Chapter five SOIL WATER AND WATER FLOW 5-1 Introduction Water can flow through the interconnected soil pore. Water in the pore is under pressure, the pressure is measured relative to the atmospheric pressure. Water table ( W.T) : is the level at which the water pressure is atmospheric, also called phreatic surface. Notes : Below water table the soil is assumed to be fully saturated - The level of water table changes according to climate conditions and also construction operation can change it. - Artesian conditions can exist if an inclined layer of high permeability is confined locally by an overlying layer if low permeability. Water in soil is 1- Either static : the hydrostatic pressure depend on the depth below the water table. 2- Or seepage through the soil under hydraulic gradient. her Bernoulli's equation applies to the pore water. 5-2 Fluid flow in soils: The problems of fluid flow in soil are 1
1- Rate of flow of fluid through an earth dams ( eg. Determination of rate of leakage through an earth dam). 2- Problems involving compression (eg. Determination of rate of settlement of foundation ). 3- Problems involving strength (eg. The evaluation of factor of safety of a given soil under a given loading ). 5-2-1 Permeability Definition- The property of soils that allows water to pass through them at some rate. This property is a product of the granular nature of the soil, although it can be affected by other factors (such as water bonding in clays) Different soils have different perm abilities, understanding of which is critical to the use of the soil as a foundation or structural element Soil and rock are porous materials Fluid flow takes place through interconnected void spaces between particles and not through the particles themselves No soil or rock material is strictly impermeable Flow path on soils Straight path in soil problems but is a winding path in actual The study of flow of water through porous media is necessary for- Estimation Seepage Loss 2- Estimation Pore Water Pressures 3- Evaluation Quicksand Conditions 4- Dewatering System Design 2
5-Drainage System Design 5-2-1-1 Hydraulic gradient : According to Bernoulli's equation, the total head of a point under motion can be given by: Where In reality, an energy balance of the soil as it flows through the ground Kinetic Component can usually be ignored then + Z = hp + he ht= p γw and this is defined as the piezometer head therefore, in soil engineering problems the total head = piezometer head = pressure head + elevation head 3
The loss of head between A & B, can be given by h can be expressed in non-dimensional form as hydraulic gradient i= h L where L =length of flow over which loss of head h 5-3 capillary in soils 4
Water can rise and remain above the line of atmospheric pressure ( phreatic line ) in a very fine pore due to attraction ( surface tension ) between adjacent molecules in the surface. at phreatic line u = 0 The water is drawn upwards by this force until, at height h, the weight of water in the column is in equilibrium with the magnitude of the surface tension. Then if atmospheric pressure = 0, equating vertical forces at the surface : 5
W= FT cos α When W= γ w πr 2 h and FT cos α = Ts2πrcos α where Ts is the surface tension Giving capillary pore pressure u= 2Ts cos α or putting u = γwh where γw unit weight of water γ w πr 2 h = Ts2πrcos α h = 2Ts cos α ( capillary head or capillary rise ) rγw r hc 1 r u= S γwh = pore water pressure due to capillary rise 100 Hence : - height of water rise depend on size of soil voids. -All point above W.T is negative charge (-ve since h is a against atmospheric pressure ) -The soil almost saturated in the capillary zone - the water pressure is negative ( less than the atmospheric pressure in capillary zone) - the negative pressure of water held above the water table results in attractive force between particles. This phenomena is called soil suction. If is a function of the pore size and water content. 5-3 Permeability : Methods that are in common use for determining the coefficient of permeability k can be classified under laboratory and field methods. Laboratory methods: 1. Constant head permeability method 2. Falling head permeability method 6
Field methods: 1. Pumping tests 2. Bore hole tests Indirect Method: Empirical correlations The various types of apparatus which are used in soil laboratories for determining the permeability of soils are called permeameters. The apparatus used for the constant head permeability test is called a constant head permeameter and the one used for the falling head test is a falling headpermeameter. The soil samples used in laboratory methods are either undisturbed or disturbed. Empirical correlations have been developed relating grain size and void ratio to hydraulic conductivity. In one dimensional, water flows through a fully saturated soil in accordance with Darcy's law q = VA Vα h L or Vαi V= ki q = kia where q is a volume of water flowing per unit time A is a cross sectional area of flow path and V is seepage velocity i= is hydraulic gradient k= coefficient pf permeability (L/t) k is depend permeability on the average pore size which is related to the followings: 1- Particle size distribution 2- Particle shape 3- Soil structure In general The smaller soil particle, the smaller is the average size of pore and lower is the coefficient of permeability. For given soil, the coefficient of permeability is a function of the void ratio. 7
