3 Grading Policy Two 60-min Mid Semester Exams ……. 30% End Semester Exam …………… %Assignment ……………………………… 10%Projects/ Term Paper -…………………… 20%TOTAL %Course Website:
4 Soil Mechanics Review Soil behavour is complex: AnisotropicNon-homogeneousNon-linearStress and stress history dependantComplexity gives rise to importance of:TheoryLab testsField testsEmpirical relationsComputer applicationsExperience, Judgement, FOS
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 distributionSieve/Mechanical analysis or Gradation TestHydrometer analysis for smaller than .05 to .075 mm (#200 US Standard sieve)Particle size distribution curvesWell gradedPoorly graded
8 Additional Phase Relationships Typical Values of Parameters:
9 Atterberg LimitsLiquid 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.
10 Clay Mineralogy Clay fraction, clay size particles Particle size < 2 µm (.002 mm)Clay mineralsKaolinite, Illite, Montmorillonite (Smectite)- negatively charged, large surface areasNon-clay minerals- e.g. finely ground quartz, feldspar or mica of "clay" sizeImplication of the clay particle surface being negatively charged double layerExchangeable ions- Li+<Na+<H+<K+<NH4+<<Mg++<Ca++<<Al+++- Valance, Size of Hydrated cation, ConcentrationThickness of double layer decreases when replaced by higher valence cation - higher potential to have flocculated structureWhen double layer is larger swelling and shrinking potential is larger
11 Clay MineralogySoils 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.
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 1945Classification system based on eight major groups (A-1 to A-8) and a group indexBased on grain size distribution, liquid limit and plasticity indicesMainly used for highway subgrades in USAUnified Soil Classification System (UCS)Originally proposed in 1942 by A. CasagrandeClassification system pursuant to ASTM Designation D-2487Classification system based on group symbols and group namesThe USCS is used in most geotechnical work in Canada
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 gradedGroup names: several descriptionsPlasticity Chart
15 PermeabilityFlow through soils affect several material properties such as shear strength and compressibilityIf there were no water in soil, there would be no geotechnical engineering Darcy’s LawDeveloped in 1856Unit flow,Where: K = hydraulic conductivity∆h =difference in piezometric or “total” head∆L = length along the drainage pathDefinition of Darcy’s LawDarcy’s law is valid for laminar flow Reynolds Number: Re < 1 for ground water flow
18 Seepage 1-D Seepage: Q = k i A 2-D Seepage (flow nets) where, i = hydraulic gradient =∆h /∆L∆h = change in TOTAL headDownward seepage increases effective stressUpward seepage decreases effective stress2-D Seepage (flow nets)
19 Effective StressEffective stress is defined as the effective pressure that occurs at a specific point within a soil profileThe 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
20 Effective StressChanges in effective stress is responsible for volume changeThe effective stress is responsible for producing frictional resistance between the soil solidsTherefore, effective stress is an important concept in geotechnical engineeringOverconsolidation ratio, Where: σ´c = preconsolidation pressureCritical hydraulic gradient σ′ = 0 when i = (γb-γw) /γw → σ′ = 0
22 ExampleDetermine 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 datumevaluate distribution of total head with depthsubtract elevation head from total head to yield pressure headcalculate distribution with depth of vertical “total stress”subtract pore pressure (=pressure head x γw) from total stress
23 Vertical Stress Increase with Depth Allowable settlement, usually set by building codes, may control the allowable bearing capacityThe vertical stress increase with depth must be determined to calculate the amount of settlement that a foundation may undergoStress due to a Point LoadIn 1885, Boussinesq developed a mathematical relationship for vertical stress increase with depth inside a homogenous, elastic and isotropic material from point loads as follows:
24 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-
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:
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.
28 Newmark’s Influence Chart The Newmark’s Influence Chart method consists of concentric circles drawn to scale, each square contributes a fraction of the stressIn 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 increaseAdopt a scale of z=ABDraw the footing to scale and place the point of interest over the center of the chartCount the number of elements that fall inside the footing, NCalculate the stress increase as:
29 Simplified MethodsThe 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 horizontalAccording to the method, the increase in stress is calculated as follows:
30 Consolidation Settlement – total amount of settlement Consolidation – time dependent settlementConsolidation occurs during the drainage of pore water caused by excess pore water pressure
31 Settlement Calculations Settlement is calculated using the change in void ratio
37 Shear Strength Soil strength is measured in terms of shear resistance Shear resistance is developed on the soil particle contactsFailure occurs in a material when the normal stress and the shear stress reach some limiting combination
38 Direct shear testSimple, inexpensive, limited configurations
39 Triaxial Test Consolidated Drained Test may be complex, expensive, several configurationsConsolidated Drained Test
40 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 stressChanges in total stress do not change the shear strength in undrained loading
43 Unconfined Compression Test A special type of unconsolidated-undrained triaxial test in which the confining pressure, σ3, is set to zeroThe 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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