Module 7 (Lecture 24 to 28) RETAINING WALLS


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1 Module 7 (Lecture 24 to 28) RETAINING WALLS Topics 24.1 INTRODUCTION 24.2 GRAVITY AND CANTILEVER WALLS 24.3 PROPORTIONING RETAINING WALLS 24.4 APPLICATION OF LATERAL EARTH PRESSURE THEORIES TO DESIGN 24.5 STABILITY CHECKS Check for Overturning Check for Sliding Along the Base Check for Bearing Capacity Failure Example Factor of Safety Against Overturning Factor of Safety Against Sliding Factor of Safety Against Bearing Capacity Failure 25.1 OTHER TYPES OF POSSIBLE RETAINING WALL FAILURE 26.1 COMMENTS RELATING TO STABILITY 26.2 DRAINAGE FROM THE BACKFILL OF THE RETAINING WALL 26.3 PROVISION OF JOINTS IN RETAININGWALL CONSTRUCTION
2 26.4 GRAVITY RETAININGWALL DESIGN FOR EARTHQUAKE CONDITIONS 26.5 MECHANICALLY STABILIZED RETAINING WALLS 26.6 GENERAL DESIGN CONSIDERATIONS 27.1 RETAINING WALLS WITH METALLIC STRIP REINFORCEMENT Calculation of Active Horizontal and vertical Pressure Tie Force Factor of Safety Against Tie Failure Total Length of Tie 27.2 STEPBYSTEP DESIGN PROCEDURE (METALLIC STRIP REINFORCEMENT Internal Stability External Stability Internal Stability Check Tie thickness Tie length External Stability Check Check for overturning Check for sliding Check for bearing capacity 28.1 RETAINING WALLS WITH METALLIC STRIP REINFORCEMENT 28.2 Calculation of Active Horizontal and vertical Pressure Tie Force
3 Factor of Safety Against Tie Failure Total Length of Tie 28.3 STEPBYSTEP DESIGN PROCEDURE (METALLIC STRIP REINFORCEMENT General: Internal Stability: Internal Stability Check Check for overturning: Check for sliding Check for bearing capacity PROBLEMS REFERENCE
4 Module 7 (Lecture 24) RETAINING WALLS Topics 1.1 INTRODUCTION 1.2 GRAVITY AND CANTILEVER WALLS PROPORTIONING RETAINING WALLS 1.3 APPLICATION OF LATERAL EARTH PRESSURE THEORIES TO DESIGN 1.4 STABILITY CHECKS Check for Overturning Check for Sliding Along the Base INTRODUCTION In chapter 6 you were introduced to various types of lateral earth pressure. Those theories will be used in this chapter to design various types of retaining walls. In general, retaining walls can be divided into two major categories: (a) conventional retaining walls, and (b) mechanically stabilized earth walls. Conventional retaining walls can generally be classified as 1. Gravity retaining walls 2. Semigravity retaining walls 3. Cantilever retaining walls 4. Counterfort retaining walls
5 Gravity retaining walls (figure 7.1a) are constructed with plain concrete or stone masonry. They depend on their own weight and any soil resting on the masonry for stability. This type of construction is not economical for high walls. Figure 7.1 Types of retaining wall In many cases, a small amount of steel may be used for the construction of gravity walls, thereby minimizing the size of wall sections. Such walls are generally referred to as semigravity walls (figure 7.1b). Cantilever retaining walls (figure 7.1c) are made of reinforced concrete that consists of a thin stem and a base slab. This type of wall is economical to a height of about 25 ft (8 m). Counterfort retaining walls (figure 7.1d) are similar to cantilever walls. At regular intervals, however, they have thin vertical concrete slabs known as counterforts that tie the wall and the base slab together. The purpose of the counterforts is to reduce the shear and the bending moments. To design retaining walls properly, an engineer must know the basic soil parametersthat is, the unit weight, angle of friction, and cohesionfor the soil retained behind the wall and the soil below the base slab. Knowing the properties of the soil behind the wall enables the engineer to determine the lateral pressure distribution that has to be designed for. There are two phases in the design of conventional retaining walls. First, with the lateral earth pressure known, the structure as a whole is checked for stability. That includes checking for possible overturning, sliding, and bearing capacity failures.
