Test 24 - Bearing Capacity Calculations

Question 1 ప్రశ్న 1

Which combination of conditions is most consistent with the classical Terzaghi bearing-capacity analysis of a shallow continuous strip footing?

A A deeply embedded flexible pile carrying a large inclined uplift load. B A long strip footing with a horizontal rough base, essentially vertical central loading, level ground and approximately homogeneous soil governed by an idealized shear-failure mechanism. C A footing resting on several strongly anisotropic layers whose stiffness contrasts are automatically represented by one homogeneous equation. D A foundation subjected to unrestricted seismic loading and arbitrary groundwater seepage without additional analysis.

Question 2 ప్రశ్న 2

For a strip footing under Terzaghi's original general-shear formulation, the gross ultimate bearing pressure is qult = cNc + qNq + 0.5 gamma B Ngamma. Which interpretation of the three contributions is correct?

A The terms represent settlement, groundwater uplift and foundation rigidity, respectively. B Nc, Nq and Ngamma are determined entirely by foundation width and are independent of soil friction angle. C The first term represents overburden, the second represents cohesion and the third represents structural dead load. D The terms represent cohesion, surcharge at foundation level and soil self-weight contributions, with bearing factors selected consistently for the soil friction angle and adopted theory.

Question 3 ప్రశ్న 3

A rough continuous strip footing is analysed using Terzaghi's original gross ultimate bearing-capacity equation qult = cNc + qNq + 0.5 gamma B Ngamma. Given c = 15 kPa, Nc = 20, q = 20 kPa, Nq = 10, gamma = 18 kN/m3, B = 2 m and Ngamma = 8, what is qult?

A 544 kPa. B 624 kPa. C 644 kPa. D 744 kPa.

Question 4 ప్రశ్న 4

For a saturated clay analysed under an ideal undrained total-stress condition with phi_u = 0, use Terzaghi's original strip-footing factors Nc = 5.7, Nq = 1 and Ngamma = 0. If cu = 40 kPa and the total overburden surcharge at foundation level is q = 30 kPa, what are the gross and net ultimate bearing pressures, respectively?

A 258 kPa and 228 kPa. B 228 kPa and 258 kPa. C 200 kPa and 170 kPa. D 258 kPa and 258 kPa.

Question 5 ప్రశ్న 5

Using Terzaghi's original empirical equation for a square footing, qult = 1.3cNc + qNq + 0.4 gamma B Ngamma, calculate the gross ultimate bearing pressure for c = 20 kPa, Nc = 10, q = 18 kPa, Nq = 5, gamma = 18 kN/m3, B = 2 m and Ngamma = 4.

A 362.0 kPa. B 392.4 kPa. C 435.6 kPa. D 407.6 kPa.

Question 6 ప్రశ్న 6

A circular shallow footing is analysed using Terzaghi's original equation qult = 1.3cNc + qNq + 0.3 gamma B Ngamma, where B is the footing diameter. For cohesionless sand, take c = 0, q = 20 kPa, Nq = 8, gamma = 18 kN/m3, B = 3 m and Ngamma = 6. What is the gross ultimate bearing pressure?

A 240.0 kPa. B 257.2 kPa. C 214.0 kPa. D 322.0 kPa.

Question 7 ప్రశ్న 7

Consider square and circular footings having the same characteristic dimension B, founding surcharge q, soil properties and bearing-capacity factors. Using Terzaghi's original empirical square and circular equations, and assuming gamma and Ngamma are positive, which comparison is correct?

A The circular footing always has a larger cohesion contribution because its plan area is smaller. B The square footing has a smaller soil self-weight contribution because 0.4 is less than 0.3. C The square footing has a larger soil self-weight contribution per unit bearing area, while both formulations use the same 1.3 cohesion coefficient and the same surcharge term. D Both footing shapes necessarily have identical gross ultimate bearing pressures because their characteristic dimensions are equal.

Question 8 ప్రశ్న 8

A continuous strip footing has gross ultimate bearing pressure given by qult = cNc + qNq + 0.5 gamma B Ngamma. Given c = 10 kPa, Nc = 12, q = 40 kPa, Nq = 6, gamma = 20 kN/m3, B = 2 m and Ngamma = 5, determine the gross and net ultimate bearing pressures, taking net ultimate pressure as qult - q.

A 460 kPa gross and 420 kPa net. B 420 kPa gross and 460 kPa net. C 460 kPa gross and 460 kPa net. D 420 kPa gross and 380 kPa net.

Question 9 ప్రశ్న 9

A footing has gross ultimate shear pressure of 720 kPa and original overburden pressure of 60 kPa at founding level. The specified factor of safety is 3.0 on net ultimate pressure, and the settlement criterion limits net working pressure to 200 kPa. What are the net safe pressure from shear and the gross allowable working pressure, respectively?

