Chapter 1 Introduction
1.3 Organization of Thesis
This thesis is divided into the following parts:
1. Review of theories regarding the active earth pressure and model retaining wall tests. (Chapter 2)
2. A detail description for the design of NCTU KA model retaining wall.
(Chapter 3)
3. Discussion of backfill characteristics and interface characteristics.
(Chapter 4)
4. Experimental results regarding the reduction of compaction induced earth pressure with active wall movement. (Chapter 5)
5. Conclusions. (Chapter 6)
5
Chapter 2
Literature Review
The Coulomb and Rankine earth pressure theories are often applied methods to calculate the lateral force of earth pressure acting on a retaining wall.
Experimental studies of active earth pressure have been reported by Terzaghi (1934), Mackey and Kirk (1967), Bros (1972), Sherif et al. (1982), Fang and Ishibashi (1986), and Fang et al.(1997). The major findings of these researches are summarized in this chapter.
2.1 Active Earth Pressure Theories
2.1.1 The Coulomb Theory
Coulomb (1776) proposed a method of analysis that determines the resultant horizontal force on a retaining system for any slope of wall, wall friction, and slope of backfill. The Coulomb theory is based on the assumption that soil shear resistance develops along the wall and failure plane. Detailed assumptions are made as the followings:
1. The backfill is isotropic and homogeneous.
2. The rupture surface is plane, as plane BC in Fig. 2.1(a). The backfill surface is a plane surface as well.
3. The frictional resistance is distributed uniformly along the rupture surface.
4. Failure wedge is a rigid body.
6
5. There is a friction force between soil and wall when the failure wedge moves toward the wall.
6. Failure is a plane strain condition.
To create an active state, the wall is designed moved away from the soil mass.
If the wedge ABC in Fig. 2.1(a) moves down relatively to the wall, and the wall friction angle δ will develop at the interface between the soil and wall. Let the weight of wedge ABC be W and the force on BC be F. With the given value θ , and the summation of verticle forces and horizontal forces, the resultant soil thrust P can be calculated as shown in Fig. 2.1(b).
To test different wedge scenarios, the corresponding values of P can be acquired. The upper part of Fig. 2.2 illustrates the curve of P according to different wedge scenarios. And the maximum P is the Coulomb's active force Pa as Eq. (2.1).
a
Pa = total active force per unit length of wall Ka = coefficient of active earth pressure
γ = unit weight of soil
7
where
φ = internal friction angle of soil δ = wall friction angle
β = slope of back of the wall to horizontal i = slope of ground surface behind wall
2.1.2 The Rankine Theory
Rankine (1875) considered the soil in a state of plastic equilibrium and used essentially the same assumptions as Coulomb. The Rankine theory assumes that there is no wall friction and failure surfaces are straight planes, and that the resultant force acts parallel to the backfill slope. Detailed assumptions are made as the followings:
1. The backfill is isotropic and homogeneous.
2. Retaining wall is a rigid body. The wall surface is vertical to the ground and the friction force between the wall and the soil is neglected.
3. Elastic equilbrium is not applicable to the stress condition in the failure wedge.
Rankine assumed there is no friction between wall surface and backfill, and the backfill is cohesionless. The earth pressure on plane AB of Fig. 2.3(a) is the same as that on plane AB inside a semi-infinite soil mass in Fig. 2.3(b). For active condition, the active earth pressure σa at a given depth z can be expressed as:
a
a γzK
σ = (2.3)
The total active force Pa per unit length of the wall is equal to
8
The direction of resultant force Pa is parallel to the ground surface as Fig.
2.3(b), where
2.1.3 The Terzaghi Theory
The assumption of plane failure surface made by Coulomb and Rankine, however, does not apply in practice. Terzaghi (1941) suggested that the failure surface in the backfill under an active condition was a log spiral curve, like the curve bd in Fig. 2.4, but the failure surface dc is still assumed plane.
The illustration in Fig. 2.5 shows how Terzaghi and Peck (1967) calculated the active resistance with trial wedge method. The line d1c1 makes an angle of
2
45o +φ with the surface of the backfill. The arc bd1 of trial wedge abd1c1 is a logarithmic spiral formulated as the following equation
φ Fig. 2.6, the following forces per unit width of the wall are considered.
1. Soil weight per unit width in abd1f1: W1 = γ × (area of abd1f1)
9
2. The resultant force Pd1 in the zone of Rankine’s active state, acting horizontally on the vertical face d1f1 at a distance of Hd1/3 upward from d1:
Pd1 acts horizontally at a distance of Hd1/3 measured vertically upward form d1.
3. The resultant force of the shear and normal forces dF, acting along the surface of sliding bd1. At any point of the curve, according to the property of the logarithmic spiral, a radial line makes an angle φ with the normal.