6 Second, each component of the structure is checked for adequate strength, and the steel reinforcement of each component is determined. This chapter presents the procedures for determining retaining wall stability. Checks for adequate strength of each component of the structures can be found in any textbook on reinforced concrete. Mechanically stabilized retaining walls have their backfills stabilized by inclusion of reinforcing elements such as metal strips, bars, welded wire mats, geotextiles, and geogrids. These walls are relatively flexible and can sustain large horizontal and vertical displacement without much damage. In this chapter the gravity and cantilever retaining walls will be described first, followed by mechanically stabilized walls with metal strips, geotextiles, and geogrids reinforced backfills. GRAVITY AND CANTILEVER WALLS PROPORTIONING RETAINING WALLS When designing retaining walls, an engineer must assume some of the dimensions, called proportioning, which allows the engineer to check trial sections for stability. If the stability checks yield undesirable results, the sections can be changed and rechecked. Figure 7. 2 shows the general proportions of various retaining walls components that can be used for initial checks. Figure 7.2 Approximate dimensions for various components of retaining wall for initial stability checks: (a) gravity wall; (b) cantilever wall [note: minimum dimension of DD is 2 ft ( 0.6 m)]
7 Note that the top of the stem of any retaining wall should not be less than about 12 in. ( 0.3 m) for proper placement of concrete. The depth, D, to the bottom of the base slab should be a minimum of 2 ft ( 0.6 m). However, the bottom of the base slab should be positioned below the seasonal frost line. For counterfort retaining walls, the general proportion of the stem and the base slab is the same as for cantilever walls. However, the counterfort slabs may be about 12 in. ( 0.3 m) thick and spaced at centertocenter distances of 0.3HH to 0.7 HH. APPLICATION OF LATERAL EARTH PRESSURE THEORIES TO DESIGN The fundamental theories for calculating lateral earth pressure have been presented in chapter 6. To use these theories in design, an engineer must make several simple assumptions. In the case of cantilever walls, use of the Rankine earth pressure theory for stability checks involves drawing a vertical line AAAA through point A, as shown in figure 7. 3a, (which is located at the edge of the heel of the base slab. The Rankine active condition is assumed to exist along the vertical plane AAAA. Rankine active earth pressure equations may then be used to calculate the lateral pressure on the face AAAA. In the analysis of stability for the wall, the force PP aa(rankine ), the weight of soil above the heel, WW ss, and the weight of the concrete, WW cc, all should be taken into consideration. The assumption for the development of Rankine active pressure along the soil face AAAA is theoretically concrete if the shear zone bounded by the line AAAA is not obstructed by the stem of the wall. The angle, ηη, that the line AAAA makes with the vertical is ηη = 45 + αα φφ 2 2 sin 1 sin αα [7.1] sin φφ Figure 7.3 Assumption for the determination of lateral earth pressure: (a) cantilever wall; (b) and (c) gravity wall
8 Figure 7. 3 Continued A similar type of analysis may be used for gravity walls, as shown in figure 7. 3b. However, Coulomb s theory also may be used, as shown in figure 7. 3c. If Coulomb s active pressure theory is used, the only forces to be considered are PP aa(coulomb ) and the weight of the wall, WW cc. If Coulomb s earth pressure theory is used, it will be necessary to know the range of the wall friction angle δδ with various types of backfill material. Following are some ranges of wall friction angle for masonry or mass concrete walls: Backfill material Range of δδ(deg) Gravel Coarse sand Fine sand Stiff clay 1520
9 Silty clay In the case of ordinary retaining walls, water table problems and hence hydrostatic pressure are not encountered. Facilities for drainage from the soils retained are always provided. In several instances, for small retaining walls, emiempirical charts are used to evaluate lateral earth pressure. Figure 7.4 and 5 show two semiempirical charts given by Terzaghi and Peck (1967). Figure 7.4 is for backfills with plane surfaces, and figure 7.5 is for backfills that slope upward from the crest of the wall for a limited distance and then become horizontal. Note that 1 2 KK vvhh 2 is the vertical component of the active force on plane AAAA; similarly, 1 2 KK hhh 2 is the horizontal force. The numerals on the curves indicate the types of soil described in table 1. Figure 7.4 Continued
10 Figure 7.5 Chart for estimating pressure of backfill against retaining walls supporting backfills with surface that slopes upward from crest of wall for limited distance and then becomes horizontal (after Soil Mechanics in Engineering Practice, Second Edition, by K. Terzaghi and R. B. Peck. Copyright 1967 by John Wiley and Sons. Reprinted with permission) (note: 1 kn/m 3 = lb/ft 3 ) Chart for estimating pressure of backfill against retaining walls supporting backfills with surface that slopes upward from crest of wall for limited distance and then becomes horizontal (after Soil Mechanics in Engineering Practice, Second Edition, by K. Terzaghi and R. B. Peck. Copyright 1967 by John Wiley and Sons. Reprinted with permission) (note: 1 kn/m 3 = lb/ft 3 ) STABILITY CHECKS To check the stability of a retaining wall, the following steps are necessary: 1. Check for overturning about its toe 2. Check for sliding along its base 3. Check for bearing capacity failure of the base 4. Check for settlement 5. Check for overall stability This section describes the procedure for checking for overturning and sliding and bearing capacity failure. The principles of investigation for settlement were covered in chapter 4 and will not be repeated here. Some problems regarding the overall stability of retaining walls are discussed in section 5.
