Basic Geotechnical Earthquake Phần 7 docx

86 Basic Geotechnical Earthquake Engineering

middle one-third of footing. q′= 89.988 kN/m2 from Eq. (7.9). qult in Eq. (7.11) is

determined using Eq. (7.6) which makes use of Fig. 7.1. Hence qult = 330 kN/m2.

Consequently, Factor of safety = FS = 3.667.

(b) For 2 m wide square spread footing, Q = P = 600 kN, e = M/Q = 150/600

= 0.25 m. For middle one-third of footing, e can not exceed 0.33 m, and therefore

e is within middle one-third of footing. Q = 600/2 = 300 kN/m for use in Eq. (7.9).

q′ = 262.5 kN/m2 from Eq. (7.9) for 2m wide square spread footing. Furthermore,

T = 1.8 + 1.2 – 0.5 = 2.5m. c2 = 0 and c1 = 60 kN/m2. T/B = 2.5/2 = 1.25m

and c2/c1 = 0. Using these and from Fig. 7.1, Nc = 3.2. Hence qult = 249.6 kN/

m2 from Eq. (7.7) with B = L = 2 m. Consequently, Factor of safety = FS = 0.95.

Home Work Problems

1. Solve Example 7.1 assuming that both the existing 1.2 m thick and additional 1.8m thick

unliquefiable soil layer is cohesionless with effective friction angle equal to 31°. Coefficient of

earth pressure at rest is equal to 0.5. Total unit weight of soil above water table is 18.3 kN/m3

and buoyant unit weight of soil below water table is 9.7 kN/m3. Water table is at a depth of

1.2m below existing ground surface. (Ans. (a) FS = 0.8 (b) FS = 0.32)

2. Perform total stress analysis using Terzaghi equations for general and local shear failure to

find out factor of safety for 2 m wide square spread footing. Use data from Example 7.1.

(Ans. FS = 1.664)

3. Use data from Example 7.1. Assume that apart from vertical loads, the strip and the spread

footing is subjected to earthquake induced moment equal to 5 kN.m/m and 150 kN.m which

act in single (B) direction. Determine factor of safety using Eq. (7.12) (Ans. (a) FS = 4.58

(b) FS = 1.176.

4. A site consists of a sand deposit with a fluctuating groundwater table. The expected depth

of footing will be 0.5 to 1 m. Assume that groundwater table can rise to a level close to

footing base. Buoyant unit weight of sand is 9.65 kN/m3, effective friction angle for sand =

32° and pore water pressure ratio = 0.2. Using factor of safety of 5, determine allowable

bearing capacity for:

(a) 1.5m wide strip footing.

(b) 2.5m wide square spread footing.

(Ans. (a) 24.318 kPa (b) 32.424 kPa))

5. What are the guidelines to calculate undrained shear strength in the bearing capacity analysis

for cohesive soil weakened by earthquake?