foundations design 1
TRANSCRIPT
ENCE 461Foundation Anal ysis and
Design
Retaining WallsLateral Earth Pressure Theory
Retainin g Walls
� Necessary in situations where gradual transitions either take up too much space or are impractical for other reasons
� Retaining walls are analysed for both resistance to overturning and structural integrity
� Two categories of retaining walls
� Gravity Walls (Masonry, Stone, Gabion, etc.)
� In-Situ Walls (Sheet Piling, cast in-situ, etc.)
Lateral Earth Pressure Coefficient
� K = lateral earth pressure coefficient
� �x’ = horizontal effective stress
� ����������� ��������������
� ����������� ���������� ������������ �������� ������
� �� ����������������������� ��������� �
K��x '
�z'
Mohr’s Circle and Lateral
Earth Pressures
=�z'� x ' =
Development of Lateral Earth Pressure
Po
b��1 z1
2 K o
2
Note Pore Water Effect! subtract vertically add horizontally
Groundwater Effects
� Steps to properly compute horizontal stresses including groundwater effects:
� Compute total vertical stress
� Compute effective vertical stress by removing groundwater effect through submerged unit weight; plot on P
o diagram
� Compute effective horizontal stress by multiplying effective vertical stress by K
� Compute total horizontal stress by directly adding effect of groundwater unit weight to effective horizontal stress
Groundwater Effects
Conditions of Lateral Earth Pressure Coefficient
� At-Rest Condition
� Condition where wall movement is zero or “minimal”
� Ideal condition of wall, but seldom achieved in reality
� Active Condition
� Condition where wall moves away from the backfill
� The lower state of lateral earth pressure
� Passive Condition
� Condition where wall moves toward the backfill
� The higher state of lateral earth pressure
Effect of Wall Movement
Wall Movements Necessar y to Achieve Active or Passive
States
Estimates of At Rest Lateral Earth Pressure Coefficient
� Jaky’s Equation
� Modified for Overconsolidated Soils
� Applicable only when ground surface is level
� In spite of theoretical weaknesses, Jaky’s equation is as good an estimate of the coefficient of lateral earth pressure as we have
K o�1�sin� '
K o��1�sin� ' �OCRsin� '
Relationship of Poisson’s Ratio with Lateral Earth Pressure
Coefficient
K o��
1��
��2��1��1
��tan��1tan��2
(Normally Consolidated Soils)
Example of At Rest Wall Pressure
� Given
� Retaining Wall as Shown
� Find
� PA,
from At Rest Conditions
At Rest Pressure Example
� Compute at rest earth pressure coefficient
� Compute Effective Wall Force
K o�1�sin� 'K o�1�sin30º�0.5
Po
b��1 z1
2 K o
2Po
b�
1202020.52
Po
b�12000
lbsft�12
kipsft
hPA�203�6.67 ft.
(valid for all theories)
Development of Active Earth Pressure
Development of Passive Earth Pressure
Earth Pressure Theories
Rankine Earth Pressure EquationsLevel Backfills
Rankine Theor y with Inclined Backfills
Rankine Coefficients with Inclined Backfills
Inclined and level backfill equations are identical when � = 0
Example of Rankine Active Wall Pressure
� Given
� Retaining Wall as Shown
� Find
� PA,
from At Rest Conditions
Rankine Active Pressure Example
� Compute at rest earth pressure coefficient
� Compute Effective Wall Force
Po
b��1 z1
2 K a
2Po
b�
1202020.3332
Po
b�8000
lbsft�8
kipsft
K A�tan2�45º��
2�
K A�tan2�45�15��13
Rankine Passive Pressure Example
Rankine Passive Pressure Example
� Compute at rest earth pressure coefficient
� Compute Effective Wall Force
Po
b��1 z1
2 K p
2Po
b�
12020232
Po
b�72000
lbsft�72
kipsft
K P�tan2�45º�
2�
K P�tan2�4515��3
Summar y of Rankine and At Rest Wall Pressures
72,000 lbs.
12,000 lbs. 8000 lbs.
