Numerical Study by Fan and Fang

Fan and Fang (2009) used the non-linear finite element program PLAXIS

(PLAXIS BV, 2002)

to investigate the earth pressure from the at-rest to the active condition for a rigid wall close to an inclined rock face (Fig. 2.27). The wall used for analysis is 5 m high, the back of the wall is vertical, and the surface of the backfill is horizontal. Typical geometry of the backfill zone used in the study is shown in Fig. 2.27. To investigate the influence of the adjacent rock face on the behavior of earth pressure, the inclination angle β of the rock face and the spacing b between the wall and the foot of the rock face were the parameters for numerical analysis. The wall was prevented from any movement during the placing of the fill.

After the filling process, active wall movement was allowed until the earth pressure behind the wall reached the active condition. The finite element mesh, which has been examined to eliminate the influence of size effect and boundary on the results of the analyses, for a retaining wall with limited backfill space (β = 70° and b = 0.5m) is shown in Fig. 2.28. The finite element mesh consists of 1,512 elements, 3,580 nodes, and 4,536 stress points.

Base on the numerical analysis,

distributions of horizontal earth pressures with the depth (z/H) at various wall displacements for b = 0.5 m and

β = 80°

are shown in Fig.

2.29

. In the figure, the distribution of active earth pressure with depth is non-linear.

Due to the nearby rock face, the calculated active pressure is considerably less than that computed using the Coulomb’s theory.

Fig. 2.30 shows the variation of the active earth pressure coefficient (K K ) computed with finite element analysis, as a function of the

inclination of the rock face and rock face-wall spacing b, for walls under T mode.

For β ＞ 60°, the analytical active K values are less than those calculated with Coulomb’s solution. The analytical K value decreased with increasing β angle, for β angles greater than 60°. Fig. 2.31 shows the variation of the

K

a(Computed)

/K

_a(Coulomb) with the β angle for T(traslation), RT(rotation about top) and RB(rotation about base) wall movement modes.

Fig. 2.32 shows the variation of the location of resultant of active earth pressures with the β angles at various fill widths (b) for walls in T mode.The h/H value increased with increasing β angles, and it increased with decreasing fill widths (b). For walls moving in T mode, the h/H value reached up to 0.41, 0.38, and 0.34 for β angles of 90°, 80°, and 70°, respectively, at a fill width (b) of 0.5 m.

In addition, the h/H value reached up to 0.46 for β angles 90° at a fill width b = 0 m.

Fig. 2.33 shows the variation of the point of application of the active soil thrust with the β angle for b = 0.5 m. The variation of the h/H value with the β for walls in RB and T modes are similar. For β ＜ 60°, h/H = 0.333 was calculated for both T and RB modes. For β ＞ 60°, for walls in RB and T modes, the h/H increased with increasing β angles. For walls in RT mode, due to the arching stress near the top of the wall, the h/H value is considerably higher than those in RB and T modes.

Chapter 3

Experimental Apparatus

In order to study the earth pressure behind retaining structures, the National Chiao Tung University (NCTU) has built a model retaining wall system which can simulate different kinds of wall movement. All of the investigations described in the thesis were conducted in this model wall, which will be carefully discussed in this chapter. The entire facility consists of four components, namely, model retaining wall, soil bin, driving system, and data acquisition system. The arrangement of the NCTU model retaining wall system is shown in Fig. 3.1.

3.1 Model Retaining Wall

The movable model retaining wall and its driving systems are illustrated in Fig. 3.1. The model wall is a 1000-mm-wide, 550-mm-high, and 120-mm-thick solid plate, and is made of steel. Note that in Fig. 3.1 the effective wall height H is only 500 mm. The retaining wall is vertically supported by two unidirectional rollers , and is laterally supported by four driving rods. Two sets of wall-driving mechanisms, one for the upper rods and the other for the lower rods, provide various kinds of movements for the wall. A picture of the NCTU model wall facility is shown in Fig.

3.2.

Each wall driving system is powered by variable-speed motor. The motors turn the worm driving rods which cause the driving rods to move the wall back and forth. Two displacement transducers (Kyowa DT-20D) are installed at the back of retaining wall and their sensors are attached to the movable wall. Such an arrangement of displacement transducers would be effective in describing the wall

translation.

