lecture note of soil mechanics, Lecture notes of Soil Mechanics and Foundations

Download lecture note of soil mechanics and more Lecture notes Soil Mechanics and Foundations in PDF only on Docsity! Fundamentals of Geotechnical Engineering - Il Chapter 4 Soil Water, Permeability & Seepage o ue General Outline Soil Water cntd Hydrologic cycle Moisture vapour in the clouds condenses under the influence of temperature changes and fall to the earth as rain, snow, hail etc. A part of this precipitation may not reach land surface but evaporates in the air while falling or may evaporate from leaves or roofs etc. Most of the precipitation, however, falls on the land which ends up being disposed in three ways; >» Evaporates directly from the soil > Run off the surface (runoff) >» Soaks into the soil. Soil Water cntd evapotranspiration transpiration precipitation z ‘ pecenraion ine infiltration » ‘ as : ; r : ground surface vertical and iT lateral flow > © unsaturated | water table —oF unsaturated Soil Water cntd Infiltration vs Percolation vs Seepage a When rain falls upon the ground it first of all wets the vegetation or the bare soil. When the surface cover is completely wet, subsequent rain must either penetrate the surface layers, if the surface is permeable, or run off the surface towards a stream channel if it is impermeable. u If the surface layers are porous and have minute passages available for the passage of water droplets, the water infiltrates into the subsurface soil. Soil with vegetation growing on it is always permeable to some degree. Once infiltrating water has passed through the surface layers, it percolates downward under the influence of gravity until it reaches the zone of saturation at the phreatic surface. Soil Water cntd a At groundwater level, the hydrostatic pressure is zero, so another definition of water table is the level to which water will eventually rise in an unlined borehole. a The water table is not constant but rises and falls with variations of rainfall, atmospheric pressure, temperature, etc., whilst coastal regions are affected by tides. Ground water — the continous body of sub-surface water that fills the soil voids and fissures and is free to move under the influence of gravity. 10 Soil Water cntd Aeration zone (Vadose zone) > occurs between the water table and the surface > can be split into three sections. a Soil belt — zone constantly affected by precipitation, evaporation and plant transpiration. a Intermediate belt — zone where certain amount of rainwater percolating downward to the water table is held in the soil by the action of surface tension, capillarity, abdsorption and chemical action. a Capillary fringe — zone where water is drawn up above the water table into the interstices of the soil or rock owing to capillarity phenomena. 11 Soil Water cntd Classification of Soil Moisture a Adsorbed a Capillary Hygroscopic — pi Capillary water a Gravitational a Perched a Artesian remaining water adheres i to soil particles i water held in micropores : i (available water- } plantrootscan i absorb this) Wilting point — : ' © Field capacity 12 Soil Water cntd a Water adsorbed on the surfaces of soil particles is referred to as adsorbed water because of its immobility, as in bound water. a The amount of water held by adsorption depends on specific surfaces which in turn depend on particle size, shape, and gradation. a A relatively well graded material will normally have much greater adsorption power. a Adsorbed water may be removed by evaporation (oven drying of soil). 15 Soil Water cntd Capillary Water — water retained in a soil mass due to the capillary phenomenon which enables dry soil to draw water to elevation above the water table and enables a draining soil to retain water above the atmospheric line. . | 1 ||] . >» Removed by air drying. peteeytanapaaeay aga The movement and retention of | water above the ground water table is similar in many respects MN to the rise and retention of water in capillary tube. 16 Soil Water cntd Water pressure varies linearly both below & above water table. At level BB, the water pressure is yjyhz Total pressure at level BB is yh, + P, (P,=atmospheric pressure) The negative water pressure at level CC is —h2zVy. Hence the total pressure at level CC would be P, — hzYy (a) Capiliary rise (b) Stress In water in (ce) Height of copillory rise. 17 capillary tube Soil Water cntd The total force developed along the perimeter is F = 2mrT, cosa The capillary stress U would then be F 2nmrT,cosa 2T;cosa A mr? r The maximum capillary