A 240 kPa and 300 kPa. B 220 kPa and 260 kPa. C 220 kPa and 280 kPa. D 200 kPa and 200 kPa.

Question 10 ప్రశ్న 10

A surface strip footing on dry cohesionless sand is analysed using the specified equation qult = 0.5 gamma B Ngamma, with gamma = 18 kN/m3, B = 2 m and Ngamma = 20. If a factor of safety of 3.0 is applied directly to the ultimate value and settlement does not govern, what are the ultimate and safe bearing pressures?

A 180 kPa and 60 kPa. B 720 kPa and 240 kPa. C 360 kPa and 120 kPa. D 400 kPa and 133.3 kPa.

Question 11 ప్రశ్న 11

A strip footing in cohesionless soil has B = 2 m and foundation-level effective surcharge q = 36 kPa, with Nq = 10 and Ngamma = 10. Before groundwater rise, the effective unit weight adopted for the soil-weight term is 20 kN/m3. The water table then rises to footing-base level, reducing the effective unit weight used below the base to 10 kN/m3 while leaving q unchanged. Using qult = qNq + 0.5 gamma_eff B Ngamma, what are the calculated values before and after groundwater rise?

A 560 kPa before and 460 kPa after. B 460 kPa before and 560 kPa after. C 560 kPa before and 560 kPa after. D 360 kPa before and 260 kPa after.

Question 12 ప్రశ్న 12

For a cohesionless strip footing having B = 2 m, gamma = 20 kN/m3 and Ngamma = 10, the water table is permanently located more than one footing width below the foundation base. Under the idealized correction in which groundwater does not reduce the soil-weight contribution beyond that depth, what is the unmodified value of 0.5 gamma B Ngamma?

A 50 kPa. B 100 kPa. C 400 kPa. D 200 kPa.

Question 13 ప్రశ్న 13

For a strip footing with B = 2 m and foundation-level effective surcharge q = 36 kPa, take Nq = 8, gamma = 20 kN/m3 and Ngamma = 10. The water table lies 1 m below the footing base. Under a specified linear interpolation for the soil-weight correction, use W = 0.75 and qult = qNq + 0.5 gamma B Ngamma W. What is the calculated gross ultimate bearing pressure?

A 388 kPa. B 438 kPa. C 488 kPa. D 538 kPa.

Question 14 ప్రశ్న 14

A cohesionless strip footing is founded 2 m below ground level in soil that is fully submerged under hydrostatic conditions. Given gamma_sat = 20 kN/m3, gamma_w = 10 kN/m3, B = 2 m, Nq = 8 and Ngamma = 10, use the stated effective-stress bearing expression q'_ult = q' Nq + 0.5 gamma' B Ngamma, where gamma' = gamma_sat - gamma_w and q' = gamma' Df. What is the calculated value of q'_ult?

A 160 kPa. B 200 kPa. C 360 kPa. D 260 kPa.

Question 15 ప్రశ్న 15

Which set of shape factors corresponds to a square footing under the stated IS 6403-type modified bearing-capacity formulation, in which the soil-weight term is 0.5 gamma B Ngamma multiplied by s_gamma?

A sc = 1.3, sq = 1.2 and s_gamma = 0.8. B sc = 1.3, sq = 1.0 and s_gamma = 0.4. C sc = 1.0, sq = 1.0 and s_gamma = 1.0. D sc = 1.3, sq = 1.2 and s_gamma = 0.3.

Question 16 ప్రశ్న 16

Using the stated IS 6403-style net ultimate strip-footing equation qnet,ult = cNc + q(Nq - 1) + 0.5 gamma B Ngamma, take c = 15 kPa, Nc = 20, q = 25 kPa, Nq = 8, gamma = 20 kN/m3, B = 2 m and Ngamma = 5. If the factor of safety on net ultimate pressure is 2.5, what is the net safe bearing pressure?

A 200 kPa. B 250 kPa. C 230 kPa. D 575 kPa.

Question 17 ప్రశ్న 17

For a rectangular footing under the stated IS 6403 shape-factor expressions sc = sq = 1 + 0.2(B/L) and s_gamma = 1 - 0.4(B/L), calculate the shape factors when B = 2 m and L = 4 m.

A sc = sq = 1.20 and s_gamma = 0.60. B sc = sq = 1.10 and s_gamma = 0.80. C sc = sq = 1.05 and s_gamma = 0.90. D sc = sq = 1.50 and s_gamma = 0.50.

