Instructor : Dr. Jehad Hamad. Chapter (7)

Instructor : Dr. Jehad Hamad Chapter (7) 2017-2016

Soil Properties Physical Properties Mechanical Properties Gradation and Structure Compressibility Soil-Water Relationships Shear Strength Bearing Capacity Atterberg s Limits Soil Compaction Permeability

Permeability is the measure of the soil s ability to permit water to flow through its pores or voids

Applications Rate of settlement under load Dams Stability of slopes Filters

Permeability and seepage Soils are assemblages of solid particles with interconnected voids through which water can flow. The study of the flow of water through porous soil media is important in soil mechanics. 5 1/29/2017

Permeability and seepage For example: Pumping of water for underground constructions Stability analysis of earth dams Earth retaining structures subjected to 6 seepage forces. 1/29/2017

What is permeability? A measure of how easily a fluid (e.g., water) can pass through a porous medium (e.g., soils) water Loose soil - easy to flow 7 - high permeability Dense soil - difficult to flow - low permeability

Hydraulic gradient(i) Total head loss per unit length between A and B i TH A l AB TH B water length AB, along the stream line A B

Hydraulic Gradient i h L

Bernoulli s Equation The energy of a fluid particle is made of: 1. Kinetic energy fluid particle - due to velocity 2. Strain energy z - due to pressure 3. Potential energy datum - due to elevation (z) with respect to a datum 10

Bernoulli s Equation If the equation is applied to the flow of water through porous soil medium, the term containing the velocity head can be neglected since the seepage velocity is small. Velocity head + 0 fluid particle Total head = Pressure head + z Elevation head datum Total head = Pressure head + Elevation head 11 1/29/2017

Bernoulli s equation u H γ v 2 2g z Total Head Pressure Head Dynamic Head Elevation Head H: total head P: water pressure γ: unit weight of water v: velocity of water g: gravity acceleration Z: elevation head

Bernoulli s equation The seepage flow velocity in soil is very small. Therefore, the dynamic head (velocity head) can be neglected. So that the total head at any points is: u H z γ

Darcy s Law v i v - k i Negative sign refers to the hydraulic gradient that is negative. (i.e. total head decreases in the direction of flow) Hydraulic Conductivity

Darcy s Law Darcy (1856) found an equation for the discharge velocity of water through saturated soils: v = k i Permeability or hydraulic conductivity unit of velocity (cm/s) 17 1/29/2017

Permeability Values (cm/s) 10-6 10-3 10 0 clays silts sands gravels Fines Coarse For coarse grain soils, k = f (e or D 10 ) 18 1/29/2017

Flow Rate Darcy s Velocity L Flow Rate v - k i q - k i A A q

Hydraulic Conductivity Typical Values for Hydraulic Conductivity Soil cm/s

Seepage Velocity (True Velocity) Seepage Velocity v s v n

Hydraulic Conductivity Hydraulic conductivity of soils depends on several factors: Fluid viscosity Pore size distribution Grain size distribution Void ratio Degree of soil saturation

Hydraulic Conductivity k γ w η γ w η K = Unit weight of water = Viscosity of water K = Absolute permeability (L 2 )

Hydraulic Conductivity with Temp.

Determination of Coefficient of Permeability There are 2 standard types of laboratory tests for determining the coefficient of permeability of soils: Constant head test Falling head test 25 1/29/2017

Determination of Coefficient of Permeability There are 2 standard types of laboratory tests for determining the coefficient of permeability of soils: Constant head test Falling head test 1/29/2017 26

Determination of Hydraulic Conductivity in the Lab Constant Head Test Falling Head Test

Constant Head Permeameter Most suitable for coarse grained soils, that have high k : 28 1/29/2017

Constant Head Test V V q t v A t V - k i A t h V - k A t L k V L A t h

Constant Head Permeameter The total volume of water collected is: Q Avt A( ki) t Where, Q: volume of water collected A: area of cross section of the soil sample t: duration of collection of water H h h QL i Q A( k ) t k l l l Aht 30 1/29/2017

Falling Head Permeameter Suitable for fine-grained soils with low k : 31 1/29/2017

Falling Head Test

Falling Head Permeameter h dh q kia k A a L dt Where; q: rate of flow a: cross sectional area of the standpipe A: cross sectional area of the soil sample k al ln h al 1 2.3 log h 1 33 At h 2 At h 2 1/29/2017

Equivalent Hydraulic Conductivity Case I: Horizontal Flow v 1 v2 v3 v vn

Equivalent Hydraulic Conductivity Case I: Horizontal Flow

Equivalent Hydraulic Conductivity Case II: Vertical Flow v

Equivalent Hydraulic Case II: Vertical Flow Conductivity

Pumped well in confined aquifer Elevation Aquifer heads pumped well Observation well H D Plan Radial flow Impermeable stratum aquifer

