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1 CE-632 Foundation Analysis and Design Instructor: Dr. Amit Prashant, FB 304, PH# 6054. E-mail: aprashan@iitk.ac.inaprashan@iitk.ac.in

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Foundation Analysis and Design by: Dr. Amit Prashant 2 Reference Books

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Foundation Analysis and Design by: Dr. Amit Prashant 3 Grading Policy Two 60-min Mid Semester Exams ……. 30% End Semester Exam ……………........... 40% Assignment ……………………………… 10% Projects/ Term Paper -…………………… 20% TOTAL 100% Course Website: http://home.iitk.ac.in/~aprashan/ce632/http://home.iitk.ac.in/~aprashan/ce632/

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Foundation Analysis and Design by: Dr. Amit Prashant 4 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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Foundation Analysis and Design by: Dr. Amit Prashant 5 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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Foundation Analysis and Design by: Dr. Amit Prashant 6 Effect of Particle size

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Foundation Analysis and Design by: Dr. Amit Prashant 7 Basic Volume/Mass Relationships

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Foundation Analysis and Design by: Dr. Amit Prashant 8 Additional Phase Relationships Typical Values of Parameters:

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Foundation Analysis and Design by: Dr. Amit Prashant 9 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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Foundation Analysis and Design by: Dr. Amit Prashant 10 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 +

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Foundation Analysis and Design by: Dr. Amit Prashant 11 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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Foundation Analysis and Design by: Dr. Amit Prashant 12 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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Foundation Analysis and Design by: Dr. Amit Prashant 13 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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Foundation Analysis and Design by: Dr. Amit Prashant 14 Grain Size Distribution Curve Gravel: Sand:

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Foundation Analysis and Design by: Dr. Amit Prashant 15 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 Darcys 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 Darcys Law Darcys law is valid for laminar flow Reynolds Number: Re < 1 for ground water flow

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Foundation Analysis and Design by: Dr. Amit Prashant 16

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Foundation Analysis and Design by: Dr. Amit Prashant 17 Permeability of Stratified Soil

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Foundation Analysis and Design by: Dr. Amit Prashant 18 Seepage 1-D Seepage: Q = k i A 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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Foundation Analysis and Design by: Dr. Amit Prashant 19 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, σ t, minus the pore water pressure, u, σ' = σ u

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Foundation Analysis and Design by: Dr. Amit Prashant 20 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 = (γ b -γ w ) /γ w σ = 0

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Foundation Analysis and Design by: Dr. Amit Prashant 21 Effective Stress Profile in Soil Deposit

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Foundation Analysis and Design by: Dr. Amit Prashant 22 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. 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 γ w ) from total stress Steps in solving seepage and effective stress problems:

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Foundation Analysis and Design by: Dr. Amit Prashant 23 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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Foundation Analysis and Design by: Dr. Amit Prashant 24 Vertical Stress Increase with Depth For the previous solution, material properties such as Poissons 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. Boussinesqs Solution for point load-

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Foundation Analysis and Design by: Dr. Amit Prashant 25 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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Foundation Analysis and Design by: Dr. Amit Prashant 26 Stress due to a Circular Load

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Foundation Analysis and Design by: Dr. Amit Prashant 27 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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Foundation Analysis and Design by: Dr. Amit Prashant 28 Newmarks Influence Chart The Newmarks 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: 1.Determine the depth, z, where you wish to calculate the stress increase 2.Adopt a scale of z=AB 3.Draw the footing to scale and place the point of interest over the center of the chart 4.Count the number of elements that fall inside the footing, N 5.Calculate the stress increase as:

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Foundation Analysis and Design by: Dr. Amit Prashant 29 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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Foundation Analysis and Design by: Dr. Amit Prashant 30 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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Foundation Analysis and Design by: Dr. Amit Prashant 31 Settlement Calculations Settlement is calculated using the change in void ratio

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Foundation Analysis and Design by: Dr. Amit Prashant 32 Settlement Calculations

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Foundation Analysis and Design by: Dr. Amit Prashant 33 Example

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Foundation Analysis and Design by: Dr. Amit Prashant 34 Consolidation Calculations Consolidation is calculated using Terzaghis one dimensional consolidation theory Need to determine the rate of dissipation of excess pore water pressures

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Foundation Analysis and Design by: Dr. Amit Prashant 35 Consolidation Calculations

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Foundation Analysis and Design by: Dr. Amit Prashant 36 Example

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Foundation Analysis and Design by: Dr. Amit Prashant 37 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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Foundation Analysis and Design by: Dr. Amit Prashant 38 Direct shear test Simple, inexpensive, limited configurations

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Foundation Analysis and Design by: Dr. Amit Prashant 39 Triaxial Test may be complex, expensive, several configurations Consolidated Drained Test

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Foundation Analysis and Design by: Dr. Amit Prashant 40 Triaxial Test Undrained Loading ( = 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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Foundation Analysis and Design by: Dr. Amit Prashant 41 Stress-Strain Relationships

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Foundation Analysis and Design by: Dr. Amit Prashant 42 Failure Envelope for Clays

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Foundation Analysis and Design by: Dr. Amit Prashant 43 Unconfined Compression Test A special type of unconsolidated-undrained triaxial test in which the confining pressure, σ 3, is set to zero The axial stress at failure is referred to the unconfined compressive strength, q u (not to be confused with qu) The unconfined shear strength, cu, may be defined as,

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Foundation Analysis and Design by: Dr. Amit Prashant 44 Stress Path

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Foundation Analysis and Design by: Dr. Amit Prashant 45 Elastic Properties of Soil

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Foundation Analysis and Design by: Dr. Amit Prashant 46 Elastic Properties of Soil

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Foundation Analysis and Design by: Dr. Amit Prashant 47 Hyperbolic Model Empirical Correlations for cohesive soils

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Foundation Analysis and Design by: Dr. Amit Prashant 48 Anisotropic Soil Masses Generalized Hooks Law for cross- anisotropic material Five elastic parameters

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