GEOTECHNICAL ENGINEERING ECG 503 LECTURE NOTE 07 3.0 ANALYSIS AND DESIGN OF RETAINING STRUCTURES
LEARNING OUTCOMES Learning outcomes: At the end of this lecture/week the students would be able to: Understand types of retaining walls
TOPIC TO BE COVERED Types of Retaining Structures
Introduction & Overview 2.1 Introduction and overview Retaining structures such as retaining walls, basement walls, and bulkheads are commonly encountered in foundation engineering, and they may support slopes of earth mass. Proper design and construction of these structures require a thorough knowledge of the lateral forces that act between the retaining structures and the soil mass being retained.
Retaining walls are used to prevent the retained material from assuming its natural slope. Wall structures are commonly use to support earth are piles. Retaining walls may be classified according to how they produce stability as reinforced earth, gravity wall, cantilever wall and anchored wall. At present, the reinforced earth structure is the most used particularly for roadwork
3 basic components of reinforced earth wall Facing unit not necessary but usually used to maintain appearance and avoid soil erosion between the reinforces. Reinforcement strips or rods of metal, strips or sheets of geotextiles, wire grids, or chain link fence or geogrids fastened to the facing unit and extending into the backfill some distance. The earth fill usually select granular material with than 15% passing the no. 200 sieve.
Component of E.R. Wall
EARTH RETAINING STRUCTURES Types of Retaining Wall Retaining Wall The various types of earth-retaining structures fall into three broad groups. Gravity Walls Embedded walls Reinforced and anchored earth
EARTH RETAINING STRUCTURES Gravity Walls Gravity Walls Masonry walls Gabion walls Crib walls RC walls Counterfort walls Buttressed walls
EARTH RETAINING STRUCTURES Gravity Walls Unreinforced masonry wall
EARTH RETAINING STRUCTURES Gravity Walls Gabion wall
EARTH RETAINING STRUCTURES Gravity Walls Crib wall
EARTH RETAINING STRUCTURES Gravity Walls Types of RC Gravity Walls
EARTH RETAINING STRUCTURES Embedded Walls Embedded walls Driven sheet-pile walls Braced or propped walls Contiguous bored-pile walls Secant bored-pile walls Diaphram walls
EARTH RETAINING STRUCTURES Embedded Walls Types of embedded walls
EARTH RETAINING STRUCTURES Reinforced and Anchored Earth Reinforced and anchored earth Reinforced earth wall Soil nailing Ground anchors
EARTH RETAINING STRUCTURES Reinforced and anchored earth Reinforced earth and soil nailing
EARTH RETAINING STRUCTURES Stability Criteria Stability of Rigid Walls Failures of the rigid gravity wall may occur due to any of the followings: Overturning failure Sliding failure Bearing capacity failure Tension failure in joints Rotational slip failure In designing the structures at least the first three of the design criteria must be analysed and satisfied.
Types of Lateral Pressure States of Equilibrium Hydrostatic Pressure and Lateral Thrust Earth Pressure at Rest Active Earth Pressure Passive Earth pressure
Types of Lateral Pressure Hydrostatic pressure and lateral thrust Horizontal pressure due to a liquid
Earth Pressure at Rest Earth pressure at rest A Unit weight of soil = γ c tan σ h = K o σ v B Earth pressure at rest f σ v z If wall AB remains static soil mass will be in a state of elastic equilibrium horizontal strain is zero. Ratio of horizontal stress to vertical stress is called coefficient of earth pressure at rest, K o, or K o h h v K o v K z o
Earth Pressure at Rest Earth pressure at rest.. cont.
Active earth pressure Active Earth Pressure A Unit weight of soil = γ c tan σ v σ h B Earth pressure at rest f z Plastic equilibrium in soil refers to the condition where every point in a soil mass is on the verge of failure. If wall AB is allowed to move away from the soil mass gradually, horizontal stress will decrease. This is represented by Mohr s circle in the subsequent slide.