Since the resultant dF makes an angle φ with the normal to the spiral at its point of application, its line of application will coincide with a radial line and will pass through the point O1.
4. The active force per unit width of the wall P1. P1 acts at a distance of H/3 measured vertically form the bottom of the wall. The direction of the force P1 is inclined at an angle δ with the normal drawn to the back face of the
10 and P1, respectively.
The trial active forces per unit width in various trial wedges are shown in Fig.
2.7. Let P1, P2, P3, …, and Pn be the forces that respectively correspond to the trial wedges 1, 2, 3, …, and n. The forces are plotted to the same scale as shown in the upper part of the figure. A smooth curve is plotted through the points 1, 2, 3, …, n.
The maximum P1 of the smooth curve defines the active force Pa per unit width of the wall.
2.1.4 Comparison of Active Earth Pressure Coefficient K
aIn many theories, the soil mass can be described in a state of limiting equilibrium, and shear strength of soil is expressed with Mohr-Coulomb failure criterion. However, the assumptions differ in the shape of the failure surface.
Coulomb (1776) assumed that sliding would occur along a planar sliding surface.
Brinch Hansen (1953) assumed the soil wedge slip along a circular surface. Janbu (1957) restricted to a particular shape of slip surface, used the method of slices and satisfied equilibrium in approximate manner. Terzaghi (1941) proposed the logarithmic spiral slip surface.
The coefficient of active earth pressure Ka in different theories were compared by Morgenstern and Eisenstein (1970). The variation of Ka is the function of internal friction angle of backfill in Fig. 2.8, where the wall friction angle δ is
11
equal to φ and φ 2. For the case δ = φ 2, the total range of variation of Ka is generally less than 15% in Rankine’s solution. In this study, Ka values calculated with the Coulomb theory and Rankine theory are compared with experiment results.
2.2 Laboratory Model Retaining Wall Tests for Active State
2.2.1 Model by Terzaghi
Terzaghi (1934) studied the lateral pressure of compacted sand against a large scale model wall at MIT. The face of the wall is 14 ft. in width and 7 ft. in height.
The dimension of the soil bin is 14 ft. × 14 ft. × 7 ft. as illustrated in Fig. 2.9.
Twenty Goldbeck pressure cells were used to measure the variation of earth pressure, ten built into the wall and ten rested into the floor of the bin. For the wall under translation and rotation about base modes (RB), the earth pressure coefficient K (defined as σh γz) was measured at an elevation equal to one-half of the height of backfill as shown in Fig. 2.10. With a small displacement of the wall, the earth pressure reduced to the fully active state. For a compacted backfill 4.5 ft.
in height, an outward displacement of about 1.5 mm (1/1000 of the depth of the backfill) had lead the pressure to an active state. The difference of the K curve for the wall which yields by tilting (Test 1) is not obvious from that of the wall which yields parallel to its original position (Test 2).
Fig. 2.11 shows the relation between the height of the center of pressure (defined as hc/h) and the yield of the wall. According to Coulomb’s theory, the
12
resultant force for level backfill should be located at one-third of the backfill depth above the base (hc/h= 0.33). For rotation about base modes (Tilting wall, RB) mode, the height of center of pressure is decreased when the wall starts to move.
However, after the wall movement equals to 0.00036h, the height of center of pressure gradually rises with the increasing wall movement.
2.2.2 Model by Mackey and Kirk
Mackey and Kirk (1967) experimented on lateral earth pressure by using a steel model wall. This soil tank was made of steel with internal dimension of 36 in.
× 16 in. × 15 in. as shown in Fig. 2.12. In their observation, when the wall moved away from the soil, the earth pressure decreased (see Fig. 2.13) and then increased slightly to reach a constant value. Mackey and Kirk concluded that if the backfill is loose, the obtained active earth pressure would be within 14 percent off those theoretical values by the methods listed in Table 2.1.
Mackey and Kirk utilized a powerful beam of light to observe the failure surface in the backfill. It could trace the position of the shadow, formed by changes of the sand surface in different level. It was found that the failure surface due to the translational wall movement was a curve in the backfill (Fig. 2.14), rather than a plane assumed by Coulomb.
2.2.3 Model by Bros
Bros (1972) experimented on various movements of model retaining wall to find the influence by the values and distribution of active and passive earth
13
pressures. The model arrangement is illustrated in Fig. 2.15. The main structure consists of three vertical steel-frames supporting the soil bin, which is 0.7 m in width, 0.85 m in height, and 1.6 m in length. The pressure cells are diaphragm type.
