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**CE-632 Foundation Analysis and Design**

Instructor: Dr. Amit Prashant, FB 304, PH#

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Reference Books

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**Grading Policy Two 60-min Mid Semester Exams ……. 30%**

End Semester Exam …………… % Assignment ……………………………… 10% Projects/ Term Paper -…………………… 20% TOTAL % Course Website:

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**Soil Mechanics Review Soil behavour is complex:**

Anisotropic Non-homogeneous Non-linear Stress and stress history dependant Complexity gives rise to importance of: Theory Lab tests Field tests Empirical relations Computer applications Experience, Judgement, FOS

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**Soil Texture Particle size, shape and size distribution**

Coarse-textured (Gravel, Sand) Fine-textured (Silt, Clay) Visibility by the naked eye (0.05mm is the approx limit) Particle size distribution Sieve/Mechanical analysis or Gradation Test Hydrometer analysis for smaller than .05 to .075 mm (#200 US Standard sieve) Particle size distribution curves Well graded Poorly graded

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**Effect of Particle size**

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**Basic Volume/Mass Relationships**

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**Additional Phase Relationships**

Typical Values of Parameters:

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Atterberg Limits Liquid limit (LL): the water content, in percent, at which the soil changes from a liquid to a plastic state. Plastic limit (PL): the water content, in percent, at which the soil changes from a plastic to a semisolid state. Shrinkage limit (SL): the water content, in percent, at which the soil changes from a semisolid to a solid state. Plasticity index (PI): the difference between the liquid limit and plastic limit of a soil, PI = LL – PL.

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**Clay Mineralogy Clay fraction, clay size particles**

Particle size < 2 µm (.002 mm) Clay minerals Kaolinite, Illite, Montmorillonite (Smectite) - negatively charged, large surface areas Non-clay minerals - e.g. finely ground quartz, feldspar or mica of "clay" size Implication of the clay particle surface being negatively charged double layer Exchangeable ions - Li+<Na+<H+<K+<NH4+<<Mg++<Ca++<<Al+++ - Valance, Size of Hydrated cation, Concentration Thickness of double layer decreases when replaced by higher valence cation - higher potential to have flocculated structure When double layer is larger swelling and shrinking potential is larger

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Clay Mineralogy Soils containing clay minerals tend to be cohesive and plastic. Given the existence of a double layer, clay minerals have an affinity for water and hence has a potential for swelling (e.g. during wet season) and shrinking (e.g. during dry season). Smectites such as Montmorillonite have the highest potential, Kaolinite has the lowest. Generally, a flocculated soil has higher strength, lower compressibility and higher permeability compared to a non-flocculated soil. Sands and gravels (cohesionless ) : Relative density can be used to compare the same soil. However, the fabric may be different for a given relative density and hence the behaviour.

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**Soil Classification Systems**

Classification may be based on – grain size, genesis, Atterberg Limits, behaviour, etc. In Engineering, descriptive or behaviour based classification is more useful than genetic classification. American Assoc of State Highway & Transportation Officials (AASHTO) Originally proposed in 1945 Classification system based on eight major groups (A-1 to A-8) and a group index Based on grain size distribution, liquid limit and plasticity indices Mainly used for highway subgrades in USA Unified Soil Classification System (UCS) Originally proposed in 1942 by A. Casagrande Classification system pursuant to ASTM Designation D-2487 Classification system based on group symbols and group names The USCS is used in most geotechnical work in Canada

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**Soil Classification Systems**

Group symbols: G - gravel S - sand M - silt C - clay O - organic silts and clay Pt - peat and highly organic soils H - high plasticity L - low plasticity W - well graded P - poorly graded Group names: several descriptions Plasticity Chart

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**Grain Size Distribution Curve**

Gravel: Sand:

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Permeability Flow through soils affect several material properties such as shear strength and compressibility If there were no water in soil, there would be no geotechnical engineering Darcy’s Law Developed in 1856 Unit flow, Where: K = hydraulic conductivity ∆h =difference in piezometric or “total” head ∆L = length along the drainage path Definition of Darcy’s Law Darcy’s law is valid for laminar flow Reynolds Number: Re < 1 for ground water flow

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**Permeability of Stratified Soil**

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**Seepage 1-D Seepage: Q = k i A 2-D Seepage (flow nets)**

where, i = hydraulic gradient =∆h /∆L ∆h = change in TOTAL head Downward seepage increases effective stress Upward seepage decreases effective stress 2-D Seepage (flow nets)