5-3-1 Permeability in stratified soil Hydraulic conductivity of a disturbed sample may be different from that of the undisturbed sample even though the void ratio is the same. This may be due to a change in the structure or due to the stratification of the undisturbed soil or a combination of both of these factors. In nature we may find fine grained soils having either flocculated or dispersed structures. Two fine-grained soils at the same void ratio, one dispersed and the other flocculated, will exhibit different permeabilities. Soils may be stratified by the deposition of different materials in layers which possess different permeability characteristics. In such stratified soils engineers desire to have the average permeability either in the horizontal or vertical directions. The average permeability can be computed if the permeabilities of each layer are determined in the laboratory. The procedure is as follows: k, k2,..., kn = hydraulic conductivities of individual strata of soil either in the vertical or horizontal direction. Z1 Z2 zn = thickness of the corresponding strata. Z = z1+z2+z3+ Zn kh = average hydraulic conductivity parallel to the bedding planes (usually horizontal). kv - average hydraulic conductivity perpendicular to the bedding planes (usually vertical). k= γw η K where γw and η are unit weight and viscosity of the water K (L 2 ) : an absolute coefficient depend on the characteristics of the soil skeleton only 8
- The velocity by which water flow through soil is varying from point A to point B in magnitude and direction. - The average velocity at which water flows through soil is called seepage velocity (ν). Qin = Qout VA = ν s x Av.and.n= Vv V ν s = Q na = Av x L Ax L but Q A ν s = V n or ν s = = ki n Av = na = V ( discharge velocity or approach velocity ) where ν s = velocity of water through the soil between point A and B 5-3-2 Pressure Head Pore pressure needed to compute, effective stress can be obtaine from the pressure head. Pore pressure = pressure head x γw Or u = hp x γw 9
Pressure head can be either i- Measured or ii- Computed Measuring of pressure head :- 1- In laboratory by pizometer ( pressure meter ) a- Monometer or stand pipe (m). b- Boueden gage ( kn/m 2 or kpa.) 5-3-3 Effective stress in soil with fluid flow 1- Now flow σ = γw xh + γsat. X Z u= γw ( H+Z) σʹ= σ u = (γsat.-γw )Z 2- With flow a- Dawnward flow b- Upward flow At Downward flow inlet is higher than the storage tank and the flow from up to dawn as shown in figure below σ = γw x H + γsat. x H0 u= γw (H + H0 - h) σʹ= (γsat.-γw )H0 + γwh 10
σ = γw x H0 + γsat. x H u= γw (H + H0 + h) σʹ= (γsat.-γw )H - γwh Upward flow in this case the flow direction from dawn to up of soil sample as shawn in figure below. Seepage force : Is applied by moving water to the soil skelton and acts in the flow direction. Hence: We can work either with i- The total boundary force OR ii- Buoyancy force + seepage force Seepage force per unit volume (J) 11
J= seepage force Vol.of soil = haγw LA = h L γw J = iγw Notes : 1- Seepage force exerted by the flowing water act as on external force on the soil Skelton. 2- J is a constant value for a given soil mass Ex: for the figure below find the J if h= 0.6 m and L = 0.6 m J = iγw J= h 0.6 γw = 9.81 = 9.81 kn/m3 L 0.6 Force equilibrium : for the setup shown in last page a- Total weight + Boundary water force F = Zγw A + LAγt (h +Z+L)γw A F = σʹ A σ * A = LA (γt γw ) haγw = (Lγb hγw ) A σ -u = σʹ u* A L A γta (h+z+l) F γwa screen A L γba b- Submerged weight + seepage force F = LAγb haγw h F = σʹ A Hence : F Total weight + boundary water force = submerged weight + seepage force Quick condition ( Boiling ) S = shear strength, can be determine using Colomb equation as below: γwa screen 12
S = C+ σʹ tanφ Where C = cohesion of soil ( fine grained soil property ) φ = internal friction angle ( coarse grained soil property ) The boiling occure in sandy soils therefore, for cohesionless soils ( coarse grain ) C = 0 then S = σʹ tanφ then S = 0 at boiling case then σʹ = 0 Now σʹ* A = LAγb haγw == σʹ = Lγb = hγw ==== γb γw = h L = ic A(Lγb hγw) A then σʹ = 0 ic = critical hydraulic gradient, this hydraulic gradient accrue at quick condition ic = γb γw or ic = G 1 1+e where γb = G 1 1+e γw The safety factor (Fs) is the factor refer to the state of the soil condition, if the soil without boiling this is safe state while at boiling case the soil under failure condition and the soil at critical condition when the shear strength of the soil is higher than shear stress which try to fail the soil. Fs = ic where( ic) is the critical hydraulic gradient and (ie) is the exist hydraulic gradient ie Note : if γb not given can assume it (γb) = 1 and become ic 1 5-3-4 Permeability in stratified soil ( equivalent permeability ) the coefficient of permeability of a given layer of soil may vary with the direction of flow. Therefore, the equivalent permeability coefficient must be determine for both direction a- X- direction flow 13
