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The following calculations are used in this test:
Deformation
The lateral and normal deformations can be specified directly or using deformation dial readings. When using dial readings they are converted to actual deformations using a dial constant.
DL = (RL - RLi) * LDC Lateral Deformation
DN = (RNi - RN) * NDC Normal Deformation
where,
DL = Lateral deformation
DN = Normal (vertical) deformation
RL = Lateral dial reading
RLi = Initial lateral dial reading
LDC = Lateral dial constant
RN = Normal dial reading
RNi = Initial normal dial reading
NDC = Normal dial constant
Lateral Load
The lateral loads can be specified directly or using readings from a load ring. When using readings from a load ring the readings are converted to lateral loads either using load ring constants or a linear equation.
Load Ring Constant
If R < Crossover PL = R * LRC1
If R > Crossover PL = Crossover * LRC1 + (R - Crossover) * LRC2
Linear
PL = M * R + C
where,
PL = Lateral load
R = Lateral dial reading
LRC1 = Load ring constant 1
LRC2 = Load ring constant 2
M = Linear multiplier
C = Linear constant
Lateral Strain
εL = DL / d
where,
εL = Lateral strain
DL = Lateral deformation
d = Diameter for circular shear box or side width for square shear box
Cross-sectional Area
According to ASTM standard and without area adjustment:
A = π * r2 Circular
A = d2 Square
Adjusting area for lateral deformation:
A = 2 * r2 * cos-1(DL/d) - 0.5 * DL * (4*r2 - DL2)½ Circular
A = d2 - (d * DL) Square
where,
A = Cross-sectional area
r = Radius = 0.5 * d
Shear Stress
τ = PL / A
where,
τ = Shear stress
Normal Stress
σ = PN / A
where,
σ = Normal stress
PN = Normal load
Water Content
wi (%) = 100 * (Mbwt - Mbdt) / (Mbdt - Mbt) Initial
wf (%) = 100 * (Mawt - Madt) / (Madt - Mat) Final
where,
wi = Initial percentage water content
wf = Final percentage water content
Mbwt = Mass of tare and wet specimen before test
Mbdt = Mass of tare and dry specimen before test
Mbt = Mass of tare used before test
Mawt = Mass of tare and wet specimen after test
Madt = Mass of tare and dry specimen after test
Mat = Mass of tare used after test
Dry Density
ρi = Mw / Vi / (1+ wi/100) Initial
ρp = Mw / Vp / (1+ wi/100) Pre-shear
where,
ρi = Initial dry density
ρp = Pre-shear dry density
Mw = Wet sample mass
Vi = Initial sample volume
Vp = Pre-shear sample volume
wi = Initial water content (%)
Dry Unit Weight
γi = ρi * γw Initial
γp = ρp * γw Pre-shear
where,
γi = Initial dry unit weight
γp = Pre-shear dry unit weight
γw = Unit weight of water (9.807 kN/m3)
Saturation
Si (%) = 100 * Vwi / Vvi Initial
Sp (%) = 100 * Vwp / Vvp Pre-shear
where,
Si = Initial saturation
Sp = Pre-shear saturation
Vwi = Initial volume of water in sample = (Mw - Ms) / ρw
Vwp = Pre-shear volume of water in sample = [Vp * ρp * (1 + wf/100) - Ms] / ρw
Vvi = Initial volume of voids = Vi - Vs
Vvp = Pre-shear volume of voids = Vp - Vs
Vs = Volume of solids = Ms / (SG * ρw)
Ms = Mass of solids = Mw / (1 + wi / 100)
ρw = Density of water (1.0 g/cm3)
SG = Specific gravity
Void Ratio
ei = Vvi / Vs Initial
ep = Vvp / Vs Pre-shear
where,
ei = Initial void ratio
ep = Pre-shear void ratio