A continuous foundation has a width B = 1.2 m and is founded at a depth Df = 1.0 m. The soil has a unit weight gamma = 17.5 kN/m^3, cohesion c' = 14 kN/m^2, and a friction angle phi' = 20 degrees. From Table 16.1, for phi' = 20 degrees, the bearing capacity factors are Nc = 17.69, Nq = 7.44, and N_gamma = 3.64. Calculate the ultimate bearing capacity (qu) using Terzaghi's equation for general shear failure.
Explanation
This question requires a direct application of Terzaghi's ultimate bearing capacity equation for a continuous footing with general shear failure, as demonstrated in Example 16.1. The calculation involves determining the surcharge 'q' and then summing the three components of bearing capacity: cohesion, surcharge, and soil weight.
Other questions
What are the two primary conditions that must be met for a foundation to function properly?
What is the key visual difference between a general shear failure and a local shear failure in soil under a foundation?
According to Terzaghi's definition, when is a foundation considered a 'shallow foundation'?
In Terzaghi's bearing capacity equation, qu = c'Nc + qNq + 0.5 * gamma * B * N_gamma, what do the terms Nc, Nq, and N_gamma represent?
For local shear failure in a strip footing, Terzaghi's equation is modified. What modifications are made to the cohesion (c') and friction angle (phi') parameters before calculating the bearing capacity factors?
How is Terzaghi's ultimate bearing capacity equation for a strip footing (qu = c'Nc + qNq + 0.5*gamma*B*N_gamma) modified for a square footing?
What is the correct approach to account for the groundwater table when it coincides exactly with the bottom of the foundation (Case II)?
If the groundwater table is located at a depth D below the bottom of a foundation of width B, where D is less than B (Case III), how is the unit weight 'gamma' in the third term of the bearing capacity equation modified?
What is the relationship between the net ultimate bearing capacity (qu(net)), the ultimate bearing capacity (qu), and the effective stress at the foundation level (q)?
A continuous footing has an ultimate bearing capacity (qu) of 6000 lb/ft^2. The effective stress at the foundation level (q) is 300 lb/ft^2. If a factor of safety (Fs) of 3 is required, what is the net allowable bearing capacity (q_all(net))?
What is the primary difference in the assumed failure mechanism between Terzaghi's bearing capacity theory and the general bearing capacity theory (e.g., Meyerhof, Vesic)?
In the modified general ultimate bearing capacity equation, what is the purpose of the depth factors (lcd, lqd, lgd)?
For an undrained condition with phi = 0 and vertical loading, the general bearing capacity equation (qu = c_u * lcs * lcd * Nc + q) simplifies. What is the value of the bearing capacity factor Nc in this case?
In the case history presented in Section 16.6, a field load test was performed on a foundation with B = 2.44 m, L = 2.74 m, and Df = 1.68 m in a saturated clay. The shape factor lcs was calculated as 1.2. How was the depth factor lcd calculated?
For a shallow foundation subjected to a load with one-way eccentricity 'e' in the x-direction on a footing of width B, what is the effective width B'?
A rectangular footing is 1.5 m by 1.0 m (L=1.5m, B=1.0m). A load is applied with an eccentricity e = 0.1 m along the B dimension (x-direction). What are the effective width (B') and effective length (L') to be used in the bearing capacity calculation?
Once the effective dimensions B' and L' are determined for an eccentrically loaded footing, how are they used in the shape factors (e.g., lqs) for the general bearing capacity equation?
What is the ultimate load (Qu) on an eccentrically loaded footing once the ultimate bearing capacity (qu) has been calculated using the effective width B'?
The reduction factor method proposed by Purkayastha and Char (1977) relates the bearing capacity of an eccentrically loaded continuous foundation to that of a centrally loaded one. The reduction factor Rk is a function of what two parameters?
A continuous foundation on granular soil has an embedment ratio Df/B = 0.5 and a load eccentricity ratio e/B = 0.1. What is the reduction factor Rk that relates the eccentrically loaded bearing capacity to the centrally loaded one?
Meyerhof (1956) proposed correlations for the net allowable bearing capacity (q_net) of foundations on sand based on what two primary factors?
In Meyerhof's settlement-based bearing capacity equations for sand, what is the maximum value for the depth factor Fd?
For a footing on sand with a width B > 1.22 m, what is the formula proposed by Meyerhof for the net allowable bearing capacity (q_net) in SI units?
What is the primary purpose of conducting a plate-load test?
