2. For a 50-story (above the ground) building with 4 floors of basement (D = 12.0 m), the average floor weight (including dead load and live load) is 15 kN/m². Assume the height of each floor of the basement is 3 m (including the thickness of the slab). The mat foundation (with a dimension of 30 m x 20 m) is situated in a thick clay layer with a saturated unit weight of 18 kN/m³ and an undrained shear strength (Su) of 30 kPa (remains constant with depth). In addition, the clay has an effective friction angle o' = 28° while c' = 0. Answer the following questions: (A) Would the mat foundation of the building be fully compensated? (B) The factor of safety for bearing capacity in a short-term condition. (C) The factor of safety for bearing capacity in a long-term condition. (Use FS = qu(net)/q, where the generalized bearing capacity equation is given by qu(net) = c'NcFcs Fcd Fci + YDNqFqsFqa Fai + 0.5yB Ny Fys Fya Fyi - YDf and q is the net average applied pressure on soil). Figure, Tables, and Equations: qu5.14c 1+0.195- 52) (1+0.4%)+9 9.-5.14c14 5.14c. (1+0.195)(1 +0.4%) Qu(net) qu-q= 5.14c, 1+ 0.195 Pile: Meyerhof's method Q₁ = 4,9 = 4,q'N₁₁ ≤ A¸¶₁ q₁ = 0.5ptan o' TABLE 12.6 Interpolated Values of N Based on Meyerhof's Theory (10.11) B Soil friction angle, ' (deg) 20 21 N₁₁ (10.12) all(net) Qu(net) FS = 1.713c,(1+0.195)(1 +0.4%) (10.13) B 26 27 28 General bearing capacity equation qu= c'NcFcs Fca Fci+q'NqFqsFqaFqi + 0.5yBNy Fys Fya Fyi Shape factors by De Beer Depth factors by Hansen (1970) (1970) 29 Inclination factors by Meyerhof (1963) and Hanna and Meyerhof (1981) 33 2222222222223 12.4 13.8 15.5 17.9 24 21.4 25 26.0 29.5 34.0 39.7 46.5 30 56.7 68.2 81.0 96.0 Fcs = 1+ B N L-Ne 34 Во 115.0 Fcd = 1 +0.4() Fci = Fqi = (1 900)2 35 143.0 36 168.0 B = Fas 1+) tan op' Fqd = 1 + 2 tan op' (1 - sin p')² - Df 37 194.0 Fyi = (1 - B 38 231.0 B Fys = 1-0.4(7) Fyd = 1 39 276.0 40 346.0 41 420.0 42 525.0 Shallow foundation: TABLE 6.2 Bearing Capacity Factors From Eqs. (6.30), (6.29), and (6.31) 43 650.0 TABLE 6.2 Bearing Capacity Factors From Eqs. (6.30), (6.29), and (6.31) (Continued) 44 780.0 45 930.0 $' N₂ N Ny $' N No N₁ $' No 22 N₁ Ny $' No Na 16.88 7.82 7.13 37 55.63 42.92 66.19 Ny 23 18.05 8.66 8.20 38 61.35 48.93 78.03 0 5.14 1.00 0.00 11 8.80 2.71 1.44 24 19.32 9.60 9.44 39 67.87 55.96 92.25 1 5.38 1.09 0.07 12 9.28 2.97 1.69 The critical depth for skin friction in piles 25 20.72 10.66 10.88 40 75.31 64.20 109.41 2 5.63 1.20 0.15 13 9.81 3.26 1.97 26 22.25 11.85 12.54 41 83.86 73.90 130.22 3 5.90 1.31 0.24 14 10.37 3.59 2.29 27 23.94 13.20 14.47 42 93.71 85.38 155.55 4 6.19 1.43 0.34 15 10.98 3.94 2.65 28 25.80 14.72 16.72 43 105.11 99.02 186.54 L'≈ 15D 5 6.49 1.57 0.45 16 11.63 29 4.34 27.86 16.44 19.34 44 118.37 115.31 224.64 3.06 30 30.14 18.40 22.40 45 133.88 134.88 271.76 6 6.81 1.72 0.57 17 12.34 4.77 3.53 31 32.67 20.63 25.99 46 152.10 158.51 330.35 7 7.16 1.88 0.71 18 13.10 5.26 4.07 32 35.49 23.18 30.22 47 173.64 187.21 403.67 The unit frictional resistance or the unit skin friction 8 7.53 2.06 0.86 19 13.93 5.80 4.68 33 38.64 26.09 35.19 48 199.26 222.31 496.01 9 7.92 2.25 1.03 20 14.83 6.40 5.39 34 42.16 29.44 41.06 49 229.93 265.51 613.16 10 8.35 2.47 1.22 21 15.82 7.07 6.20 35 46.12 33.30 48.03 50 266.89 319.07 762.89 (continued) 36 50.59 37.75 56.31 f = Ko tan 8'

