{\sigma} = 0$).

Answer: A is correct — The ultimate bearing capacity for a strip footing on purely cohesive soil is $q_f = 5.7c + \bar{\sigma}$.

Exam Tip: Always check for $\phi=0$ conditions in questions regarding clay; it significantly simplifies Terzaghi's general bearing capacity equation by eliminating the surcharge and unit weight terms for $N_q$ and $N_{\gamma}$.

Examoogle · Answer

Option B: $q_f = c + \bar{\sigma}$

Examoogle · Answer

Option C: $q_f = 5.7 c$

Examoogle · Answer

Option D: All of the mentioned

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