The earth pressures were measured with the deforming diaphragm with electric-resistivity strain gauges. In the study, clean, dry, quartz sand from Odra-river was used. The dense state was obtained by vibrating sand of each 12-15 cm layer with electric vibrator.
The outward translation of the wall caused the mobilization of friction between the backfill and side-wall, which tends to decrease the measured lateral pressures. The coefficient of horizontal earth pressure K as a function of wall displacement S is shown in Fig.2.16. It was concluded that the active condition was reached at the wall displacement of 0.0006h (h = height of backfill) under a translational mode. Fig. 2.17 shows that the active conditions are reached at the wall displacement of 0.0035h and 0.0012h~0.0018h, under RB and RT mode respectively.
2.2.4 Model by Sherif, Ishibashi, and Lee
Sherif et al. (1982) compared their experiment results of active static and dynamic earth pressure with Coulomb and Mononobe-Okabe equations. Their experiments were conducted at the University of Washington. The model system consists of four components: (1) shaking table and soil box; (2) loading and control units; (3) retaining wall; and (4) data acquisition system.
The shaking table was 3 m in length and 2.4 m in width, as shown in Fig.
14
2.18(a). It was made of steel. The rigid soil box of 2.4 m in length, 1.8 m in width, and 1.2 m in height was built on the shaking table. The movable model retaining wall and its driving system are shown in Fig. 2.19. The model wall consists of the main frame and the center wall. The center wall was 1 m in width, 1 m in height, and 0.127 m in thickness. Six soil pressure transducers were mounted on the center line of the wall surface at different depths to measure the soil pressure distribution against the main body of the center wall (Fig. 2.18b).
Fig. 2.20 illustrates different values of Ksh, h/H and tanδ relative to wall displacements, where δ is wall friction angle, (h/H) represents the point of application of the soil thrust, and Ksh is the static horizontal coefficient of earth pressure. The density of the loose Ottawa sand is ρ =1.54 g/cm3, and the corresponding angle φ is 31.5°. The speed of wall movement stayed constant as 1.5 x10-3 in/sec. The pattern of wall movement was translational. In Fig. 2.20, the Kh value of loose soil gradually decreases until the displacement of the wall movement is significant. The value of Kh remains stable regardless of the soil density after the displacement reaches H/1000. Sherif et al. concluded that the experiment Ka,h showed obvious correlation with the Coulomb theory, shown as Fig. 2.21.
2.2.5 Model by Fang and Ishibashi
Fang and Ishibashi (1986) conducted their experiments with respect to the distribution of the active stresses applying three different wall movement modes:
(1) rotation about top, (2) rotation about heel, and (3) translation. Their
15
experiments were also conducted at the University of Washington.
In Fig. 2.22, there is a sharp fall in the pressure behind the lower pressure transducer SPT3, SPT4, SPT5 and SPT6 with wall rotation. And then it stays constant. On the other hand, there is an initial increase in the upper transducer SPT1 and SPT2 with increasing wall rotation. The possible reason may be the arching formed in the upper portion of the backfill soil. Figure 2.23 shows the typical change of lateral stress distribution in different stages of wall rotation. It shows that the arching phenomenon dominates the backfill performance behind the upper portion of the wall when wall rotated about the top.
Figure 2.24 shows the typical horizontal pressure distribution behind a wall rotated about the base. It shows that the lateral pressure of the upper elevation decreases very quickly. However, there is only a very gentle decline in the lateral pressure near the base of the wall with wall rotation. The fully active state is difficult to be reached near the base. In brief, the value of horizontal earth pressure coefficient Kh drops dramatically at the beginning and then keeps constant.
Accordingly the total thrust in Fig. 2.25 is not be able to return to the position of H/3 above the bottom of the wall, which means the existence of the remaining part of the extra stress near the base of the wall.
Figure 2.26 shows the lateral earth pressure measured at various depths. The lateral pressure falls rapidly due to the translational wall displacement. Most of the measurements reach the minimum value at approximately 10 10× −3 in. (0.25 mm) wall displacement and then stay stable thereafter.
16
Figure 2.27 shows the horizontal earth pressure distributions at different translational wall movements. The measured active stress is slightly higher than Coulomb's solution at the upper one-third of wall height, approximately in agreement with Coulomb's prediction in the middle one-third, and lower than Coulomb' at the lower one-third of wall surface. However, the magnitude of the active total thrust Pa at S = 20 10× −3 in. (0.5 mm) is almost the same as the value calculated apply to the Coulomb theory.
Figure 2.28 shows the Ka is the function of soil density and internal friction angle. The value of Ka decreases while the angle of φ increases. There might be a underestimation of the coefficient Ka in Coulomb’s solution for rotational wall movement.
