3: STRESSES IN SOIL FROM EXTERNAL LOADINGS
- Page ID
- 123394
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 3.1: Introduction to Part 3
- This page discusses calculating the minimum distance between storage tanks on stiff saturated clay to prevent soil stress overlap. It employs linear elasticity theory for stress calculation, utilizing Young's modulus and Poisson's ratio for analytical solutions. The page mentions the use of plane-strain and axisymmetric models for analyzing stress distribution and teases further elaboration on stress and pressure concepts in upcoming chapters.
- 3.2: Stresses in the soil due to a point load
- This page discusses modeling the load from structures like electric power poles as a point load on a homogeneous elastic half-space. It outlines how to calculate additional soil stresses using specific equations, which must be added to existing geostatic stresses to find the total soil stress. Key parameters impacting the calculations include the Poisson ratio and distances from the load, which affect various stress components.
- 3.3: Stresses in the soil due to a line load
- This page explores modeling rail track loading on soil as an "infinitely long" line load in a homogeneous elastic half-space. It details the calculation of additional soil stresses under plane-strain symmetry, focusing on stress increments and distances from the load. Additionally, it addresses line loads near retaining wall crests, offering formulas for horizontal stress distribution and resulting horizontal force per meter.
- 3.4: Stresses in the soil due to a strip pressure
- This page discusses modeling stresses on soil surfaces using an infinite strip pressure on a homogeneous elastic half-space. It notes the significance of plane-strain symmetry for calculating additional stresses, defines stress increment components and angles (to be provided in radians, including negatives), and references figures for clarity on the relationships involved.
- 3.5: Stresses in the soil due to a circular pressure
- This page covers the modeling of stress in soil due to a circular footing, commonly seen with structures such as tanks and silos. It describes how uniform vertical pressure and axisymmetric loading lead to specific stress increments in a homogeneous elastic half-space. The text references equations that detail the vertical and radial stress components, influenced by the soil's Poisson ratio and the radius of the pressure zone.
- 3.6: Stresses in the soil due to a rectangular pressure
- This page examines the complexities of vertical stress distribution from a rectangular footing on a homogeneous elastic half-space, emphasizing that it deviates from simple models. It proposes a 2:1 stress distribution approximation for depths exceeding the footing width and notes the utility of Fadum charts for stress calculations, with further exploration of various geometries to follow.
- 3.7: Discussion
- This page discusses stress increment calculations in soils under external loading, focusing on how total stresses are resisted by pore water pressure and the soil skeleton. It emphasizes effective stress changes leading to soil settlement and the principle of superposition for summing stress increments. The text details methods for estimating vertical stress from complex pressure distributions and introduces the concept of influence depth.
- 3.9: Additional problems
- This page explores engineering challenges in stress calculations under various load conditions, validating Saint-Venant’s principle through the analysis of vertical stress increments with depth. It contrasts horizontal stresses on flexible and rigid retaining walls due to line loads and discusses decision-making for sewage pipeline placement. The document concludes with a vertical stress calculation related to an embankment.
- 3.10: Example 3.1
- This page discusses the vertical stress calculation in soil from a water tank on a ring foundation, detailing a tank height of 4 meters and an external radius of 5 meters. The total load on the foundation is 3141 kN, resulting in a pressure of 111 kPa on the ring footing. It applies the principle of superposition to analyze compressive and tensile stresses on the soil at a depth of 5 meters.
- 3.11: Example 3.2
- This page examines the numerical estimation of stresses under a ring-type foundation using PLAXIS, comparing it with an analytical method. It models soil as linear elastic, starting from a 20 m x 20 m area while analyzing stress influence depth. The study involves a coarse mesh, footing pressure application, and a soil unit weight of zero. Results indicate strong alignment in stress distribution near the footing but discrepancies at deeper levels, with accuracy enhanced in a deeper model.