ACTIVE EARTH PRESSURE (RANKINE S) (in simple stress field for c=0 soil) Fig. 1 σz σx = Ko σz ø σx A Ko σz σz
Active Earth Pressure Based on the diagram : Ratio a coefficient v K a of Rankine' s active earth pressure (K a is the ratio of the effective stresses) Therefore : K a a v tan 2 (45 - ) 2 1 - sin 1 sin It can be shown that : a z tan z K a 2 (45 - ) 2-2c K a - 2c tan (45 - ) 2
Active pressure distribution Active Earth Pressure - 2c K a - 2c K a z o z z K a z Ka - 2c K a
Active Earth Pressure Active pressure distribution Based on the previous slide, using similar triangles show that : z o 2c K a where z o is depth of tension crack For pure cohesive soil, i.e. when = 0 : 2c z o
Active pressure distribution Active Earth Pressure z For cohesionless soil, c = 0 a v K a z K a z K a
Passive Earth Pressure 2.2.4 Passive earth pressure A Unit weight of soil = γ c tan σ v σ h B Earth pressure at rest f z If the wall is pushed into the soil mass, the principal stress σ h will increase. On the verge of failure the stress condition on the soil element can be expressed by Mohr s circle b. The lateral earth pressure, σ p, which is the major principal stress, is called Rankine s passive earth pressure
PASSIVE EARTH PRESSURE (RANKINE S) (in simple stress field for c=0 soil) Fig. 2 σz σx = Ko σz ø Ko σz σz σx P
Shear stress LATERAL EARTH PRESSURE Passive Earth Pressure f c D tan b Mohr s circle representing Rankine s passive state. A c O K o σ v a σ v C σ p Normal stress D
Passive Earth Pressure Referring to previous slide, it can be shown that : p v tan z K p 2 (45 ) 2c tan (45 ) 2 2 2c K p For cohesionless soil : p v K p tan 2 (45 ) 2 1 1 sin sin
Passive pressure distribution Passive Earth Pressure z For cohesionless soil, p v K p z K p 2c K p z K p
Earth Pressure LATERAL EARTH PRESSURE Earth Pressure In conclusion Passive pressure At-rest pressure Active pressure Wall tilt Wall tilt
Rankine s Theory Types of Lateral Pressure Initial work done in 1857 Develop based on semi infinite loose granular soil mass for which the soil movement is uniform. Used stress states of soil mass to determine lateral pressures on a frictionless wall Assumptions : Vertical frictionless wall Dry homogeneous soil Horizontal surface
Types of Lateral Pressure Active pressure for cohesionless soil
Effect of surcharge Types of Lateral Pressure Effect of a stratified soil
Types of Lateral Pressure Effect of sloping surface
Types of Lateral Pressure Active pressure, ' ha K a ' v cos Passive pressure, ' hp K p ' v cos where K a cos - cos (cos (cos 2 2 - cos ') 2 2 - cos ') and K p cos cos (cos (cos 2 2 2 - cos ') 2 - cos ') 1 K a
Types of Lateral Pressure Tension cracks in cohesive soils
Types of Lateral Pressure Effect of surcharge (undrained)
Types of Lateral Pressure Passive resistance in undrained clay
Stability Criteria The stability of the retaining wall should be checked against : (i) FOS against overturning (recommended FOS = 2.0) FOS Resisting moment Disturbing moment (ii) FOS against sliding (recommended FOS = 2.0) FOS R V tan (0.5 - R H 0.7) P p c w B
Stability Analysis The stability of the retaining wall should be checked against : 2.3.1 FOS against overturning (recommended FOS = 2.0) FOS Resisting moment Disturbing moment V P h P p.. overturning about A A
Stability Criteria 2.3.2 FOS against sliding (recommended FOS = 2.0) FOS R V tan (0.5 - R H 0.7) P p c w B V P h P p Friction & wall base adhesion
Stability Criteria 2.3.3 For base pressure (to be compared against the bearing capacity of the founding soil. Recommended FOS = 3.0) R V qb 1 B 6e B Now, Lever arm of base resultant x Thus eccentricity Moment R V e B 2 - x