1- Assume a cross section of unit length passing through H layer and perpendicular to the direction of flow. q= V*A A = 1* H H = h1+ h2 + h3 + h4 +.,hn When V = average discharge velocity q= v1*1*h1+v2*1*h2+v3 *h3*1+v4*1*h4 + vn*1*hn qtotal = q1+ q2+ q3+ q4+., qn ieq. = i1= i2 = i3= i4.., in Vav. = kheq. *ieq kheq. *ieq * H = kh1*h1*i1+ kh2*h2*i2+ kh3*h3*i3+ kh4*h4*i4+, khn*hn*in kheq.= kh1 h1+ kh2 h2+ kh3 h3+ kh4 h4+,khn hn H OR 2- The vertical flow 14
In this case the velocity of flow through all the layers is the same. However, the total head loss (h) is equal to the summation of the head loss in each layer. 5-3-5 Types of flow Direction of flow 1- Dawn-ward fluid flow 2- Upward fluid flow 3- Flow through multi-layered soil 4- Horizontal fluid flow 5- Flow through inclined layer for first three types the flow is vertical flow while number four deals with the horizontal flow in soil. Also the fifth items deal with the inclined soil therefore the flow will be inclined flow. In next section will be discuss each type of flow individually. 15
5-4 Determination of the permeability coefficient A- Laboratory methods 1- Constant head permeability test method ( for coarse grain soil ) A steady flow under constant head is maintained through the soil and volume of water per unit time (q) is measure k= ql Ah soil must be fully saturation during the test, vacuum is applied to specimen before the test to bring (S close to 100%) if a high degree of saturation it to be maintained during the test, deaired water should be used. Example : In a laboratory, a constant-head permeability test was conducted on a brown sand with a trace of mica. For the constant-head permeameter (Figure above), the following data were obtained: 1. Quantity of water discharged during the test = 25cm 3. 2. Length of specimen between manometer outlets = 11.43 cm. 3. Time required for given quantity of water to be discharged = 65.0 s. 4- Head (difference between manometer levels) = 5.5 cm. 5. Temperature of water = 20 0C. 6. Diameter of specimen 10.16 cm. Required Coefficient of permeability. Solution. 16
2- Falling head As shown in Figure below, the velocity of fall in the burette is given by v = dh with the minus sign used to indicate a falling dt (and therefore decreasing) head. The flow of water into the specimen is therefore qin = a dh, and the dt flow through and out of the specimen is, from qout = k h A. l Equating qin and qout gives Therefore 17
Or Where a is cross sectional area of stand pipe. A is cross sectional area of specimen k= permeability coefficient of soil test. h1 = initial height of water before the test. h2 = finial height of water after the test. h the difference in total head between the top and bottom at time (t). L = length of specimen. The coefficient of permeability as determined by both methods is the value for the particular water temperature at which the test was conducted. This value is ordinarily corrected to that for 20 C by multiplying the computed value by the ratio of the viscosity of water at the test temperature to the viscosity of water at 20 C. Permeability determined in a laboratory may not be truly indicative of the in situ permeability. There are several reasons for this in addition to the fact that the soil in the permeameter does not exactly duplicate the structure of the soil in situ, particularly that of nonhomogeneous soils and granular materials. For one thing, the flow of water in the permeameter is downward, whereas flow in the soil in situ may be more nearly horizontal or in a direction between horizontal and vertical. Indeed, the permeability of a natural soil in the horizontal direction can be considerably greater than that in its vertical direction. For another thing, naturally occurring strata in the in situ soil will not be duplicated in the permeameter. Also, the relatively smooth walls of the permeameter afford different boundary conditions from those of the in situ soil. Finally, the hydraulic head in the permeameter may differ from the field gradient. Another concern with the permeability test is any effect from entrapped air in the water and test specimen. To avoid this, the water to be used in the test should be de-aired by boiling distilled water and keeping it covered and non-agitated until used. Example 18
B- In situ tests method 1- Well pumping test - This method most suitable for use in homogenous coarse soil strata. - This method involves continuous pumping at constant rate from a well ( 300mm diam. At test ) which penetrate to the bottom of the stratum under test. - A screen of filter is placed in the bottom of the well to prevent ingress of soil particles. Perforated casing is used to support the sides of the well. - Radially steady state seepage towards the well. The water table will be drawn down to form a cone of depression. - Water levels are observed in number of bore holes spaced on radial lines at varies distances from the pumping well. 19
