Calculations

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Navigation:  Chapter 9 Geotechnical Data Management > Geotechnical Tests > Entering Test Data > Soil and Aggregates Tests > Direct Shear >

Calculations

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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