11 Check for Overturning Figure 7. 6 shows the forces acting on a cantilever and a gravity retaining wall, based on the assumption that the Rankine active pressure is acting along a vertical plane AAAA drawn through the heel. PP pp is the Rankine passive pressure; recall that its magnitude is PP pp = 1 2 KK ppγγ 2 DD 2 + 2cc 2 KK pp DD (Chapter 6 equation 58) Figure 7.6 Check for overturning: assume that Rankine pressure is valid: Table 1 types of Backfill for Retaining Walls
12 1. Coarsegrained soil without admixture of fine soil particles, very permeable (clean sand or gravel). 2. Coarsegrained soil of low permeability due to admixture of particles of silt size. 3. Residual soil with stones, fine silty sand, and granular materials with conspicuous clay content. 4. Very soft or soft clay, organic silts, or silty clay. 5. Medium or stiff clay, deposited in chunks and protected in such a way that a negligible amount of water enters the spaces between the chunks during floods or heavy rains. If this condition of protection cannot be satisfied, the clay should not be used as backfill material. With increasing stiffness of the clay, danger to the wall due to infiltration of water increases rapidly. From Soil Mechanics in Engineering Practice, Second Edition, by K. Terzaghi and R. B. Peck. Copyright 1967 by John Wiley and Sons. Reprinted with permission. Where γγ 2 = unit weight of soil in front of the heel and under the base slab KK pp = Rankine passive earth pressure coefficient = tan 2 (45 + φφ 2 /2) cc 2, φφ 2 = cohesion and soil friction angle, respectively The factor of safety against overturning about the toethat is, about point C in figure may be expressed as FFFF (overturning ) = Σ MM RR Σ MM OO [7.2] Where Σ MM OO = sum of the moments of forces tending to overturn about point CC Σ MM RR = sum of the moments of forces tending to resist overturning about point CC The overturning moment is Σ MM OO = PP h HH 3 [7.3] Where PP h = PP aa cos αα For calculation of the resisting moment, Σ MM RR (neglectingpp PP ), a table (such as table 2) can he prepared. The weight of the soil above the heel and the weight of the concrete (or masonry) are both forces that contribute to the resisting moment. Note that the force PP vv
13 also contributes to the resisting moment. PP vv is the vertical component of the active force PP aa, or PP vv = PP aa sin αα [7.4] The moment of the force PP vv about C is MM vv = PP vv BB = PP aa sin αα BB [7.5] Where BB = width of the base slab Table 2 Procedure for Calculation of Σ MM RR Section (1) Area (2) Weight/unit length of wall (3) Moment arm measured from C (4) Moment about C (5) 1 AA 1 WW 1 = γγ 1 AA 1 XX 1 MM 1 2 AA 2 WW 2 = γγ 2 AA 2 XX 2 MM 2 3 AA 3 WW 3 = γγ cc AA 3 XX 3 MM 3 4 AA 4 WW 4 = γγ cc AA 4 XX 4 MM 4 5 AA 5 WW 5 = γγ cc AA 5 XX 5 MM 5 6 AA 6 WW 6 = γγ cc AA 6 XX 6 MM 6 PP vv BB MM vv Σ VV Σ MM RR Note: γγ 1 = unit weight of backfill γγ 2 = unit weight of concrete Once Σ MM RR is known, the factor of safety can be calculated as FFFF (overturning ) = MM 1+MM 2 +MM 3 +MM 4 +MM 5 +MM 6 PP aa cos αα(hh /3) MM vv [7.6]
