Stability of Retaining Cantilever Walls.

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1 Stability of Retaining Cantilever Walls. Cantilever Walls 12/3/2010 Institution: Vocational Training Development Institute Course: Draughting and Building Technology Course Title: Theory and Design of Structures (2) Student s Name: Shavaun Thomas ID#: Lecturer: D. Reid

2 2 Definition to a Retaining Wall. A retaining wall is a structure that retains (holds back) any material (usually earth) and prevents it from sliding or eroding away. It is so designed to resist the material pressure of the material that it is restraining. What is a Cantilever Retaining Wall? A cantilever retaining wall is one that consists of a wall which is connected to a foundation. A cantilever wall restrains a significant amount of soil, as a result it must be properly engineered. They are the most common type used as retaining walls. Cantilever wall rest on a slab foundation. This slab foundation is also loaded by back-fill and thus the weight of the backfill and surcharge also stabilizes the wall against overturning and sliding. An Introduction to the Stability of Retaining Walls. One of the principal differences between the Code of Practice BS 8002:19941 and the earlier CP2:19512 lies in the philosophy of factor of safety. BS 8002:1994 introduced the concept of a partial factor of safety. The advantage of this is its ability to operate directly upon those parts of the calculation subject to the greatest unknowns, usually the soil strength. In BS 8002 : 1994 the partial factor is applied to tan ɸ', where ɸ' is the angle of friction of the soil. Properties such as soil unit weight, which can normally be more reliably estimated, are not affected by application of the partial factor as they would be by the lumped factor approach of CP2 : However, by factoring tan ɸ', not only the magnitude but also the line of action of the force is altered, and the inclination factors in the bearing capacity calculation may be significantly affected.

3 3 Bearing capacity and sliding stability theory differ. Whatever the philosophy adopted for the factor of safety, the angle of friction ɸ FB mobilized at the required factor of safety against bearing capacity failure will not be equal to the angle of friction ɸ FS mobilized at the required factor of safety against sliding instability. Therefore retaining walls dimensioned on the basis of bearing capacity and of sliding stability would be of different sizes.

4 Picture showing a retaining wall cross-sectional design. 4

5 5 Stability as it relates to Retaining Walls (Cantilever Walls). Bearing capacity and sliding stability theory differs. Whatever the philosophy adopted for the factor of safety, the angle of friction f FB mobilized at the required factor of safety against bearing capacity failure will not be equal to the angle of friction f FS mobilized at the required factor of safety against sliding instability. Therefore retaining walls dimensioned on the basis of bearing capacity and of sliding stability would be of different sizes. The usual method of designing cantilever retaining walls is first to dimension the wall foundation with respect to the bearing capacity provided by the foundation. Such method usually involves calculating the factor of safety against bearing capacity failure, which must normally be as required by the code of practice to which the engineer is working. With the foundation base width chosen, the wall s stability against sliding is next determined. Again, this must also be to the factor of safety required by the code of practice. When designing cantilever retaining walls or more modern gravity type, the following cases are normally considered. Bearing capacity failure. In such a case, the sum of the cantilever wall weight plus the vertical component of the active trust acting on the back of the wall, without the vertical component or any inactive forces on the front of the wall, proofs greater than the foundation soil s capacity, failure occurs. Sliding stability. In such condition an outward movement of the retaining wall occurs. It moves away from the backfill, and due to the horizontal imbalances between the horizontal component of the active trust acting on the back of the wall, the sum of the sliding resistance at the base and the

6 6 horizontal component of any inactive force acting on the front of the wall. Water forces acting on the back of the wall and on the underside of the foundation, will result to instability. Overturning or (toppling). Retaining walls rotate at a pivot along its toe. This disturbing moment is due to the horizontal component of the active trust and the horizontal water or soil force, while the restoring moments are due to the buoyant wall weight, the vertical component of the active trust along with the horizontal component of the inactive force. The toe remains horizontal throughout. The case relates to a retaining wall foundation placed on rock, thus it is not expected to collapse, however, if this is otherwise it said that the position of the line of action disturbing force will change. Overall stability. Generally of most importance on sloping ground, the retaining wall is considered to be just part of the stability of the site as a whole, and so, is designed as such. The inclination of the retaining wall, and any structure contained within the soil forming the gradient, contribute greatly to instability. Important notes to consider when doing Calculations relating to Retaining Walls. Lateral earth pressure is normally calculated based on Rankine or Coulomb s theories. Lateral earth pressure is assumed distributed triangularly. The location of resultant is at 1/3 of height. If there is surcharge, lateral earth pressure from surcharge is distributed uniformly. The resultant is at ½ of height. The lateral earth pressure is calculated at the edge of heel. The rotating point for overturning is normally assumed at bottom of toe. The height of soil used to calculate lateral earth pressure should be from top of earth to the bottom of footing.

7 7 Elements that resisting overturning are weight of stem, weight of footing, weight of soil above footing. If there is a surcharge, the weight of surcharge can also be considered. The factor of safety against overturning is resisting moment divided by overturning moment. Acceptable factor of safety is between 1.5 to 2. The driving force that causes retaining wall to slide is the lateral earth pressure from soil and surcharge. The forces that resist sliding are passive pressure at toe, the friction at the base of the footing; and the passive pressure against the key if used. The factor of safety against sliding is the total resisting force divided by total driving force. Acceptable factor of safety is between 1.5 to 2. Calculating Bearing Capacity: The bearing pressure is calculated as follows 1. The center of the total weight from the edge of toe is X= M R M o W Where W is total weight of retaining wall including stem, footing, earth and surcharge The eccentricity, e = B/2-X 2. If e B/6, the maximum and minimum footing pressure is calculated as

8 8 Q max = W x e Q min = W 1-6 x e B B B B Where, Q max, Q min are maximum and minimum footing pressure, B is the width of footing. 4. If e > B/6, Q min is zero, Q max = 2 x W 3 B/2- e 5. Q max should be less than allowable soil bearing capacity of footing soil. Calculating Factor of Safety: 1. The driving force for sliding is calculated as P h = ½ γ K a H 2 + q K a H 2. The friction resisting force at the base of footing is calculated as F R = μ W where m is friction coefficient between concrete and soil. m is often taken as tan (2/3 f). f is internal friction of the soil 3. The passive resistance at the toe of retaining wall is calculated as

9 9 P y = ½ γ K y h Where Kp is passive earth pressure coefficient, h is the height from top of soil to bottom of footing at toe. If a key is used to help resist sliding, h is the height from top of soil to the bottom of the key. 4. The factor of safety is calculated as FS= F R + P y + P k P k + P k Calculating Overturning (toppling): The factor of safety against overturning is calculated as 1. The overturning moment is calculated as M o = 1/6 γ K a H 3 + 1/2 q K a H 2 Where g is unit weight of soil, K a is active pressure coefficient, and H is the height from top of earth to bottom of footing, q is surcharge. 2. The resisting moment is calculated as M R = W s X s +W f X f +W e X e +W k X k +W q X q where Ws,Wf,We,Wk,Wq are weight of stem, footing, earth, key and surcharge, X s,x f,x e,x k,x q are distance from the center of stem, footing, earth, key, and surcharge to the rotation point at toe.

10 10 The factor of safety against overturning is calculated as FS= M R M o

11 11 References. Jamal, H. (2010, July 03). Retrieved December 03, 2010, from Trenter, N. (January 2004). Geotechnical Engineering. Codes of practise & standards/design method & aids/retaining walls, (n.d.). Retrieved December 03, 2010, from