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Critical State
• Definition:
It is the soil state at which shearing occurs at constant volume and constant shearing stress
At critical state, soil density and stress are in equilibrium, that is, the soil has no need to contract or dilate
Sand – Effect of DR
q
εd
• Drained no excess pore pressure
• CD triaxial tests on dense and loose sand specimens
• Same initial confining stress but different initial DR
1 3q σ σ= −
Loose specimen
Dense specimen
q
εd
1 3q σ σ= −
Loose specimen
Dense specimen
volε
Loose specimen
Dense specimen
εd
(contraction)
(dilation)
Drained no excess pore pressure
Dilative
Contractive
CRITICAL STATE
Sources of shear strength
• Friction between soil particles
• Particle rearrangement
• Interlocking between particles
Sources of shearing strength
• Shearing strength of contractive sands is due primarily to friction between soil particles and particle rearrangement
• Shearing strength of dilative sands is due to interlocking between particles that has to be overcome by dilation (for dilation to occur, energy must be supplied to the soil for it to overcome the confining stress)
Sand – Effect of confinement
q =σ’1-σ’3
εd
• Drained no excess pore pressure
• CD triaxial tests on contractive sand specimens
• Same initial DR but different initial confining stress
σ’3
2σ’3
3σ’3
qcs
2qcs
3qcs
• Drained no excess pore pressure
• CD triaxial tests on dilative sand specimens
• Same initial DR but different initial confining stress
q =σ’1-σ’3
εd
σ’3qcs
1/2qcs
1/4qcs
1/2 σ’3
1/4 σ’3
Sand – Effect of confinement
σ ′
τ
Critical-state envelope
σ’3 2σ’3 3σ’3
φc
Critical-state envelope
A
1/2σ’31/4σ’3
dilative contractive
τcs
2τc
3τc
1/2τc
1/4τc
• Drained no excess pore pressure
• CD triaxial tests on dilative sand specimens
• Same initial DR but different initial confining stress
q =σ’1-σ’3
εd
σ’3qcs
qpeak
qpeak
1/2 σ’3
1/4 σ’3
Sand – Effect of confinement
σ ′
τ
Peak and critical-state envelopes
σ’3 2σ’3 3σ’3
φc
Critical-state envelope
A
1/2σ’31/4σ’3
Peak envelope
dilative contractive
τc
2τc
3τc
τpeak
τpeak
σ ′
τ
Peak and critical-state friction angles
φc
Critical-state envelope
Peak envelope
dilative contractive
φpeak
φpeak
Higher φpeak
Confinement
Lower φpeak until φc is reached
Critical-state friction angle
– Also called constant-volume φ
– The φ at very large strains
φc= 28o to 36o silica sands
φc= 37o to 44o carbonate sands