Chapter 2 Seepage in Soil

“In engineering practice, difficulties with

soils are almost exclusively due not to

the soils themselves, but to the water

contained in their voids. On a planet

without any water there would be no

need for soil mechanics”.Karl Terzaghi

Definitions

• Groundwater table (GWT) or Phreatic surface) – top ofgroundwater flow

• Phreatic zone – subsurface below GWT

• Vadose zone – subsurface above GWT• Aquifer - a geologic formation that is under GWT and is

capable of yielding water as a water supply.– Confined Aquifer - soil or rock below the land surface that is saturated

with water.

– Unconfined Aquifer - an aquifer whose upper water surface (watertable) is at atmospheric pressure.

• Aquaclude - geologic formation that can not transmit waterrapidly.

• Artesian water - groundwater that is under pressure.

Total head: ht = hv + he + hp

1 1. hv ~ 0 in groundwater flowbecause seepage flow is slow

2. he depends on the location ofdatum z

3. hp depends on water pressure insoil pores

4. Seepage flow in soil is alwaysfrom a higher total head to a

lower total head.

Relation between the Pressurehead (hp, in meter) ) & Pore waterpressure (u, in kPa) :

u hp w(unit :kPa)

(unit :m)hp u

w

o

Total Head at Point “P”

h hp zGround surface

GWT

P hpis measured verticallydown from GWT or piezometer

hphp

zz

z is measured vertically up

from the datum

o

Datum

Example (Coduto p. 265)Compute the pore water pressure at points A and B

el.(m)9089

87

83

80

Groundwater Flow in Soil

The total head difference (h) is the driving force ofgroundwater flow in soil.

1m X X

P1m

P1m

Impermeable stratum

No GW flow

Impermeable stratum

GW flow from X to P

Important Reminder

• The absolute value of the total head is notimportant because it depends on theselection of datum;

• To solve groundwater flow problems, weselect a datum and use it as the reference forthe total heads at all points of interests;

• Groundwater always flows from a higher totalhead to a lower total head, regardless thelocation of datum.

Darcy’s Law

h

Soil Sample

AL

Darcy (1856) found that the flow rate in a porous medium(e.g. soil) is

1. proportional to the total head difference h2. proportional to the cross-sectional area A perpendicular

to the flow direction3. inversely proportional to the length of the soil sample L

Darcy’s s Law

Q = kh i A

Q (m3/s) = flow rate

kh (m/s) = coefficient of permeability or hydraulic conductivity.

i = hydraulic gradient [ - ]

A = cross-sectional area perpendicular to direction of flow (m2)

Alternatively, Darcy’s Law may be expressed interms of Flow Velocity

q=ki (unit: m/s)

where i hydraulic gradient [-]

q = Q/A Darcy velocity (m/s)

Hydraulic Gradient, i

dh

dxi

The negative sign of hydraulic gradient – toensure the flow direction is towards the positivehydraulic gradient

We often use i = h/L in 1D calculation – butremember to indicate the direction of flow

Darcy’s Law is valid when

The flow is laminar (no turbulence) – this is valid forflow in all soils;

Soil is nearly saturated – S ~ 100%;

The flow is steady (time independent) – known as thesteady state seepage flow

Hydraulic Conductivity kh

• The most reliable way of determining kh isfrom experiments (lab or in-situ)

• Empirical equations have been developedunder specific conditions

• Everything else being equal, khis the highestwhen a soil is saturated

Typical kh Values

10-1 10-2 10-3 10-4 10-5 10-6 10-7 10-8 10-9 10-1010-11 10-12

Gravels Sands Silts Homogeneous Clays

Fissured & Weathered Clays

Unit: meter/second, m/s

X 100, cm/s

Constant head device –

for kh measurement of granular soils

Falling head device

for kh measurement of fine grained soils

Empirical Estimate of kh

Kozeny-Carman Equation(Read pp. 280 - 282)

• For sandy soils only

•

kh e3

1ekh is a function of– Grain size

– Shape factor

– Void ratio

– Unit weight of fluid

– Viscosity of fluid

Seepage Velocity

In Darcy’s law, q = i k, where q is the “apparent” flow velocity.

The “true” flow velocity is the velocity of water molecules flowing

through a tortuous path in soil – seepage velocity v.

The relationship between the seepage velocity (v) and Darcy

velocity (q) is q

nv

Therefore the seepage velocity is always higher then Darcy’s

velocity

Computing 1 1--DGroundwater Flow

Flow Rate Q = k i A(unit: m3/s)

q=ki (unit: m/s, or cm/s)Flow Velocity

Steps:

1.

2 2.

3.

Calculate the hydraulic gradient, i = h/L ;

Measure the hydraulic conductivity, kh;Determine the area perpendicular to the groundwater flow, A.