Coulomb Theor y
K p�cos2����
cos2�cos������1�sin����sin�� �
cos�����cos� ����
2
K a�cos2�����
cos2�cos�����1sin����sin��� �
cos����cos��� ��
2�
Typical Values of Wall Friction
Example of Coulomb Theor y
� Given
� Wall as shown above
� Find
� KA, K
P, P
A
Solution for Coulomb Active Pressures
� Compute Coulomb Active Pressure
� KA = 0.3465
� Compute Total Wall Force
� PA = 8316 lb/ft of wall
Solution for Coulomb Passive Pressures
� Compute Coulomb Passive Pressure
� KP = 4.0196
� Compute Total Wall Force
� PA = 96,470 lb/ft of wall
Walls with Cohesive Backfill
� Retaining walls should generally have cohesionless backfill, but in some cases cohesive backfill is unavoidable
� Cohesive soils present the following weaknesses as backfill:
� Poor drainage
� Creep
� Expansiveness
� Most lateral earth pressure theory was first developed for purely cohesionless soils (c = 0) and has been extended to cohesive soils afterward
Theor y of Cohesive
Soils
Active Case(Overburdendriving)
Passive Case(Wall Driving)
1sin�1�sin�
� tan2��
4�
2�
Rankine Pressures with Cohesion (Level Backfill)
�3��1 tan2��
4��
2��2c tan�
�
4��
2�
�1�� H
K A��3
�1
�tan2��
4��
2��
2c� H
tan��
4��
2�
� Active
� Passive
�1��3 tan2��
4�
2�2c tan�
�
4�
2�
�3�� H
K P��1
�3
�tan2��
4�
2�
2c� H
tan��
4�
2�
Overburden Driving
Wall Driving
Comments on Rankine
Equations
� Valid if wall-soil friction is not taken in to account
� Do not take into consideration soil above critical height
� Do not take into consideration sloping walls
� For practical problems, should use equations as they appear in the book
H c�2c
� K a
Equivalent Fluid Method
� Simplification used to guide the calculations of lateral earth pressures on retaining walls
� Can be used for Rankine and Coulomb lateral earth pressures
� Can be used for at rest, active and passive earth pressures
� Transforms the soil acting on the retaining wall into an equivalent fluid
Example of Equivalent Fluid Method
� Given
� Wall as shown above
� KA = 0.3465
� KP = 4.0196
� �w
= 3 degrees
� Find
� Forces acting on the wall (both horizontal and vertical)
Example of Equivalent Fluid� Compute Equivalent Fluid Unit Weights (Active
Case)Gh��K acos�w
Gh�1200.3465cos3ºGh�41.52pcfGv��K asin�w
Gv�1200.3465sin3ºGv�2.18pcf
Example of Equivalent Fluid� Compute Wall Load (Active Case)
Pa
b�
Gh H 2
2Pa
b�
41.52202
2�8304 lb/ft
V a
b�
Gv H 2
2V a
b�
2.18202
2�436 lb/ft
Example of Equivalent Fluid� Compute Equivalent Fluid Unit Weights (Passive
Case)Gh��K pcos�w
Gh�1204.0196cos3ºGh�481.69pcfGv��K psin�w
Gv�1204.0196sin3ºGv�25.24pcf
Example of Equivalent Fluid� Compute Wall Load (Passive Case)
Pp
b�
Gh H 2
2Pp
b�
481.69202
2�96338 lb/ft
V p
b�
Gv H 2
2V p
b�
25.24202
2�5048 lb/ft
Terzaghi Model
� Assumes log spiral failure surface behind wall
� Requires use of suitable chart for K
A
and KP
� Not directly used in this course, but option in SPW 911
Presumptive Lateral Earth Pressures
� Based on Terzaghi theory
� Suitable for relatively simple retaining walls in homogeneous soils
� Classifies soils into five types:
1. “Clean” coarse grained soils
2. Coarse grained soils of low permeability; mixed with fine grained soils
3. Residual soils with granular materials and clay content
4. Very soft clay, organic silts, or silty clays
5. Medium or stiff clay, very low permeability
Presumptive Lateral Earth Pressures
Presumptive Lateral Earth
Pressures
Effects of Surface Loadin g
Surchar ge and Groundwater Loads
Homework Set 5
� Reading
� McCarthy: Chapter 16
� Coduto: Chapters 22, 23, 24 & 25
� Homework Problems
� McCarthy: 16-1, 16-8, 16-12a, 16-17
� Coduto: 25.3 (Hand and Chart Solutions); 25.5 (SPW 911)
� Due Date: 17 April 2002
Questions