Fundamentals of Geotechnical Engineering (MindTap Course List)
5th Edition
ISBN: 9781305635180
Author: Braja M. Das, Nagaratnam Sivakugan
Publisher: Cengage Learning
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Chapter 17, Problem 17.5P
To determine
Find the elastic settlement at the center and corner of the foundation.
Find the settlement if the foundation is rigid.
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A foundation (Figure 1) transmits a stress of 100 kPa on the surface of a soil deposit.
a. Evaluate increases of vertical stresses points A, B, and C at the depth of 2m and Sm (2
points)
b. At what depth is the increase in vertical stress below A less than 10% of the surface
stress?
6 m
+2 m-
A
2 m
-4 m-
Figure 1: Plan of foundation
A vertical column load, P = 600 kN, is applied to a rigid square concrete foundation. The
foundation rests at a depth Df= 0.75 m on a uniform dense sand with the following properties:
average modulus of elasticity, Es = 20,600 kN/m², and Poisson's ratio, µs = 0.3. Calculate the
required foundation dimensions if the allowable settlement under the center of the foundation is
25mm.
600 kN
Foundation
0.75 m
Вхв
Soil
Hs = 0.3
E, = 20, 600 kN/m²
5.0 m
Rock
A flexible foundation is 2 m x 4 m rests on granular soil at ground level. It carries a uniformly distributed load of 160 kN/m2. The sand has an elastic modulus of 39 MPa , a Poisson's Ratio of 0.3 and is 5 m thick. Estimate the elastic settlement below the center of the loaded foundation. Give your answer in cm rounded to 2 decimal places.
Chapter 17 Solutions
Fundamentals of Geotechnical Engineering (MindTap Course List)
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- The subgrade reaction of a sandy soil obtained from the plate load test (plate dimensions 1 m × 0.7 m) is 18 MN/m3. What will be the value of k on the same soil for a foundation measuring 5 m × 3.5 m?arrow_forwardA 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)…arrow_forwardA3-m thickness of compacted earth fill is placed across an area as preparation for constructing an industrial building. An item of heavy industrial equipment will be placed at a location within the building and supported on a foundation installed at the surface of the compacted soil fill. The equipment has a total weight of 5,000 kN. The supporting foundation will be 5 m by 5 m. What net stress increase results beneath the center of the foundation in the original soil mass 2 m below the natural ground surface? Use 19 kN/m2 for the soil unit weight. Assume the Boussinesq conditions apply.arrow_forward
- The initial principal stresses at a certain depth in a clay soil are 100 kPa on the horizontal plane and 50 kPa on the vertical plane. Construction of a surface foundation induces additional stresses consisting of a vertical stress of 45 kPa, a lateral stress of 20 kPa, and a counterclockwise (with respect to the horizontal plane) shear stressof 40 kPa. Determine the change shearing stress in kPa.arrow_forwardThe initial principal stresses at a certain depth in a clay soil are 200 kPa on the horizontal plane and 100 kPa on the vertical plane. Construction of a surface foundation induces additional stresses consisting of a vertical stress of 45 kPa, a lateral (horizontal) stress of 20 kPa, and a counterclockwise (with respect to the horizontal plane) shear stress of 40 kPa. Plot Mohr's circle (1) for the initial state of the soil and (2) after construction of the foundation. Determine (a) the change in magnitude of the principal stress, (b) the change in maximum shear stress, and (c) the change in orientation of the principal stress plane resulting from the construction of the foundation.arrow_forward绘图 编辑 3.12 For a strip foundation, the width is 1.2m, buried depth is 1.2m, the standard value of the load applied on the foundation F=155KN/m, the soil layer is distributed as follows: from the ground to the depth of 1.2m is the land fill, =18KN/m³; the depth in the range of 1.2~1.8m is silty clay, fak=155kPa, E,=8.1Mpa, y=19KN/m³; below the depth of 1.8m is the mucky clay, fak=102kPa, E,=2.7Mpa. Try to check the base pressure and the bearing capacity of the weak sub-layer. Ground F=155KN/m OLand fill 18KN/m³ 1.2m O Silty clay La-155kPa;E-8.1Mpa;y-19KN/m³ -0, 1.0 O Mucky clay -0, H1.0 Sak-102kPa;E,-2.7Mpa 1.2marrow_forward
- Estimate the increase in vertical stress at 0.5 m depth intervals, within the clay layer, below point A (See figure below). The foundation exerts a uniform vertical stress of 120 kPa at ground level. Using these values estimate the settlement due to the clay layer. (Hand in any graphs used) 5m 5m 2m 3m Very Dense Sand 2m 1.5m Clay E=3.5 MPa 2m Bedrock Soil profile A Plan of building 3m Soil profile and plan for Question 4 3m FAarrow_forwardThe initial principal stresses at acertain depth in a clay soil are 200 kPa on the horizontal plane and 100 kPa on the vertical plane.Construction of a surface foundation induces additional stresses consisting of a vertical stress of 45 kPa, a lateral stress of 20 kPa, and a clockwise(with respect to the horizontal plane) shear stress of 40 kPa. Determine the change in shearing stress in kPa.arrow_forwardA rectangular foundation 6m x 12m carries a uniform pressure of 150 kN/m2 near the surface of a soil mass. Determine the vertical stresses at a depth of 6m below point A: 12 m 4 m 6 m 2 m A Select one: a. 0.040 b. 0.043 c. 0.0427 d. 0.044arrow_forward
- Foundation Ao Bx L Soil u, = Poisson's ratio E, = = modulus of elasticity H Rock Figure 11.43 11.2 Refer to Figure 11.43. A square rigid foundation measuring 1.8 m x 1.8 m in plan is supported by 8 m (H) of layered soil with the following characteristics: Layer type Thickness (m) E, (kKN/m?) Ya (KN/m?) Loose sand 0-2 20,680 17.6 Medium clay Dense sand 2- 4.5 7580 18.3 19.1 4.5 – 8 58,600 Given that P = 450 kN; D; = 1 m; and u, settlement of the foundation. = 0.3 for all layers, estimate the elastic O Cngagelamirg 2014 ©Cengage Learring 2014arrow_forwardProblem II. The initial principal stresses at a certain depth in a clay soil are 100 kPa on the horizontal plane and 50 kPa on the vertical plane. Construction of a surface foundation induces additional stresses consisting of a vertical stress of 45 kPa, a lateral stress of 20 kPa, and a counterclockwise (with respect to the horizontal plane) shear stress of 40 kPa. a. Plot Mohr's circle (1) for the initial state of the soil and (2) after construction of the foundation. b. Determine the change in magnitude of the principal stresses. C. the change in maximum shear stress d. the change in orientation of the principal stress plane resulting from the construction of the foundation.arrow_forward= Figure 2 shows a rectangular shallow foundation. The foundation measures 1.5 m x3 m (B x L) in plan. The clay layer is normally consolidated with: Ce=0.27; He 3 m; e 0.92; average effective stress on the clay layer due to applied foundation load Ao=24 kN/m². Determine the primary consolidation settlement of the foundation. Sand Y = 16.5 kN/m³ Sand Yat 17.8 kN/m³ Normally consolidated clay Ysat 18.2 kN/m³ = 0.92; C = 0.27 170 kN/m² 1m 1.5 m Ground water table --- --- 15 m 3 marrow_forward
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