Permeability & Seepage 58 1/29/2017

Seepage Terminology concrete dam h L datum TH = h L TH = 0 soil 59 impervious strata 1/29/2017

Seepage Terminology Equipotential line is simply a contour of constant total head. h L concrete dam datum TH = h L TH = 0 TH=0.8 h L soil 60 impervious strata 1/29/2017

Stresses due to Flow Static Situation (No flow) h w L z X At X, v = w h w + sat z soil u = w (h w + z) v ' = ' z 61 1/29/2017

S t r e s s e s due to F l o w D o w n w a r d F l o w At X, v = w h w + sat z 62 as for static case u = w h w + w (L-h L )(z/l) = w h w + w (z-iz) = w (h w + z ) - w iz Reduction due to flow v ' = ' z + w iz Increase due to flow h h w u = L w h w z L X soil f l o w u = w (h w +L-h L ) 1/29/2017

Upward Flow At X, Stresses due to Flow flow v = w h w + sat z as for static case h L u = w h w + w (L+h L )(z/l) = w h w + w (z+iz) = w (h w +z) + w iz Increase due to flow v ' = ' z - w iz h w L z X soil u = w h w u = w (h w +L+h L ) 63 Reduction due to flow 1/29/2017

Flow nets Flow nets are useful in the study of seepage through porous media. A flow net consists of 2 sets of lines which for an isotropic (having equal properties in all directions) material are mutually perpendicular. 64 1/29/2017

Flow nets Lines drawn in the direction of flow are called flow lines (Ѱ-lines) Those perpendicular to the flow lines are called equipotential lines (Φ-lines) 65 1/29/2017

Seepage Terminology Stream line is simply the path of a water molecule. From upstream to downstream, total head steadily decreases along the stream line. h L TH = h L concrete dam datum TH = 0 soil 66 impervious strata 1/29/2017

Seepage Terminology Equipotential line is simply a contour of constant total head. h L concrete dam datum TH = h L TH = 0 TH=0.8 h L soil 67 impervious strata 1/29/2017

Flow net A network of selected stream lines and equipotential lines. concrete dam curvilinear square 90º soil 68 impervious strata 1/29/2017

Sketching of Flow Nets For practical purposes, flow nets can be obtained by sketching. The boundary conditions must be satisfied. An impermeable surface represents a flow line The interface between water and a porous medium is an equipotential line. 69 1/29/2017

Sketching of Flow Nets The procedure is: Draw geometry of the problem to a CHOSEN SCALE Prepare a first sketch of flow net trying to form equal sided figures and satisfying the boundary conditions Prepare an improved new sketch of flow net Correct the second sketch locally!!!example!!! 70 1/29/2017

Calculation of Seepage Loss through or beneath dams Let : Nd : Total number of equal drops in head Nf : Total number of flow channels Dl : side of a typical square of the flownet k : coefficient of permeability h : total drop in head between first and last lines 71 1/29/2017

Quantity of Seepage (Q) Q kh N f L Nd # of flow channels.per unit length normal to the plane # of equipotential drops h L concrete dam head loss from upstream to downstream 72 impervious strata 1/29/2017

Heads at a Point X Total head = h L - # of drops from upstream x h Elevation head = -z Pressure head = Total head Elevation head h N L d datum TH = h L TH = 0 concrete dam z h L h X 73 impervious strata 1/29/2017

Piping in Granular Soils At the downstream, near the dam, the exit hydraulic gradient i exit h l h L concrete dam l datum h = total head drop soil 74 impervious strata 1/29/2017

Piping in Granular Soils If i exit exceeds the critical hydraulic gradient (i c ), firstly the soil grains at exit get washed away. This phenomenon progresses towards the upstream, forming a free passage of water ( pipe ). h L concrete dam datum no soil; all water 75 impervious strata soil 1/29/2017

Piping in Granular Soils Piping is a very serious problem. It leads to downstream flooding which can result in loss of lives. Therefore, provide adequate safety factor against piping. F piping i i c exit concrete dam typically 5-6 76 impervious strata soil 1/29/2017

Piping Failures Baldwin Hills Dam after it failed by piping in 1963. The failure occurred when a concentrated leak developed along a crack in the embankment, eroding the embankment fill and forming this crevasse. An alarm was raised about four hours before the failure and thousands of people were evacuated from the area below the dam. The flood that resulted when the dam failed and the reservoir was released caused several millions of dollars in damage. 77 1/29/2017

Piping Failures 78 Fontenelle Dam, USA (1965) 1/29/2017

Quick condition When flow is in the upward direction an unstable quick condition or boiling occurs when the upward seepage force per unit volume reaches the submerged unit weight of the soil. This condition usually occurs in sands. Determination of submerged unit weight of soil is needed by using the mass-volume relationships. (Lecture 1) 79 1/29/2017

