IIT Bombay 24092009 Lecture 22 Soil with water

IIT Bombay 24/09/2009 Lecture: 22 Soil with water Sub-topics q Permeability measurement Ground failure due to soil liquefaction in 1964 Niigata earthquake, Japan CE 303 22 Instructor: AJ

IIT Bombay Confined and unconfined aquifer http: //en. wikipedia. org/wiki/Aquifer CE 303 22 Instructor: AJ

IIT Bombay Field tests Pump-out from well at constant rate until water level in the observation wells is steady Record flow and water levels in the observation wells Minimum 2 observation wells (standpipes) unconfined flow pumping test CE 303 confined flow pumping test 22 Instructor: AJ

IIT Bombay Unconfined flow pumping test GWT is assumed originally to be at rest • Aquifer is underlain by impermeable stratum • Test well extends to bottom of permeable stratum • Test well is perforated over section below GWT • Pumping generates radial flow of water towards test well • GWT takes curved surface called drawdown water table • Hydraulic gradient is assumed constant at any radius CE 303 22 Instructor: AJ

IIT Bombay Flow though cylindrical surface at radius r is constant This flow equals flow out of well Using Darcy’s law q = ki. A dh = k (2 pr )h dr or CE 303 dr 2 p = k h dh r q flow through elementary cylinder dh Hydraulic gradient i = dr Area of flow A = (2 pr )h p r ln 2 = k h 22 - h 12 r 1 q æç r 2 ö÷ ln Integrating q è r 1 ø = or k p h 22 - h 12 ( ) ( 22 ) Instructor: AJ

IIT Bombay Confined flow pumping test GWT is assumed originally to be at rest in the upper impermeable strata • Aquifer is confined above and below by impermeable strata • For all values of r, drawdown surface is within the above impermeable stratum CE 303 22 Instructor: AJ

IIT Bombay From Darcy’s law q = ki. A dh =k A dr Note that A = (2 pr )D q=k or CE 303 dh (2 pr )D dr dr 2 p. D =k dh r q Integrating 22 r 2 2 p. D (h 2 - h 1 ) =k r 1 q r ln æç 2 ö÷ q è r 1 ø = or k 2 p. D (h 2 - h 1 ) ln Instructor: AJ

IIT Bombay Typical values of permeability CE 303 22 Instructor: AJ

IIT Bombay Typical values of permeability Permeability (cm/s) 1 10 -2 10 -3 Pervious (Good drainage) Clean gravel Sand and/ or gravel, no fines 10 -4 10 -5 10 -6 10 -7 Slightly pervious (poor drainage) Fine sand, sandy Silty silt, silt clay 10 -8 10 -9 Practically impervious Homogenous clay Determined by constant head test Determined by falling head test ……… Inferred by 1 -D consolidation test Benchmark values : 1 cm/s between laminar and turbulent ~ boundary 10 -9 cm/s ~ lower limit of soil permeability (some recentflow -4 10 cm/s ~ boundary between-11 pervious and poorly drained soils measurements k as gravels low as 10 fromcm/s for highly plastic clays) Also separates clean-sands and sandy-gravels CE 303 22 Instructor: AJ

IIT Bombay Empirical relationship between k and soil properties k = Cd e 2 C = composite shape factor de = representative grain size = viscosity g w e 3 1+ e Other factors influencing permeability : Soil fabric Adsorption of cation on clay surface k of montmorillonite is increased if K is replaced by Ca Effective stress CE 303 22 Instructor: AJ

IIT Bombay Permeability of stratified soils Average horizontal / vertical permeability is taken in layered deposits Average permeability in the horizontal direction k. H = 1 (k 1 H 1 + k 2 H 2 ) (H 1 + H 2 ) Average permeability in the vertical direction H 1 + H 2 k. V = é H 1 H 2 ù ê + ú k k ë 1 2û CE 303 22 Instructor: AJ

IIT Bombay CE 303 22 Instructor: AJ