Flow through Anisotropic Soils

( k

Flow through Anisotropic Soils

kvkH kiHi

Hi )

HH

i

i

i

ikH kiH

Hi

Example: Calculate khand kv for the layered soil

k = k1= 10-6m/s

k = k2= 10-10m/s

d1= 1 m

d2= 1 m

Layer 1Aquifer

Layer 2Aquitar

kH k1 d1 k 2 d2

d1 d2

k Vd1 + d2

d1 d2

k1 k 2

Lessons learnt

When subsurface soil is stratified

• Horizontal seepage is controlled by aquifer;

• Vertical seepage controlled by aquitar

Seepage PressureWhen water flows through a soil, the viscous drag tends to move soil grainsand produces a force, known as a seepage pressure.

Upward flow

• Liquefaction : If an upward flowing water passing through a sand, and theseepage pressure equals to the submerged weight of the sand, the inter-granular pressure becomes zero. The sand then is in a "quick" conditionand is incapable to support a load on its surface.

• Erosion: the upward flowing water tends to remove some of the fines, oftenknown as "piping”.

• Bottom heave (blow out): If the upward flowing water passing through aclay, and the seepage pressure equals to the submerged weight of the clay,the clay will heave and crack.

Downward flow

Downward flowing water will generate additional pressure on soil, which isequivalent to additional loading on soil, generating settlement.

Soil liquefaction/piping• Soil suddenly

suffer atransition from asolid state to aliquefied state

• Occur in looseto moderatelysaturatedgranular soilsduring cyclicloading

Blowout / Bottom Heave of Clays inExcavation

Clay

Sand AquiferPiezometer

Conditions for Liquefaction, Piping and Blowout

u2

(z=z2, h=h2 , u=u2)

Elevation

(z=z1, h=h1 ,u=u1)

u1

Area =APlan

A soil element experiencing upward flow of water

Uplift Force A(u 1 u 2 )

Force due to Soil weight A sat (z 2 z1)

u2 Pore water pressure

u2 w(h2 z2)

u1 w(h 1z1)

u1

Uplift Force

Force due to weight

A(u 1 u 2 )

A sat (z 2 z1)

For piping to occur, uplift force > soil weight

A(u2 u1) Asat(z2 z1)

w(h1 h2)w(z1 z2) sat(z2 z1)

w(h1 h2) sat(z2 z1) w(z2 z1)

( h1 h2)

(z2 z1)

sat w

w

u2

(z=z2, h=h2 )

( h1 h2)

(z2 z1)

sat w

w

(z=z1, h=h1)

u1

But = i = Hydraulic gradient( h1 h2)

(z2 z1)

so the condition for piping may be written as

i > ic

Critical Hydraulic Gradient for Piping/Blowout

ic Gs 1

1e

sat w

w

1. When the upward hydraulic gradient in soil i > ic ,

liquefaction/piping/blowout will occur in soil.

2. Critical hydraulic gradient is a soil property and is not relatedto the hydro-geologic condition of the site.

3. FS against liquefaction/piping/blowout:

4. FS = 2 is required in design

i c

iF .S .

Example: Basal stability of landfillWaste bulk unit weight = 7 kN/m3

50 m x 50 mz

?m10 m

B

11m

CL, bulk unit weight = 20 kN/m3

A

Piezometer

SP

1.2.

Calculate the maximum excavation can be made for this landfill;If the excavation has to be 6.5 m deep to meet the design capacity, whatwould you do?

Erosion problems in earth works•

•

Seepage pressure below or within dams has led to several catastrophicfailures.

It may be prevented if we cover the surface, where the seepage emerges,with coarser materials that help the escape of the water but prevent theerosion of the fines. If the seepage pressure has a rather great upwardcomponent, it may be necessary to add weight to the top of the filter tocounterbalance the upward forces.

38

Impact

•

•••

•

Discharge of a mixture of 600-700 thousand cubic metres of red mud andwater.Nine people were killed, and approx. 120 people were injured.The spilling red mud flooded 800 hectares of surrounding areas.The main component contained in the red mud is Fe2O3 (iron oxide - whichgives it its characteristic red colour) at 40-45%. Other components areAl2O3, SiO2, CaO, TiO2, and Na2O, according to MAL.The red mud contains:

– 110 mg/kg for arsenic,– 1.3 mg/kg for mercury,

– 660 mg/kg for chromium (of which 0.46 mg/kg for the highly toxic hexavalentchromium Cr-VI),

– 40 mg/kg for antimony,– 270 mg/kg for nickel,– 7 mg/kg for cadmium.

39

Ajka Tailings Dam Failure (2010- -10-4)

WE West

North

40

41

42

43

Summary y

1. The total head governs the seepage flow in soil, which includes– elevation head– pressure head– velocity head, which is negligible in soils

2. The seepage flow is always from a higher total head to a lowertotal head;

3. Darcy’s law states that the seepage flow depends on– Hydraulic conductivity of soil and– Hydraulic gradient of the site

4. The true seepage velocity in soil is higher than Darcy’s s velocityalong a torturous path;

5. The Seepage will generate pore water pressure in soil– Upward pressure – piping and blow out– Downward pressure – settlement

6. The seepage flow in earth works can be controlled by––

Selection of soilCompaction