2.2.6 Model Study by Fang et al.
Fang et al. (1997) presented experimental data of earth pressure acting against a vertical rigid wall, which moved away from or toward a mass of dry sand with an inclined surface. The instrumented NCTU retaining-wall facility was used to investigate the variation of earth pressure induced by the translational wall movement.
Based on their experimental data, it has been found that the earth-pressure distribution is essentially linear at each stage of wall movement. As shown in Fig.
2.29, the wall movement required for the loose backfill to reach an active stage increase with an increasing backfill inclination. Fig. 2.30 shows the experimental active earth-pressure coefficients for various backfill sloping angles are in good
17
agreement with the values calculated by Coulomb’s theory. It may be observed in the figure that it is not appropriate to adopt the Rankine theory to determine active earth pressure against a rigid wall with sloping backfill.
2.3 Effects of Soil Compaction in Earth Pressure
Compaction a soil can produce a stiff, settlement-free and less permeable mass. It is usually accomplished by mechanical means that cause the density of soil to increase. At the same time the air voids are reduced and the coordination number of the grains is increased. It has been realized that the compaction of the backfill material has an important effect on the earth pressure on the wall.
Several theories and analytical methods have been proposed to analyze the residual lateral earth pressures induced by soil compaction. Most of these theories introduce the idea that compaction represents a form of overconsolidation, where stresses resulting from a temporary or transient loading condition are retained following removal of this load.
2.3.1 Study of Peck and Mesri
Based on the elastic analysis, Peck and Mesri (1987) presented a calculation method to evaluate the compaction-induced earth pressure. The lateral pressure profile can be determined by four conditions on σh, as illustrated in Fig. 2.31 and summarized in the following.
1. Lateral pressure resulting from the overburden of the compacted backfill,
18
h φ γz
σ =(1−sin ) (2.10)
2. Lateral pressure limited by passive failure condition,
h φ γz
σ =tan2(45+ /2) (2.11)
3. Lateral pressure resulting from backfill overburden plus the residual horizontal stresses,
where ∆σh is the lateral earth pressure increase resulted from the surface compaction loading of the last backfill lift and can be determined based on the elastic solution.
4. Lateral pressure profile defined by a line which envelops the residual lateral pressures resulting from the compaction of individual backfill lifts.
This line can be computed by Eq. 2.13
φ γ
Fig. 2.31 indicates that near the surface of backfill, from point a to b, the lateral pressure on the wall is subject to the passive failure condition. From b to c, the overburden and compaction-induced lateral pressure profile is determined by Eq. 2.12. From c the lateral pressure increases with depth according to Eq. 2.13 until point d is reached. Below d, the overburden pressure exceeds the peak stress in effective in compaction. In the lower part of the backfill, the lateral pressure is directly related to the effective overburden pressure.
19
2.3.2 Study of Chen
Chen (2003) reported some experiments in non-yielding retaining wall at National Chiao Tung University (Fig. 2.32) to investigate influence of earth pressure due to vibratory compaction. Air-dry Ottawa sand was used as backfill material. Vertical and horizontal stresses in the soil mass were measured in loose and compacted sand. Based on his test results, Chen (2003) proposed four points of view: (1) the compaction process does not result in any residual stress in the vertical direction. The effects of vibratory compaction on the vertical overburden pressure are insignificant, as indicated in Fig. 2.33 and Fig. 2.34; (2) after compaction, the lateral stress measured near the top of backfill is almost identical to the passive earth pressure estimated with Rankine theory (Fig. 2.35). The compaction-influenced zone rises with rising compaction surface. Below the compaction-influenced zone, the horizontal stresses converge to the earth pressure at-rest, as indicated in Fig. 2.35(e); (3) when total (static + dynamic) loading due to the vibratory compacting equipment exceeds the bearing capacity of foundation soils, the mechanism of vibratory compaction on soil can be described with the bearing capacity failure of foundation soils (Fig. 2.36); (4) the vibratory compaction on top of the backfill transmits elastic waves through soil elements continuously. For soils below the compaction-influenced zone, soil particles are vibrated. The passive state of stress among particles is disturbed. The horizontal stresses among soil particles readjust under the application of a uniform
20
overburden pressure and constrained lateral deformation, and eventually converge to the at-rest state of stress.
21
Chapter 3
Design of NCTU K A Model Retaining Wall Facility
The design of NCTU KA model retaining wall facility are discussed in this chapter. The model wall in this study is assumed a rigid body, such as a gravity retaining wall. At the beginning of design, two important testing parameters have been considered: (1) the wall height, and (2) the maximum wall displacement.
The KA model wall facility is designed to investigate active earth pressure. At
The KA model wall facility is designed to investigate active earth pressure. At