For a plate-load test on sandy soil, how is the ultimate bearing capacity of a full-sized footing (qu(footing)) estimated from the ultimate bearing capacity of the test plate (qu(plate))?
A plate-load test using a 700-mm diameter plate on sandy soil determines an ultimate bearing capacity of 280 kN/m^2. What is the estimated ultimate bearing capacity of a circular footing with a 1.5 m diameter?
For a plate-load test on clay, how is the settlement of a full-sized footing (Se(footing)) at a given load intensity 'q' estimated from the settlement of the test plate (Se(plate))?
Which of the following is NOT listed as a factor that the bearing capacity of foundations depends on in the summary section?
What is the key limitation of allowable bearing capacity relationships based on settlement considerations, such as those in Section 16.8, according to the chapter's summary?
For a soil with a friction angle phi' = 35 degrees, what are the Terzaghi bearing capacity factors Nc, Nq, and N_gamma from Table 16.1?
A square footing with side B is to be designed. The soil is cohesionless (c' = 0) with a friction angle phi' = 35 degrees and a unit weight of 18.15 kN/m^3. The footing is at a depth of 1 m, and a factor of safety of 3 is required. The footing must support a total allowable load Q_all = 294.3 kN. Using Terzaghi's equation for a square footing, what is the required size B?
What is the general bearing capacity factor Nq, according to Reissner (1924) and Prandtl (1921), as a function of the soil friction angle phi'?
According to Meyerhof's shape factors for a rectangular footing (Table 16.4), how is the shape factor for cohesion, lcs, calculated for a soil with a friction angle phi' greater than or equal to 10 degrees?
What is the value of Meyerhof's inclination factor for cohesion, lci, for an inclined load making an angle 'alpha' with the vertical?
A square footing (B=L=1.2m) is founded at Df = 1m. The soil has c'=0 and a friction angle phi'=32 degrees. The groundwater table is at the bottom of the foundation. The unit weight of the soil above the water table is 16 kN/m^3 and the saturated unit weight is 19.5 kN/m^3. Calculate the ultimate bearing capacity (qu) using the general bearing capacity equation.
In the context of shallow foundations, what does the term 'gross allowable bearing capacity' refer to?
The bearing capacity of a footing on sand is found to be 2000 kN/m^2 using Meyerhof's formulas. The soil has an N60 value of 20 and an allowable settlement of 25 mm. The footing is 2m wide with a Df/B ratio of 0.5. Is this design acceptable?
What type of bearing capacity failure is typically associated with a dense sand or a stiff soil?
For a footing with two-way eccentricity, how is the effective area determined?
What is the primary reason for the wide variation in the bearing capacity factor N_gamma obtained by different investigators?
A plate-load test is conducted in a sandy soil using a 1 ft x 1 ft square plate. The ultimate load per unit area (qu) for the test was found to be 3850 lb/ft^2. What is the total allowable load (Q_all) for a 6 ft x 6 ft footing, using a factor of safety of 4?
What is the definition of a strip footing for practical considerations?
For an undrained condition (phi=0), the bearing capacity factors are Ng=0 and Nq=1. What happens to Terzaghi's bearing capacity equation for a strip footing?
A square footing of 5 ft by 5 ft is to be built. The base is 4 ft below the ground surface. The soil has a total unit weight of 105 lb/ft^3, a saturated unit weight of 118 lb/ft^3, c'=0, and phi'=35 degrees. The groundwater table is located 6 ft below the ground surface. What is the gross allowable load, Q_all, for a factor of safety of 3, using Terzaghi's equation?
The general bearing capacity equation presented in Section 16.5 (qu = c'Nc + qNq + 0.5*gamma*B*N_gamma) is in the same form as Terzaghi's equation. What is the key difference?
In Meyerhof's system of modification factors, for a rectangular footing with a vertically applied load, which factors are equal to 1?
An eccentrically loaded continuous foundation supported on granular soil has a width B = 1.5 m and embedment depth Df = 0.75 m. The load has an eccentricity e = 0.15 m. Calculate the ultimate load per unit length, Qu(eccentric), if the centrally loaded capacity Qu(centric) is 275.28 kN/m.
What is the key advantage of the cone penetration test (CPT) over the standard penetration test (SPT)?
For a shallow foundation on sand, design is often governed by settlement rather than shear failure. Meyerhof's formulas (Eq. 16.46-16.50) are used to estimate the net allowable bearing capacity based on a tolerable settlement. What N60 values are used in these equations?