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SHEAR STRENGTH IYULVI ZAIKA
MATERIKeruntuhan mohr coulomb,
stress paths,
kuat geser tanah non kohesif dan kohesif,
evaluasi kuat geser di lapangan,
tegangan normal dan tegangan geser pada sebuah bidang
Strength of different
materials
Steel
Tensile
strength
Concrete
Compressive
strength
Soil
Shear
strength
Presence of pore waterComplexbehavior
Shear strength of soilSoil cannot resist tension
Soil can resist compression.
For excessive compression failure occurs in the form of shearing along the internal surface within the soil
Structural Strength of soil = f ( soil’s shear strength)
Shear Strength◦ Soil’s ability to resist sliding
◦ Important for
◦ foundation design
◦ Lateral earth pressure calculations
◦ Slope stability analysis
Shear Strength due to sliding friction
SlidingForce
Normal Force
Shear Strength due to sliding friction
Normal Force
SlidingForce
What is Shear Strength?
Shear strength in soils is the resistance to movement between particles due to physical bonds from:
A.Particle interlocking
b.. Atoms sharing electrons at surface contact points
C.. Chemical bonds (cementation) such as crystallized calcium carbonate
Influencing Factors on Shear Strength
The shearing strength, is affected by:
––soil composition,: mineralogy, grain size and grain size distribution, shape of particles, pore fluid type and content, ions on grain and in pore fluid.
–– Initial state: State can be describe by terms such as:
loose, dense, over--consolidated, normally
consolidated, normally
consolidated, stiff, soft, etc.
––Structure : Refers to the arrangement of particles within the soil mass; the manner in which the particles are packed or distributed. Features such as layers, voids, pockets, cementation, etc, are part of the structure.
Embankment
Strip footing
Shear failure of soilsSoils generally fail in shear
At failure, shear stress along the failure surface(mobilized shear resistance) reaches the shear strength.
Failure surface
Mobilized shear resistance
Retaining wall
Shear failure of soilsSoils generally fail in shear
Retaining wall
Shear failure of soils
At failure, shear stress along the failure surface(mobilized shear resistance) reaches the shear strength.
Failure surface
Mobilized shear resistance
Soils generally fail in shear
Shear failure mechanism
The soil grains slideover each other alongthe failure surface.
No crushing ofindividual grains.
failure surface
Shear failure mechanism
At failure, shear stress along the failure surface ()reaches the shear strength (f).
Mohr-Coulomb Failure Criterion(in terms of total stresses)
f is the maximum shear stress the soil can take without failure, under normal stress of .
tan cf
c
CohesionFriction angle
f
Mohr-Coulomb Failure Criterion(in terms of effective stresses)
f is the maximum shear stress the soil can take without failure, under normal effective stress of ’.
’
'tan'' cf
c’
’
Effective cohesion Effective
friction anglef
’
u '
u = pore water
pressure
Mohr-Coulomb Failure Criterion
'tan'' ff c
Shear strength consists of two components: cohesive and frictional.
’f
f
’
'
c’ c’
’f tan ’ frictional component
c and are measures of shear strength.
Higher the values, higher the shear strength.
NOTE
Mohr Circle of stress
Soil element
’1
’1
’3’3
q
’
q
q
2cos22
2sin2
'
3
'
1
'
3
'
1'
'
3
'
1
Resolving forces in and directions,
2'
3
'
1
2'
3
'
1'2
22
Mohr Circle of stress
2'
3
'
1
2'
3
'
1'2
22
’
2
'
3
'
1
2
'
3
'
1
'
3 '
1
Mohr Circle of stress
2'
3
'
1
2'
3
'
1'2
22
’
2
'
3
'
1
2
'
3
'
1
'
3 '
1
PD = Pole w.r.t. plane
q
(’, )
Soil elements at different locations
Failure surface
Mohr Circles & Failure Envelope
X X
X ~ failure
YY
Y ~ stable
’
'tan'' cf
Mohr Circles & Failure Envelope
Y
c
c
c
Initially, Mohr circle is a point
c+
The soil element does not fail if the Mohr circle is contained within the envelope
GL
Mohr Circles & Failure Envelope
Y
c
c
c
GL
As loading progresses, Mohr circle becomes larger…
.. and finally failure occurs when Mohr circle touches the envelope
’
2
'
3
'
1 '
3 '
1
PD = Pole w.r.t. plane
q
(’, f)
Orientation of Failure Plane
’
’1
’1
’3’3
q
’
’1
’1
’3’3
’
Failure envelope
(90 – q)
Therefore,
90 – q ’ = q
q 45 + ’/2
Mohr circles in terms of total & effective stresses
= X
v’
h’X
u
u+
v’h’
effective stresses
uvh
X
v
h
total stresses
or ’
Failure envelopes in terms of total & effective
stresses
= X
v’
h’X
u
u+
v’h’
effective stresses
uvh
X
v
h
total stresses
or ’
If X is on failure
c
Failure envelope in
terms of total stresses
’
c’
Failure envelope in terms
of effective stresses
Mohr Coulomb failure criterion with Mohr circle
of stress
X
’v = ’1
’h = ’3
X is on failure ’1’3
effective stresses
’’ c’
Failure envelope in terms
of effective stresses
c’ cot’ (’1 ’3)/2
(’1 ’3)/2
2'sin
2'cot'
'
3
'
1
'
3
'
1
c
Therefore,
Mohr Coulomb failure criterion with Mohr circle
of stress
2'sin
2'cot'
'
3
'
1
'
3
'
1
c
( ) ( ) 'cos'2'sin'
3
'
1
'
3
'
1 c
( ) ( ) 'cos'2'sin1'sin1 '
3
'
1 c
( )( ) ( )'sin1
'cos'2
'sin1
'sin1'
3
'
1
c
2
'45tan'2
2
'45tan2'
3
'
1
c
If c=0 then
𝑠𝑖𝑛𝜑 =𝜎1𝑓−𝜎3𝑓
𝜎1𝑓+𝜎3𝑓
Or
𝜎1
𝜎3=
1+𝑠𝑖𝑛𝜑
1−sin 𝜑= 𝑡𝑎𝑛2 45 +
𝜑
2
’1’3
effective stresses
’’
Failure envelope in terms
of effective stresses
(’1 ’3)/2
exercisesA cylindrical soil (sand) sample was subjected to axial principal stress (1) and radial principal stress (3). The soil can not support additional stress when 1’= 300kPa and 3’=100 kPa. Determine the friction angle and the inclination of the slip plane to the horizontal.
Stress Point
31
t
s
hv
(v-h)/2
(v+h)/2
stress pointstress point
2hvs
2hvt
X
v
h
Stress Path
32
t
s
Stress path adalah tempattitik tegangan
Stress path
Stress path adalah cara yang lebih mudah digunakan untuk melihatProses pembebanan dari awal sampai mencapaiselubung keruntuhan
During loading…
SELUBUNG KERUNTUHAN
33
t
s
c
c cos
tan-1 (sin )
failure
During loading (shearing)….
stress path
FIELD TESTVANE SHEAR
Measure undrained shear strength of soil
Suitable for very soft clay to medium stiff clay
Principle of equipment operation : vane pushed and rotated
The vane shear equation :
𝑠𝑢 =2𝑇
𝜋𝑑3 ℎ 𝑑+1
3
Where:
T : Maximum torque
H : height of vane
d : diameter of vane
Standard Penetration Test (SPT)