weight-volume relations soil can be considered as a 3-phased material air, water, solids
Post on 22-Dec-2015
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3-Phase Soil Block
Weightlb g kg kN
SoilPhase
Volumeft3 cc m3
WA = 0 Air VA
WT WW
Water VW
VV
VT
WS Solids VS
Weight Relations Water content, w
w = [WW/WS] x 100%
may be > 100% for clays Total (Moist,Wet) Unit Weight
= T = WET = WT / VT
Dry Unit Weightd = WS / VT
Table 2.2
Volumetric Relations Void Ratio, e
e = VV / VS
may be > 1, especially for clays Porosity, n
n = [VV / VT] x 100%
0% < n < 100% Degree of Saturation, S
S = [VW / VV] x 100%
0% < S < 100%
Inter-relationships Wet -> Dry Unit Weight
d = WET / (1+w/100)
WS = WT / (1+w/100)
Dry Unit Weight @ Saturation (Zero Air Voids)zav = W / (w/100+1/Gs)
Soil Block Analysis Use given soil data to completely fill
out weight and volume slots Convert between weight and volume
using specific gravity formula
Known Weight: V = W / Gs w
Known Volume: W = V Gs w
w=1g/cc=9.81kN/m3=1000kg/m3=62.4lb/ft3
Example Soil Block AnalysisGiven: WT=4kg, VT=0.002m3, w=20%, Gs=2.68
WS = WT / (1+w/100)
WS = 4kg / (1+20/100) = 3.333 kg
WW = WT – WS
WW = 4kg – 3.333 kg = 0.667 kg
Checkw = WW/WS x 100%
w = 100% x 0.667 / 3.333 = 20.01% OK
Example Soil Block AnalysisVS = WS / GSw
VS = 3.333kg / (2.68 x 1000 kg/m3) = 0.00124 m3
VW = WW/GSw
VW = 0.667kg / (1 x 1000kg/m3) = 0.00067 m3
VA = VT – VS - VW
VA = 0.00200–0.00124–0.00067 = 0.00009m3
VV = VA + VW
VV = 0.00067+0.00009 = 0.00076m3
Example Soil Block AnalysisT = 4.0kg/0.002m3 = 2000 kg/m3=19.62 kN/m3=124.8lb/ft3
D = 3.333kg/0.002m3=1666.5kg/m3=16.35 kN/m3
D = 19.62kN/m3 / 1.20 =16.35 kN/m3
e = 0.00076/0.00124 = 0.613n = 100x0.00076/0.002 = 38.0%S = 100x0.00067/0.00076 = 88.2%
Modified Soil Block AnalysisGiven: WT = 4 kg, VT = 0.002 m3
WT / VT ratio must remain unchanged
4 kg / 0.002 m3 = 120 kg / X
X = 0.06 m3 = VT
Modified Soil Block AnalysisVS = WS / GSw
VS = 100kg / (2.68 x 1000 kg/m3) = 0.0373 m3
VW = WW/GSw
VW = 20kg / (1 x 1000kg/m3) = 0.0200 m3
VA = VT – VS - VW
VA = 0.0600–0.0373–0.0200 = 0.0027m3
VV = VA + VW
VV = 0.0027+0.0200 = 0.0227m3
Modified Soil Block AnalysisT = 120kg/0.06m3 = 2000 kg/m3=19.62 kN/m3
D = 100kg/0.06m3=1666.7kg/m3=16.35 kN/m3
e = 0.0227/0.0373 = 0.609 (0.613)n = 100x0.0227/0.06 = 37.8% (38.0%)S = 100x0.02/0.0227 = 88.1% (88.2%)
Saturation Assumption
If a soil is partially saturated, we can get to full saturation by direct replacement of air with water.
It is further assumed that there will be
no increase in total volume.
In Situ Comparators
Relative Density, Dr
Dr=100% x [emax – ein situ] / [emax – emin]
O% < Dr < 100%
Relative Compaction, R%R% = [d-in situ / d-max,lab] x 100%
R% may be > 100%
Consistency of Soil Plasticity Index, PI
PI = LL - PL Activity, A
A = PI / % Clay Liquidity Index, LI
LI = [w – PL] / [LL – PL]
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