stress occurs when a = 0. Hence 20 Soil Water cntd Y =p Cosa _ 2Ts COS a _ _ 27s Ty, COS Tn Ts lg ag Ts |__sSAND y WATER 5.5L 2r 21 Soil Water cntd Rise of Water in Capillary Tube of Uniform Internal Diameter When thin glass tube, open at both ends, is dipped into water, the water will rise in the tube to a certain height. The capillary rise can easily be related to the surface tension by considering the equilibrium of capillary column. Let the surface tension per unit perimeter = T, The contact angle = a Force acting upward = 27rT, cosa Force acting downward = h, yr For equilibrium condition heYwtr? = 2nrT, cosa 22 Soil Water cntd Factors affecting capillary rise in soils a Positions of the ground water table a Evaporation opportunity Discontinuous moisture zone a Grain size of the soil ae 1 Capillary fringe ze J = / \ Capillary saturation zone Capittary flow 100% Saturation zone > capillary is more pronounced in fine grained soils than in course grained . Video: Capillary rise with varying tube diameters 25 Soil Water cntd Gravitational Water : completely free to move through or drain from soil under the influence of gravity. The flow of gravitational water is caused by the action of gravity which tends to pull water downward to a lower elevation. The gravitational pull acts to overcome resistance to movement or flow of water which is due to viscous drag along the side walls of pore spaces in the case of soil. 26 2. Permeability > Introduction > Darcy‘s Law > Hydraulic Gradient > Determination of Permeability > Permeability in Stratified Soils 27 Permeability Bernoulli‘s equation for total head: H = Z + Py? In soils where ve \ cntd 2 Yw 2g ocity of flow is very low, H = Z + - Ww h=H,—Hy =Z,+ 14-2, +12 Z Yw Yw 30 Permeability cntd Hydraulic Gradient — loss of head per unit length of flow. water length AB, along the stream line 31 Permeability cntd Darcy‘s Law v=ki v=discharge velocity, which is the quantity of water flowing in unit time through a unit gross cross-sectional area at right angles to the direction of flow k=hydraulic conductivity (coefficient of permeability) q=vA=kiA Darcy’s law given is true for laminar flow through the void spaces. 32 Permeability cntd (after Casagrande and Fadum, 1939) k (cm/sec) Soils type Drainage conditions 10! to 10? Clean gravels Good 10! Clean sand Good 107 to 10-4 Clean sand and gravel mixtures Good 10-5 Very fine sand Poor 10° Silt Poor 1077 to 10-9 Clay soils Practically impervious Coefficient of Permeability k (m/s) 10° 107° 1o-? 107? 107+ 10-5 1o-® 10-? 107 107% to-' tor"! Drainage Good Poor Practically Impervious Soil Clean gravel Clean sands, clean sand Very fine sands, organic and inorganic | “Impervious” soils, e.g., homogeneous types and gravel mixtures silts, mixtures of sand silt and clay, glacial | clays below zone of weathering till, stratified clay deposits, etc. “Impervious” soils modified by effects of vegetation and weathering 35 Permeability cntd Methods of determining hydraulic conductivity LI Empirical Methods L) Kozeny-Carman / Taylor’s Formula LL) Hazen’s Formula LJ Laboratory Methods L) Constant Head Test U) Falling Head Test QO) Capillary Permeability Test L) Oedometer Test (Indirectly) LI Field Methods L) Pumping In Test / Pumping Out Tests L) Unconfined / Confined Aquifer L) Constant Head / Falling Head x6 Permeability cntd Empirical Methods LU) Taylor’s Formula C, is a constant related to shape that can be obtained from laboratory experiments. LL) Hazen’s Formula k=C-D2, (unit: cm/s) where C is a constant varying between 0.4 and 1.4 where D,, is in mm. 37 Permeability cntd Laboratory Methods Falling Head Test -used for fine-grained soils because the flow of water through these soils is too slow to get reasonable measurements from the constant-head test. = Acompacted soil sample or a sample extracted from the field is placed in a metal or acrylic cylinder. = Porous stones are positioned at the top and bottom faces of the sample to prevent its disintegration and to allow water to percolate through it. Standpipe Fine—-grained soil =e To beaker 40 Permeability cntd Water flows through the sample from a standpipe attached to the top of the cylinder. The head of water (h) changes with time as flow occurs through the soil. At different times, the head of water is recorded. Let dh be the drop in head over a time period dt. The velocity or rate of head loss in the tube is _ dh Oe Ot and the inflow of water to the soil is dh (dz)in =av= oe where a is the cross-sectional area of the tube. 41 Permeability cntd The outflow using Darcy’s law is: h (qz)our = Aki = Ake where A is the cross-sectional area, L is the length of the soil sample, and h is the head of water at any time t. The continuity condition requires that (q,)in = (Gz)out dh _ tt “dt L Ak (® hodh — dt = -| — aL J, h, ht Video: Falling head test 42 Permeability cntd The equation, called the simple well formula, is derived using the following assumptions. 