14 Check for Sliding Along the Base The factor of safety against sliding may be expressed by the equation FFFF (sliding ) = Σ FF RR Σ FF dd [7.7] Where Σ FF RR = sum of the horizontal resisting forces Σ FF dd = sum of the horizontal driving forces Figure 7. 7 indicates that the shear strength of the soil immediately below the base slab may be represented as ss = σσ tan δδ + cc aa Where δδ = angle of friction between the soil and the base slab cc aa = adhesion between the soil and the base slab Figure 7.7 Check for sliding along the base
15 Thus the maximum resisting force that can be derived from the soil per unit length of the wall along the bottom of the base slab is RR = ss(area of cross section) = ss(bb 1) = BBBB tan δδ + BBBB aa However, BBBB = sum of the vertical force = Σ VV (see table 2) So RR = (Σ VV) tan δδ + BBBB aa + PP pp [7.8] The only horizontal force that will tend to cause the wall to slide (driving force) is the horizontal component of the active force PP aa, so Σ FF dd = PP aa cos αα [7.9] Combings equations (7, 8, and 9) yields FFFF (sliding ) = (Σ VV) tan δδ+bbbb aa +PP pp PP aa cos αα [7.10] A minimum factor of safety of 1.5 against sliding is generally required. In many cases, the passive force PP pp is ignored for calculation of the factor of safety with respect to sliding. In general, we can write δδ = kk 1 φφ 2 and cc aa = kk 2 cc 2. In most cases, kk 1 and kk 2 are in the range of 1 2 to 2 3. Thus FFFF (sliding ) = (Σ VV) tan (kk 1φφ 2 )+BBBB 2 cc 2 +PP pp PP aa cos αα [7.11] In some instances, certain walls may not yield a desired factor of safety of 1.5. To increase their resistance to sliding, a base key may be used. Base keys are illustrated by broken lines in figure It indicates that the passive force at the toe without the key is PP pp = 1 2 γγ 2DD 2 KK pp + 2cc 2 DD KK pp However, it a key is included, the passive force per unit length of the wall becomes PP pp = 1 2 γγ 2DD 1 2 KK pp + 2cc 2 DD 1 KK pp Where KK pp = tan 2 (45 + φφ 2 /2)
16 Because DD 1 > DD, a key obviously will help increase the passive resistance at the toe and hence the factor of safety against sliding. Usually the base key is constructed below the stem and some main steel is run into the key. Another possible way to increase the value of FFFF (sliding ) is to consider reducing the value of PP aa [see equation (11)]. One possible way to do so is to use the method, developed by Elman and Terry (1988). The discussion here is limited to the case in which the retaining wall has to horizontal granular backfill (figure 7. 8). In figure 7. 8, the active force, PP aa, is horizontal (αα = 0) so that Figure 7.8 Retaining wall with sloped heel PP aa cos αα = PP h = PP aa And PP aa sin αα = PP vv = 0 However, PP aa = PP aa(1) + PP aa(2) [7.12] The magnitudes of PP aa(2) can be reduced if the heel of the retaining wall is sloped as shown in figure 7. 8b. For this case, PP aa = PP aa(1) + AAAA aa(2) [7.13] The magnitude of A, as shown in figure 7. 9, is valid for αα = 45. However, note that in figure 7. 8a
17 Figure 7.9 Variation of A with friction angle of backfill [equation (14)] PP aa(1) = 1 γγ 2 1KK aa (HH DD ) 2 And PP aa = 1 γγ 2 1KK aa HH 2 Hence PP aa(2) = 1 γγ 2 1KK aa [HH 2 (HH DD ) 2 ] So, for the active pressure diagram shown in figure 7. 8b, PP aa = 1 γγ 2 1KK aa (HH DD ) 2 + AA γγ 2 1KK aa [HH 2 (HH DD ) 2 ] [7.14] Sloping the heel of a retaining wall can thus be extremely helpful in some cases.
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