STRESS-STRAIN BEHAVIOR,VOLUME CHANGE, ANDSHEARING OF SANDS

CRITICAL STATE

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

SOURCES OF DRAINED SHEAR STRENGTH

What factors contribute to thestrength of sand?

• Density

• Confinement

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

e

e at critical state

Contractive specimen

Dilative specimen

εd

Critical-state void ratio

ecs

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

σ ′

τ

Critical-state envelope

σ’3 2σ’3 3σ’3

φc

A

Critical-state envelope

2τc

3τc

τc

• 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