1. The water-bearing layer (called an aquifer) is unconfined and nonleaky. 2. The pumping well penetrates through the water-bearing stratum and is perforated only at the section that is below the groundwater level. 3. The soil mass is homogeneous, isotropic, and of infinite size. 4. Darcy’s law is valid. 5. Flow is radial toward the well. 6. The hydraulic gradient at any point in the water-bearing stratum is constant and is equal to the slope of groundwater surface (Dupuit’s assumption). 45 Permeability cntd Let dz be the drop in total head over a distance dr. Then, according to Dupuit’s assumption, the hydraulic radient is i = a 8 7 dr The area of flow at a radial distance r from the center of the pumping well is A= 2mrz where z is the thickness of an elemental volume of the pervious layer. From Darcy’s law, the flow is 46 Permeability cntd Rearanging and integrating the equation between the limits 7, and rz and h, and hz mdr h2 a | = 2ke | zdz T4 hy _ _ dein@,/7) m(h3 — hf) NB. Pumping test is only practical for coarse-grained soils. 47 Permeability cntd Pumped Well Observation wells “7 ] _ T ] t7-R rn L os ee I I ae _ | er | ' Tt {| |N Case 2 | a | “1 |]. when : - | r | ho< Hy H | | / | h | fern a poh |} \| Ho>Ho Confine h 1 Ln ao + ! 1 I 2 1 H aquifer 7 nl] > er | ! 1 +. 7 nO I pire yt | | a | Impermeable stratum 50 Permeability cntd Case 1: When h, > H, A = 2mrH, andi = dh/dr Q =kiA = k(dh/dr)(2mrH,) dr 2nkH, r Q dh 0 Q Jn, [- dr 2mkH, (™ Tr. k= Q In(%2/7;) ~ 2H [hz — hy] 51 Permeability cntd Case 2: When h, < Hy The flow pattern close to the well is similar to unconfined aquifer whereas at distances further from the well the flow is artesian. _ Q In(7;{/T) ~ w[2HH, — H2 — h?2] Radius of influence, R; , for stabilized flow condition is given by: R; = 3000D,Vk (m) 52 Permeability cntd Flow parallel to soil layers The flow through the soil mass as a whole is equal to the sum of the flow through each of the layers. Consider a unit width (in the y direction) of flow dx = Av=(1x Ho )Kx(eqyl = (1 X Z,)kyyi + 1 X Za) koi +... +1 X 2, ) Kyni where H, is the total thickness of the soil mass, ky¢eq) is the equivalent permeability in the horizontal direction, Z, to Z,, are the thickness of the first to the nth layers, k,., to k,, are the horizontal hydraulic conductivities og the first to the nth layer. 1 Kx(eq) = y, Zuko + Zk x2 + w+ Znk xn) 55 Permeability cntd Flow normal to soil layers The head loss in the soil mass is the sum of the head losses in each layer. where AH is the total head loss, Ah, to Ah, are the head losses in each of the n layers.. AH Ah, Ah, Ah, Ka(eq) y= Ka = 2 = hen where kz eq) is the equivalent hydraulic conductivity in the vertical direction and k,, to kz, are the vertical hydraulic conductivities of the first to the nth layer. k “2 oe z(eq) ~ Z| 22 kn + + Kes +...4+ a 56 Permeability cntd Equivalent Hydraulic Conductivity Req = Jkxceaykzcea) NB. Values of kz(eq) are generally less than ky (eq) - sometimes as much as 10 times less. 57 3. Seepage > Introduction > Laplace Equation > Flow Nets > Sketching (Isotropic / Anisotropic) > Interpretation (Flow rate, piping) > Design of Filters 60 Seepage Introduction Seepage: flow of water through the soil pores under pressure gradient. Flow is not one directional only and is not uniform over the entire area perpendicular to the flow. 61 Seepage cntd Laplace‘s Equation >» describes the flow of water through soils. Flow of water through soils is analogous to steady-state heat flow and flow of current in homogeneous conductors. The popular form of Laplace’s equation for two- dimensional flow of water through soils is 0*H 0*H Kx gua + Ke Ga = © where H is the total head and k, and k, are the hydraulic conductivities in the X and Z directions. 62 Seepage cntd a The solution of any differential equation requires knowledge of the boundary conditions which are complex for most “real” structures. As a result, it is difficult to obtain an analytical solution or closed- form solution for these structures. a We have to resort to approximate solutions, which we can obtain using numerical methods such as finite difference, finite element, and boundary element. Q One is an approximate method called flownet sketching; a simple and flexible method which conveys a picture of the flow regime. It is the method of choice among geotechnical engineers. 