Question 18 ప్రశ్న 18

A modified net ultimate bearing-capacity calculation uses qnet,ult = cNc sc dc ic + q(Nq - 1)sq dq iq + 0.5 gamma B Ngamma s_gamma d_gamma i_gamma. Given c = 20 kPa, Nc = 10, sc = 1.10, dc = 1.20, ic = 1, q = 20 kPa, Nq = 5, sq = 1.10, dq = 1.10, iq = 1, gamma = 20 kN/m3, B = 2 m, Ngamma = 4, s_gamma = 0.80, d_gamma = 1.10 and i_gamma = 1, what is qnet,ult?

A 400.0 kPa. B 420.8 kPa. C 452.0 kPa. D 431.2 kPa.

Question 19 ప్రశ్న 19

An inclined-load bearing-capacity exercise specifies qnet,ult = q(Nq - 1)iq + 0.5 gamma B Ngamma i_gamma for a cohesionless strip footing, with all other correction factors equal to unity. Given q = 30 kPa, Nq = 10, iq = 0.81, gamma = 18 kN/m3, B = 2 m, Ngamma = 10 and i_gamma = 0.64, what is qnet,ult?

A 333.9 kPa. B 351.0 kPa. C 450.0 kPa. D 218.7 kPa.

Question 20 ప్రశ్న 20

A rectangular footing has original dimensions B = 2.0 m and L = 3.0 m and carries a vertical resultant of 896 kN. The resultant has eccentricities eB = 0.20 m along the B direction and eL = 0.10 m along the L direction. Using the specified effective-area approximation B' = B - 2eB and L' = L - 2eL, what are the effective bearing area and average effective-area load pressure?

A 6.00 m2 and 149.3 kPa. B 5.12 m2 and 175.0 kPa. C 4.48 m2 and 200.0 kPa. D 3.20 m2 and 280.0 kPa.

Question 21 ప్రశ్న 21

For a Terzaghi-type local-shear approximation, the modified cohesion is c_local = (2/3)c and the reduced friction angle satisfies tan(phi_local) = (2/3)tan(phi). If c = 30 kPa and phi = 30 degrees, what are the modified cohesion and friction angle approximately? Take tan(30 degrees) = 0.57735.

A 30 kPa and 30.0 degrees. B 20 kPa and 21.1 degrees. C 20 kPa and 20.0 degrees exactly. D 45 kPa and 45.0 degrees.

Question 22 ప్రశ్న 22

A strip footing is analysed for local shear using the explicitly supplied Terzaghi-type approximation qult = c_local Nc_local + qNq_local + 0.5 gamma B Ngamma_local. Given c_local = 20 kPa, Nc_local = 12, q = 25 kPa, Nq_local = 5, gamma = 18 kN/m3, B = 2 m and Ngamma_local = 4, what are the gross and net ultimate bearing pressures, respectively?

A 412 kPa gross and 437 kPa net. B 365 kPa gross and 340 kPa net. C 437 kPa gross and 437 kPa net. D 437 kPa gross and 412 kPa net.

Question 23 ప్రశ్న 23

For a continuous strip footing in drained cohesionless soil, use the IS 6403-type general-shear NET equation qnet,ult = q(Nq - 1) + 0.5 gamma B Ngamma, with no additional shape, depth, inclination or groundwater corrections. At the specified effective friction angle, the adopted bearing factors are Nq = 18.40 and Ngamma = 22.40. If q = 36 kPa, gamma = 18 kN/m3 and B = 2 m, what is qnet,ult?

A 1029.6 kPa. B 1065.6 kPa. C 626.4 kPa. D 1426.8 kPa.

Question 24 ప్రశ్న 24

In an ideal homogeneous soil, a strip footing is evaluated with the original gross equation qult = cNc + gamma Df Nq + 0.5 gamma B Ngamma, while all parameters except foundation depth remain unchanged. The depth increases from 1 m to 2 m, with gamma = 18 kN/m3 and Nq = 8. If net ultimate pressure is defined as qult - gamma Df, by how much does the calculated NET ultimate bearing pressure increase?

A 144 kPa. B 126 kPa. C 18 kPa. D 108 kPa.

Question 25 ప్రశ్న 25

A rectangular footing measures 2.0 m by 2.5 m at a depth of 1.0 m in level homogeneous soil of unit weight 18 kN/m3. Its calculated net safe bearing pressure against shear is 400 kPa, but the maximum net pressure satisfying settlement requirements is 260 kPa. Assuming uniform vertical contact pressure and using gross allowable pressure = allowable net pressure + gamma Df, what maximum total GROSS vertical load at the base is permitted?

A 1300 kN. B 2000 kN. C 1390 kN. D 1480 kN.

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