Stability Analysis V P h P p Base pressure on the founding soil
Worked example : Stability Analysis Figure below shows the cross-section of a reinforced concrete retaining structure. The retained soil behind the structure and the soil in front of it are cohesionless and has the following properties: SOIL 1 : u = 35 o, d = 17 kn/m 3, SOIL 2 : u = 30o, = 25 o, d = 18 kn/m 3, sat = 20 kn/m 3 The unit weight of concrete is 24 kn/m 3. Taking into account the passive resistance in front of the wall, determine a minimum value for the width of the wall to satisfy the following design criteria: Factor of safety against overturning > 2.5 Factor of safety against sliding > 1.5 Maximum base pressure should not exceed 150 kpa
Stability Analysis THE PROBLEM 30 kn/m 2 0.5 m SOIL 1 2.0 m 4.0 m GWT SOIL 2 2.9 m SOIL 2 0.6 m 4.5 m 2.0 m
Stability Analysis THE SOLUTION 30 kn/m 2 0.5 m 4.0 m W1 SOIL 1 W3 GWT 2.0 m P 1 P 3 W41 SOIL 2 SOIL 2 W2 2.9 m P 2 P 4 P P P 5 P 6 0.6 m 4.5 m 2.0 m
Stability Analysis Determination of the Earth Pressure Coefficients o 1- sin 35 K a 1 o 1 1 1 1 sin sin sin sin 1 1 sin 35 o 1- sin 30 K a 2 o sin 30 0.271 0.333 o 1 sin 30 K p 2 o 1 1 sin sin 1 sin 30 3.00
ELEM. FORCE (kn/m) TOTAL Stability Analysis L. ARM (m) MOMENT (knm/m) HORIZONTAL Active P1 0.271 x 30 x 2 16.26 4.5 73.17 P2 0.333 x 30 x 3.5 34.97 1.75 61.20 P3 0.5 x 0.271 x 17 x 2 x 2 9.21 4.17 38.41 P4 0.333 x 17 x 2 x 3.5 39.63 1.75 69.35 P5 0.5 x.333 x (20-9.81) x 3.5 x 3.5 20.78 1.167 24.25 P6 0.5 x 9.81 x 3.5 x 3.5 60.09 1.167 70.13 SUM 180.94 336.50 Passive Pp 0.5 x 3 x 18 x 1.5 x 1.5 60.75 0.5 30.38 VERTICAL W1 0.5 x 4.9 x 24 58.8 1.75 102.90 W2 0.6 x 4.5 x 24 64.8 2.25 145.80 W3 2 x 2.5 x 17 + 2.9 x 2.5 x 20 + 30 x 2.5 305 3.25 991.25 W4 0.9 x 1.5 x 18 24.3 0.75 18.23 SUM 452.9 1288.55
Stability Analysis To check for stability of the retaining wall (i) FOS against overturning > 2.5 FOS Resisting moment 1288.55 3. 83 Disturbing moment 336.50 2.5, thus it is OK (ii) FOS against sliding > 1.5 FOS o RV tan 0.5 Pp 452. 9 tan 25 0.5 x 60.75 1. 34 R 180. 94 H 1.5 Thus it is not OK
(iii) For base pressure R V qb 1 B Stability Analysis 6e B Now, Lever arm of base resultant x Moment R V 1288.55-336.5 452.9 2.10 Thus eccentricity e B 2 - x 2.25-2.10 0.15 Therefore 452.9 6 x 0.15 q b 1 4.5 4.5
q b = 120.8 and 80.5 kpa Stability Analysis Since maximum base pressure is less than the bearing pressure of the soil, the foundation is stable against base pressure failure. DISTRIBUTION OF BASE PRESSURE 120.8 kpa 80.5 kpa In conclusion the retaining wall is not safe against sliding. To overcome this the width of the base may be increased or a key constructed at the toe.
Group assignment NO. 1: Form a group of 6 members in each group. Your task is to write up a case study which involve a dam case failure in Malaysia and a slope failure in Malaysia. Your report shall consists of the history of each case, as examples; amount of dam in Malaysia, their purpose, operation, etc. Make sure your case study are not the same as others groups. Penalties will be given accordingly for those who ignore the warnings. Date of submission : 08 October 2009
Group assignment NO. 2: Form a group of 6 members in each group. Your task is to write up a case study which involve a ground improvement technique. Your shall selected a real project which will consists of real soil problems and technique to overcome the problems. Make sure your case study are not the same as others groups. Penalties will be given accordingly for those who ignore the warnings. Date of submission : 15 October 2009