65 Seepage Stream line is simply the path of a water molecule. From upstream to downstream, total head steadily decreases along the stream line. concrete dam soil- impervious strata 66 Seepage cntd Equipotential line is simply a contour of constant total head. concrete dam H=0.8 h_ impervious strata 67 Seepage cntd 5. The head loss between each consecutive equipotential line is constant. 6. A flow line cannot intersect another flow line (i.e. flow cannot occur across flow lines.) 7. An equipotential line cannot intersect another equipotential line. 8. The velocity of flow is normal to the equipotential line. 9. Flow lines and equipotential lines are orthogonal (perpendicular) to each other. 10. The difference in head between two equipotential lines is called the potential drop or head loss. 70 Seepage cntd Flow nets construction methods 1. Analytical method — based on the Laplace equation although rigorously precise, is not universally applicable in all cases because of the complexity of the problem involved. 2. Electrical analog method — extensively made use of in many important design problems. 3. Scaled model method — useful to demonstrate the fundamentals of fluid flow, but their use in other respects is limited because of the large amount of time and effort required to construct such models. 4. Graphical method — used in most of the cases in the field of soil mechanics where the estimation of seepage flows and pressures are generally required. 71 Seepage cntd Graphical methods LI The graphical method developed by Forchheimer (1930) has been found to be very useful in solving complicated flow problems. L) A. Casagrande (1937) improved this method by incorporating many suggestions. LI The main drawback of this method is that a good deal of practice and aptitude are essential to produce a satisfactory flow net. UL In spite of these drawbacks, the graphical method is quite popular among engineers. 72 Seepage Upstream Sheet pile Vv Upstream Downstream datum D=25.7m Downstream ‘ Drainage pipe 75 Seepage cntd Flow Net Construction for Anisotropic Soils 0°H 0°H Mx yz + Me pa = © LetC = /k,/k, and x; = Cy. Ox, Ox OH _ OH Ox, _ OH ax Ox, 0x ~~ Ox, 0*H 07H Jae 76 Seepage cntd Through substitution, Laplace equation becomes C? oH + ott = 0 0x,?2 Az? Simplifying 07H / 0*H | 0 Ax,2 Azz Implication: for anisotropic soils we can use the procedure for fl ownet sketching described for isotropic soils by scaling the x distance by /k,/k,. i.e. one must draw the structure and flow domain by multiplying the horizontal distances by /k,/k,. 77 Seepage cntd EXERCISE 4.3.3 An excavation is proposed for a site consisting of a homogeneous, isotropic layer of silty clay, 14.24 m thick, above a deep deposit of sand. The groundwater is 2 m below ground level outside the excavation. The groundwater level inside the excavation is at the bottom (see Figure on next slide). The void ratio of the silty clay is 0.62 and its specific gravity is 2.7. What is the limiting depth of the excavation to avoid heaving? Assume artesian condition is not present. NB. Heaving will occur if i > i, 80 cntd Seepage EXERCISE 4.3.3 81 Seepage cntd Piping in Granular Soils At the downstream, near the dam, Ah the exit hydraulic gradient 1 .=— exit Al hy, datum concrete es soil impervious strata 82 Seepage cntd EXERCISE 4.3.4 A bridge pier is to be constructed in a riverbed by constructing a cofferdam (see figure in the next slide). A cofferdam is a temporary enclosure consisting of long, slender elements of steel, concrete, or timber members to support the sides of the enclosure. After construction of the cofferdam, the water within it will be pumped out. Determine (a) the flow rate using k = 1 x 107* cm/s and (b) the factor of safety against piping. The void ratio of the sand is 0.59. There was a long delay before construction began, and a 100-mm layer of silty clay with k = 1 x 10-© cm/s was deposited at the site. What effect would this silty clay layer have on the factor of safety against piping? 85 Seepage cntd EXERCISE 4.3.4 ¥ 3m == Top of sand 3 3 3 w 3 7h Impervious clay — Top of sand 86 Seepage cntd Filters >» used for facilitating drainage and preventing fines from being washed away. >» used in earth dams and retaining walls. Filter Materials: granular filter =" Granular soils = Geotextiles Two major criteria: LJ Retention L) Permeability 87