Quick Condition in Granular Soils During upward flow, at X: v ' = ' z - w iz w z ' w i Critical hydraulic gradient (i c ) If i > i c, the effective stresses is negative. i.e., no inter-granular contact & thus failure. - Quick condition flow h L h w z L X soil 80 1/29/2017

Trench supported by sheet piles 5m 6m 6m 6m Uniform sand Impermeable clay

Trench supported by sheet piles 5m 6m h=6m Nh=10 Nf=2.5+2.5 6m 6m Uniform sand Impermeable clay

Excavation supported by a sheet pile Steel sheet Water pumped away Uniform sand Shale

Reduced sheet penetration; possible liquefaction v = 0 Steel sheet Uniform sand Shale

Reduced sheet penetration; possible liquefaction v = 0 Reservoir Tail water Uniform sand Shale

Concrete dam or weir Reservoir Tail water Uniform sand Shale

Concrete dam with cut-off; reduces uplift pressure Reservoir Uniform sand Shale

Pumped well in confined aquifer Elevation Aquifer heads pumped well Observation well H D Plan Radial flow Impermeable stratum aquifer

Clay dam, no air entry reservoir atmospheric line drain clay Shale

Clay dam, no air entry atmospheric line reservoir drain clay Shale

Clay dam, no air entry Observation well atmospheric line reservoir drain clay Shale

Clay dam, no air entry, reduced drain; seepage out of downstream face reservoir atmospheric line Not possible clay Shale

Clay dam, with air entry reservoir drain clay Shale

Clay dam, no capillary, reduced drain; seepage out of downstream face reservoir clay Shale

Flow of water in earth dams The drain in a rolled clay dam will be made of gravel, which has an effectively infinite hydraulic conductivity compared to that of the clay, so far a finite quantity of flow in the drain and a finite area of drain the hydraulic gradient is effectively zero, i.e. the drain is an equipotential

Flow of water in earth dams The phreatic surface connects points at which the pressure head is zero. Above the phreatic surface the soil is in suction, so we can see how much capillarity is needed for the material to be saturated. If there is insufficient capillarity, we might discard the solution and try again. Alternatively: assume there is zero capillarity, the top water boundary is now atmospheric so along it and the flow net has to be adjusted within an unknown top boundary as the phreatic surface is a flow line if there is no capillarity.

Flow of water in earth dams If h y then h y cons in the flow net, so once we have the phreatic surface we can put on the starting points of the equipotentials on the phreatic surface directly

Unsteady flow effects Consolidation of matrix Change in pressure head within the soil due to changes in the boundary water levels may cause soil to deform, especially in compressible clays. The soil may undergo consolidation, a process in which the voids ratio changes over time at a rate determined by the pressure variation and the hydraulic conductivity, which may in turn depend on the voids ratio.

Breakdown of rigid matrix Liquefaction (tensile failure) The total stress normal to a plane in the soil can be separated into two components, the pore pressure p and the effective inter-granular stress : By convention in soils compressive stresses are +ve. Tensile failure occurs when the effective stress is less than the fracture strength fracture, and by definition for soil fracture=0. When the effective stress falls to zero the soil particles are no longer in contact with each other and the soil acts like a heavy liquid. This phenomenon is called liquefaction, and is responsible to quick sands. p

Large upward hydraulic gradients: Uniform soil of unit weight Upward flow of water

standpipe Water table and datum Critical head Pressure hcrit Critical potential Head h h z crit crit z Plug of Base area A Uniform soil of unit weight Gap opening as plug rises Upward flow of water

At the base of the rising plug, if there is no side friction: v p. z h crit. w So if v =0 then v = p and :. z h. h z. crit w crit w i crit h crit z w w, icrit=0.8~1.0

where icrit is the critical hydraulic gradient for the quick sand Condition. As 18~20 kn/m 3 for many soils (especially sands and silts) and w 10 kn/m 3 : i crit h z crit 20 10 10 1.0

Frictional (shear failure) Sliding failure of a gravity concrete dam due to insufficient friction along the base:

Reservoir H 1 W Tail water H 2 U p. ds W Uniform sand

Stresses due to Flow Static Situation (No flow) h w L z X At X, v = w h w + sat z soil u = w (h w + z) v ' = ' z 112 1/29/2017

S t r e s s e s due to F l o w D o w n w a r d F l o w At X, v = w h w + sat z 11 3 as for static case u = w h w + w (L-h L )(z/l) = w h w + w (z- i z ) = w (h w + z ) - w iz Reduction due to flow v ' = ' z + w iz Increase due to flow h h w u = L w h w z L X soil f l o w u = w (h w +L-h L ) 1/29/2017