Question

Outdoor storage containers for a manufacturing facility impose a total loading of $5,500 \mathrm{kN}$ when full. The storage containers will be supported on a concrete pad foundation constructed near the soil surface. Space constraints require the foundation to have a length twice the width. The soil at the site is a clay; undrained shear tests indicate that the cohesion $c$ is $105 \mathrm{kPa}$ (the angle of internal friction is zero). The soil rigidity index is 60 . Determine the required foundtion size based on the extended bearing capacity equation and a factor of salety of 3.

   Outdoor storage containers for a manufacturing facility impose a total loading of $5,500 \mathrm{kN}$ when full. The storage containers will be supported on a concrete pad foundation constructed near the soil surface. Space constraints require the foundation to have a length twice the width. The soil at the site is a clay; undrained shear tests indicate that the cohesion $c$ is $105 \mathrm{kPa}$ (the angle of internal friction is zero). The soil rigidity index is 60 . Determine the required foundtion size based on the extended bearing capacity equation and a factor of salety of 3.
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Essentials of soil mechanics and foundations : basic geotechnics
Essentials of soil mechanics and foundations : basic geotechnics
David F. McCarthy 7th Edition
Chapter 14, Problem 19 ↓

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5B\gamma'_{f}N_{\gamma}$ Where: $Q_u$ = Ultimate bearing capacity of the soil $c$ = Cohesion of the soil = $105 \mathrm{kPa}$ $N_c$ = Bearing capacity factor for cohesion = 5.14 (for clay) $\sigma'_{vo}$ = Effective vertical stress at the base of the  Show more…

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Outdoor storage containers for a manufacturing facility impose a total loading of $5,500 \mathrm{kN}$ when full. The storage containers will be supported on a concrete pad foundation constructed near the soil surface. Space constraints require the foundation to have a length twice the width. The soil at the site is a clay; undrained shear tests indicate that the cohesion $c$ is $105 \mathrm{kPa}$ (the angle of internal friction is zero). The soil rigidity index is 60 . Determine the required foundtion size based on the extended bearing capacity equation and a factor of salety of 3.
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Key Concepts

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Extended Bearing Capacity Equation
This equation provides a means to calculate the ultimate load that a foundation can support by incorporating not only the basic soil properties such as cohesion and unit weight, but also factors such as foundation shape, size, and embedment, as well as the effects of water. It extends the classical bearing capacity formulas to account for additional conditions that affect stability, making it a critical tool in geotechnical design.
Shallow Foundation Design
Shallow foundations are structures used to transfer building loads to the soil near the surface. Their design involves understanding soil mechanics, load distributions, and the potential for uneven settlement. Key considerations include the foundation size, shape, and the stress distribution in the soil, which need to be optimized within the constraints of the site.
Undrained Soil Behavior
Undrained conditions refer to situations where the soil does not have time to consolidate or drain water under load, common in clays during rapid loading. Under these conditions, the shear strength is governed primarily by the soil's cohesion, and this behavior is critical when evaluating the soil's capacity to support loads without experiencing failure.
Soil Cohesion
Cohesion in soils, particularly in clays, is the component of shear strength that is independent of interparticle friction. It represents the 'stickiness' of the soil and plays a major role in the bearing capacity of undrained conditions, where the soil's resistance to shear failure is based mainly on this intrinsic quality.
Factor of Safety
The factor of safety is a design criterion used to ensure that structures have an adequate margin against failure. In foundation design, it is used to reduce the calculated ultimate bearing capacity to a safe allowable capacity, accounting for uncertainties in loading conditions, soil properties, and construction practices.
Foundation Aspect Ratio
The aspect ratio of a foundation, which is the relationship between its length and width, affects the distribution of stresses in the soil and the overall stability of the foundation. A specified aspect ratio, such as a length twice the width, influences design decisions by dictating the geometric constraints that impact bearing capacity calculations.
Soil Rigidity Index
The soil rigidity index is a measure that characterizes the stiffness of the soil, which in turn affects how the soil deforms under loading. In foundation design, it provides insight into the elastic behavior of the soil and helps in assessing whether the assumptions of the bearing capacity models remain valid under the expected loading conditions.

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P5.8. Find the dimension of a square footing to carry a column load 2000kN. The base of footing will be placed at 1.0m below the level of surrounding ground surface and the minimum factor of safety 3.0 is required. Soil around the footing is medium dense sandy soil with ϕ' = 35° (c'=0) and the total unit weight of soil γ = 19.0 kN/m³. The water table is well below the footing level and you can ignore its effect. (ANS: 1.8m) P5.9. Repeat P5.8 assuming one of the water table is at the footing base and the saturated unit weight of the soil is γsat = 20.8 kN/m³. (ANS: 1.95m) P5.10. Repeat P5.8 assuming the footing is rectangular and one of the dimensions is 2m. Determine the other dimension. (ANS: 1.7m) P5.11. Repeat P5.8 assuming the soil is clay with the following shear strength parameters: c' = 15kPa and ϕ' = 20°. (ANS: 3.1m)

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