Q3. A mat foundation is shown in figure below. The design considerations are L 12 m, B -10 m, Df 2.2 m, Q = 30 MN, x1 =2 m, x2 2 m, x3 -5.2 m, and preconsolidation pressure oe = 180 kN/m?. Calculate the consolidation settlement: under the center of the mat. • Under the corner of the mat Size of mat = BXL Sand Dr y = 16.0 kN/m3 X1 Groundwater table Sand Yeat = 18.0 kN/m Clay = 17.5 kN/m3 EYsat e, = 0.88 C = 0.38 C; = 0.1

A water tank is required to be constructed with a circular foundation having a diameter of 20m founded at a depth of 5m below the ground surface. The estimated distributed load on the foundation is 400 kN/m2. Assuming that the subsoil extends to a great depth and is isotropic and homogeneous, determine the stresses  at points (i) z = 10 m, r = 0, (ii) z = 10 m, r = 10 m, (iii) z = 20 m, r = 0 and (iv) z = 20m, r = 10m, where r is the radial distance from the central axis. Use the Influence Diagram below to calculate the I. Neglect the effect of the depth of the foundation on the stresses.

A mat foundation, 15 m x 15 m, is made of reinforced concrete and to be supported by a three-layer soil profile, as shown. The mat is 1 m thick, and the average stress on the surface of the slab assessed from the structural engineering analysis is 75 kPa. (Unit weight of concrete = 23.58 kN/m^3) The 5-m thick sand layer immediately below the mat foundation has been compacted to standard Proctor specifications, most likely to optimum moisture content, which is why its moist density is given. (A) Determine the pre-construction effective stress at Point A (bottom of the clay layer). This is the in situ effective stress (overburden pressure) measured from the ground surface prior to the placement of the mat foundation. (B) Determine the vertical stress increase induced by the mat foundation at Point A using the “Influence Chart,” commonly referred to as the “Spider Web.” (C) Determine the vertical stress increase induced by the mat foundation at Point A using the “Stress Isobars.” (D)…

It is proposed to build an 8 story building with a footprint of 15 m X 20 m, resting on a mat foundation of the same dimensions, in a saturated clay where cu = 50 kN/m², y = 19.0 kN/m³. Assume approximately 15 kN/m² per floor for the live and dead loads. a. At what depth would you place the mat to make this a fully compensated foundation? b. What should be the factor of safety if the mat is placed at 3.0 m depth?

Raft foundations

The plan of a rectangular foundation shown in figure transmits a uniform contact pressure of 120 kN/m². Determine the vertical stress induced by this loading at point B under a depth of 5 m. (40 marks) 25.0- 15.0 6.0- 4.0 B•

I need detailed help solving this exercise from Foundation Engineering. Step by step, please.

Soil mechanics

A strip foundation 8 m wide lies at ground level and applies a uniform pressure of 80 kPa. Determine the increase in vertical stress at 5 m below the ground level: a) beneath the center of the foundation b) beneath its edge c) 4 m away from the edge