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Effective Stress Effective stress is defined as the effective pressure that occurs at a specific point within a soil profile The total stress is carried partially by the pore water and partially by the soil solids, the effective stress, σ’, is defined as the total stress, σt, minus the pore water pressure, u, σ' = σ − u

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Effective Stress Changes in effective stress is responsible for volume change The effective stress is responsible for producing frictional resistance between the soil solids Therefore, effective stress is an important concept in geotechnical engineering Overconsolidation ratio, Where: σ´c = preconsolidation pressure Critical hydraulic gradient σ′ = 0 when i = (γb-γw) /γw → σ′ = 0

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**Effective Stress Profile in Soil Deposit**

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Example Determine the effective stress distribution with depth if the head in the gravel layer is a) 2 m below ground surface b) 4 m below ground surface; and c) at the ground surface. Steps in solving seepage and effective stress problems: set a datum evaluate distribution of total head with depth subtract elevation head from total head to yield pressure head calculate distribution with depth of vertical “total stress” subtract pore pressure (=pressure head x γw) from total stress

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**Vertical Stress Increase with Depth**

Allowable settlement, usually set by building codes, may control the allowable bearing capacity The vertical stress increase with depth must be determined to calculate the amount of settlement that a foundation may undergo Stress due to a Point Load In 1885, Boussinesq developed a mathematical relationship for vertical stress increase with depth inside a homogenous, elastic and isotropic material from point loads as follows:

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**Vertical Stress Increase with Depth**

For the previous solution, material properties such as Poisson’s ratio and modulus of elasticity do not influence the stress increase with depth, i.e. stress increase with depth is a function of geometry only. Boussinesq’s Solution for point load-

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**Stress due to a Circular Load**

The Boussinesq Equation as stated above may be used to derive a relationship for stress increase below the center of the footing from a flexible circular loaded area:

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**Stress due to a Circular Load**

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**Stress due to Rectangular Load**

The Boussinesq Equation may also be used to derive a relationship for stress increase below the corner of the footing from a flexible rectangular loaded area: Concept of superposition may also be employed to find the stresses at various locations.

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**Newmark’s Influence Chart**

The Newmark’s Influence Chart method consists of concentric circles drawn to scale, each square contributes a fraction of the stress In most charts each square contributes 1/200 (or 0.005) units of stress (influence value, IV) Follow the 5 steps to determine the stress increase: Determine the depth, z, where you wish to calculate the stress increase Adopt a scale of z=AB Draw the footing to scale and place the point of interest over the center of the chart Count the number of elements that fall inside the footing, N Calculate the stress increase as:

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Simplified Methods The 2:1 method is an approximate method of calculating the apparent “dissipation” of stress with depth by averaging the stress increment onto an increasingly bigger loaded area based on 2V:1H. This method assumes that the stress increment is constant across the area (B+z)·(L+z) and equals zero outside this area. The method employs simple geometry of an increase in stress proportional to a slope of 2 vertical to 1 horizontal According to the method, the increase in stress is calculated as follows:

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**Consolidation Settlement – total amount of settlement**

Consolidation – time dependent settlement Consolidation occurs during the drainage of pore water caused by excess pore water pressure

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**Settlement Calculations**

Settlement is calculated using the change in void ratio

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**Settlement Calculations**

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Example

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**Consolidation Calculations**

Consolidation is calculated using Terzaghi’s one dimensional consolidation theory Need to determine the rate of dissipation of excess pore water pressures

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**Consolidation Calculations**

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Example

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**Shear Strength Soil strength is measured in terms of shear resistance**

Shear resistance is developed on the soil particle contacts Failure occurs in a material when the normal stress and the shear stress reach some limiting combination

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Direct shear test Simple, inexpensive, limited configurations

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**Triaxial Test Consolidated Drained Test**

may be complex, expensive, several configurations Consolidated Drained Test

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**Triaxial Test Undrained Loading (f = 0 Concept)**

Total stress change is the same as the pore water pressure increase in undrained loading, i.e. no change in effective stress Changes in total stress do not change the shear strength in undrained loading

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**Stress-Strain Relationships**

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**Failure Envelope for Clays**

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**Unconfined Compression Test**

A special type of unconsolidated-undrained triaxial test in which the confining pressure, σ3, is set to zero The axial stress at failure is referred to the unconfined compressive strength, qu (not to be confused with qu) The unconfined shear strength, cu, may be defined as,

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Stress Path

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**Elastic Properties of Soil**

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**Elastic Properties of Soil**

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Hyperbolic Model Empirical Correlations for cohesive soils

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**Anisotropic Soil Masses**

Generalized Hook’s Law for cross-anisotropic material Five elastic parameters

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