- Analysis is made on the assumption that the hydraulic gradient at distance ( r ) from the center of well. 1- Is constant with depth 2- Equal to the slop of water table i cr = dh dr where h is a height of water table at distance ( r) " this is Dupuit assumption " In pumping test method there are two formula can used to determine the permeability coefficient. The type of formula used depend on the soil stratum condition as confined stratum or unconfined stratum. 1- Pumping test in unconfined stratum soil 20
Example: A pumping test was performed in a well penetrating an unconfined aquifer to evaluate the coefficient of permeability of the soil in the aquifer. When equilibrium flow was reached, the following data were obtained: 1. Equilibrium discharge of water from the well = 200 gl/min. 2. Water levels (h1 and h2) is 15ft and 18 ft at distances from the well (r1 and r2) of 60 and 180 ft, respectively. 21
2- Pumping test method with confined stratum 22
Example A pumping test was performed in a well penetrating a confined aquifer to evaluate the coefficient of permeability of the soil in the aquifer. When equilibrium flow was reached, the following data were obtained: 1. Equilibrium discharge of water from the well = 200 gl/min. 2. Water levels (h1 and h2) is 15ft and 18 ft at distances from the well (r1 and r2) of 60 and 180 ft, respectively. 3. Thickness of aquifer= 20 ft. Required Coefficient of permeability of the soil in the aquifer. 23
3- Empirical Relations for Hydraulic Conductivity Several empirical equations for estimating hydraulic conductivity have been proposed over the years. Granular Soil For fairly uniform sand (that is, a small uniformity coefficient), Hazen (1930) proposed an empirical relationship for hydraulic conductivity in the form: k= CD 2 10 C= a constant that varies from 1.0 to 1.5 D10 = the effective size (mm) The above equation is based primarily on Hazen s observations of loose, clean, filter sands. A small quantity of silts and clays, when present in a sandy soil, may change the hydraulic conductivity substantially. 24
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Examples 1- The permeability coefficient of a sand at a void ratio of 0.55 is 0.1 ft/min. estimate its permeability coefficient at avoid ratio of 0.7. Use Casagrande empirical relationship 2- for normally consolidated clay soil, the following are given: Estimate the permeability coefficient of clay at void ratio of 1.2.Use Samarasingh et. al. relation. 26
3- A pumping test from Gravity well in a permeable layer underlain by an impervious stratum was made. When steady state was reached, the following observations were made q = 100 gpm; h1 = 20 ft; h2 = 15 ft; r1= 150 ft; and r2 = 50 ft. Determine the permeability coefficient of the permeable layer. 27
4- A permeable soil layer is underlain by an impervious layer, as shown in Figure below. With k = 5.3x10-5 m/sec for the permeable layer, calculate the rate of seepage through it in m 3 /hr/m width if H= 3 m and α= 8. Solution 28
Problems 29
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5-For a falling-head permeability test, the following are given: length of specimen = 380 mm; area of specimen = 6.5 cm 2 ; k= 0.175 cm/min. What should be the area of the standpipe for the head to drop from 650 cm to 300 cm in8 min? 6- For a falling-head permeability test, the following are given: Length of soil specimen= 700 mm Area of the soil specimen= 20 cm 2 Area of the standpipe= 1.05 cm 2 Head difference at time t = 0 is 800 mm Head difference at time t= 8 min is 500 mm a. Determine the absolute permeability of the soil. b. What is the head difference at time = 6 min? Assume that the test was conducted at 20= o C, and at 20= o C, γw= 9.789 kn/m 3 and η= 1.005x10 3 Ns/m 2. 7- A sand layer of the cross-sectional area shown in Fig. below has been determined to exist for a 800 m length of the levee. The hydraulic conductivity of the sand layer is 2.8 m/day. Determine the quantity of water which flows into the ditch in m 3 /min. 31
8- A permeable soil layer is underlain by an impervious layer, as shown in Figure7.28. With k= 5.2 x 10 4 cm/sec for the permeable layer, calculate the rate of seepage through it in m 3 /hr/m length if H= 3.8 m and α= 8 o. 9-The hydraulic conductivity of a sand at a void ratio of 0.5 is 0.022 cm/sec. Estimate its hydraulic conductivity at a void ratio of 0.7. 1- For a sand, the following are given: porosity, n = 0.31 and k = 0.2 ft/min. Determine k when n = 0.4. 2- The maximum dry density determined in the laboratory for a quartz sand is 1800 kg/m 3. In the field, if the relative compaction is 80%, determine the hydraulic conductivity of the sand in the field-compaction condition (given that D10 = 0.15 mm, Cu= 2.2 and Gs = 2.66). use shahada et.al formula. 32
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