Soil with water 22/09/2009 Lecture: 20 Sub-topics Capillary rise - - PowerPoint PPT Presentation

IIT Bombay

CE 303 20 Instructor: AJ

22/09/2009 Lecture: 20

Soil with water Sub-topics Capillary rise (contd.) Soil permeability

Ground failure due to soil liquefaction in 1964 Niigata earthquake, Japan

IIT Bombay

CE 303 20 Instructor: AJ

> 10 Clay 1.5 to 12 Silt 0.3 to 3.5 Fine sand 0.12 to 1.1 Medium sand 0.03 to 0.15 Coarse sand Capillary rise (m) Soil

Capillary rise in different soils

IIT Bombay

CE 303 20 Instructor: AJ

Empirical method Terzaghi and Peck (1967)

( )

10 c

eD C cm in h =

where D10 = effective grain size in cm C = empirical constant (between 0.1 and 0.5 cm2) Alternate theoretical height of capillary rise : replace d by 20% of effective grain size D10

mm in is d if meters d 03 . hc=

IIT Bombay

CE 303 20 Instructor: AJ

Capillary menisci “hangs” onto particles holds particles together This attractive force Soil Suction

effective stress is increased by uc

( )

c '

u − − σ = σ

w c c

h u γ − =

c '

u + σ = σ

intergranular contact stress σ’ are introduced

IIT Bombay

CE 303 20 Instructor: AJ

σ’ ↑ ⇒ shear strength ↑

Apparent or true cohesion?? – a point to note! Examples of soil capillarity: increase in effective stress and apparent cohesion sand beach

IIT Bombay

CE 303 20 Instructor: AJ

unsupported excavations in fine sands and silts Capillary moisture allow unsupported excavations

IIT Bombay

CE 303 20 Instructor: AJ

Capillary menisci are easily destroyed by saturation due to rainfall or by evaporation

Bulking capillary menisci surrounding soil grains produces “apparent cohesion” which holds sand particles together in cluster Capillary siphoning water flow over crest of an impermeable core in dam even if the water table is lower than the crest

Moist sand

Large voids (honey-combs Bonding due to apparent cohesion

IIT Bombay

CE 303 20 Instructor: AJ

Soil permeability

Flow through soils is mostly laminar Permeability describes quantitatively the ease with which water flows through the soil

IIT Bombay

CE 303 20 Instructor: AJ

water reservoirs (constant water levels) standpipes L h1 S a n d h0 h2 Δh Datum X-sectional area A 2 1

Darcy’s Law

1-Dimensional and 2-Dimensional flow flow is same at cross-section perpendicular to flow direction

Soil permeability

IIT Bombay

CE 303 20 Instructor: AJ

Potential difference that cause flow = Total head 1 – Total head 2 Total head (or total potential) = pressure head + elevation head + velocity head Note: Potential difference is also = Δh (difference between the two water levels) ∴ to determine total head difference between 2 points, one

needs to insert standpipes at the points and note difference in water levels in standpipes

( )

2 1

h h h difference Potential + − =

standpipes

L h1 S a n d h0 h2 Δh Datum 2 1

IIT Bombay

CE 303 20 Instructor: AJ

Darcy (1856) varied the variables Δh, L and A, and established

A L h k q

• r

A L h q Δ = Δ α q = flow (units of volume/time) k = constant; defined as coefficient of permeability ki v

• r

ki A q = =

The above can also be written as

L h Δ If is the hydraulic gradient, i , then kiA q = v = superficial velocity of flow (because actual flow is through pores and not through the entire X-sectional area) We redefine permeability? …… as “superficial velocity” of flow under unit hydraulic gradient

IIT Bombay

CE 303 20 Instructor: AJ

True velocity of flow through voids is called seepage velocity vs

n V V A A v v

v v s

= ≈ =

v sA

v vA q = = Av = area of voids A = total cross-sectional area

s

nv v

• r

= n = porosity Since n < 1 ⇒ v < vs In engineering practice, v is used instead of vs Darcy’s law originally developed for clean filter sands Although some investigations indicate that k could be nonlinear at low gradients in some clays, Darcy’s law is still universally accepted to be valid for most geotechnical problems

IIT Bombay

CE 303 20 Instructor: AJ

k determined in 3 ways – laboratory tests field tests empirical approach In laboratory, a device called permeameter is used and either constant head test or falling head test conducted In field, pumping tests are usually conducted, although it would be possible in principle to utilise either constant- or falling-head test Measurement of permeability

IIT Bombay

CE 303 20 Instructor: AJ

Constant head test

Volume of water Q flowing out of soil collected in time t hAt QL iA q k

• r

kiA q = = =

Q = total discharge volume in time t

Falling head test

• Water flows through sample from

graduated standpipe

• Time taken for water to drop

from fixed height is recorded L h soil Q A A Q a h1 at t = t1 dh at t = t2 h2 L soil