To investigate the distribution of earth pressure, nine earth pressure transducers were attached to the model wall. The arrangement of the earth pressure cells should be able to closely monitor the variation of the earth pressure of the wall with depth. Base on this reason, the earth pressure transducers SPT1 through SPT9 have been arranged at two vertical columns as shown in Fig. 3.3.

A total of nine earth pressure transducers have been arranged within a narrow central zone to avoid the friction that might exist near the side walls of the soil bin as shown in Fig. 3.4. The Kyowa model PGM-02KG (19.62 kN/m² capacity) transducer shown in Fig. 3.5 was used for these experiments. To reduce the soil-arching effect, earth pressure transducers with a stiff sensing face are installed flush with the face of the wall. They provide closely spaced data points for determining variation of the earth pressure distribution with depth.

3.2 Soil Bin

The soil bin is fabricated of steel members with inside dimensions of 2,000 mm × 1,000 mm × 1,000 mm (see Fig. 3.1). Both sidewalls of the soil bin are made of 30-mm-thick transparent acrylic plates through which the behavior of backfill can be observed. Outside the acrylic plates, steel beams and columns are used to confine the side walls to ensure a plane strain condition.

The end wall that sits opposite to the model retaining wall is made of 100 mm thick steel plates. All corners, edges and screw-holes in the soil bin have been carefully sealed to prevent soil leakage. The bottom of the soil bin is covered with a layer of SAFETY-WALK to provide adequate friction between the soil and the base of the soil bin.

In order to constitute a plane strain condition, the soil bin is built very rigid so that the lateral deformations of the side walls will be negligible. The friction between the

stress induced on the side walls will be negligible. To eliminate the friction between backfill and sidewall, a lubrication layer with 3 layers of plastic sheets was furnished for all model wall experiments. The “thick” plastic sheet was 0.152 mm thick, and it is commonly used for construction, landscaping, and concrete curing. The “thin”

plastic sheet was 0.009 mm thick, and it is widely used for protection during painting, and therefore it is sometimes called painter’s plastic. Both plastic sheets are readily available and neither is very expensive. The lubrication layer consists of one thick and two thin plastic sheets were hung vertically on each sidewall of the soil bin before the backfill was deposited. The thick sheet was placed next to the soil particles. It is expected that the thick sheet would help to smooth out the rough interface as a result of plastic-sheet penetration under normal stress. Two thin sheets were placed next to the steel sidewall to provide possible sliding planes. For more information regarding the reduction of boundary friction with the plastic-sheet method, the reader is referred to Fang et al. (2004).

3.3 Driving System

As illustrated in Fig. 3.1, the variable speed motors M1 and M2 (Electro, M4621AB) are employed to compel the upper and lower driving rods, respectively.

The shaft rotation compels the worm gear linear actuators, while the actuator would push the model wall. Since only the variation of earth pressure caused by the translational wall movement is investigated, the motor speeds at M1 and M2 were kept the same for all experiments in this study.

3.4 Data Acquisition System

Due to the considerable amount of data collected by the soil-pressure transducers, a data acquisition system was used shown in Fig. 3.6. It is composed of the

DPM711B); (2) NI adaptor card; (3) AD/DA card; and (4) personal computers shown in Fig. 3.7. An analog-to-digital converter digitized the analog signals from the sensors. The digital data were then stored and processed by a personal computer.

For more details regarding the NCTU retaining-wall facility, the reader is referred to Wu (1992) and Fang et al. (1994).

Chapter 4

Interface Plate and Supporting System

A steel interface plate is designed and constructed to simulate inclined rock face near the retaining structure shown in Fig. 1.1. In Fig. 4.1, the plate and its supporting system are developed by Zheng (2008) to fit in the NCTU model retaining-wall facility. The interface plate consists of two parts: (1) steel plate; and (2) reinforcing steel beams. The supporting system consists of the following three parts: (1) top supporting beam; (2) base supporting block; and (3) base supporting boards. Details of the interface plate and its supporting system are introduced in the following sections.

4.1 Interface Plate

4.1.1 Steel Plate

The steel plate is 1.370 m-long, 0.998 m-wide, and 5 mm-thick as shown in Fig.

4.2. The unit weight of the steel plate is 76.52 kN/m³ and its total mass is 83 kg (0.814 kN). A layer of anti-slip material (SAFETY-WALK, 3M) is attached on the steel plate to simulate the friction that acts between the backfill and rock face as illustrated in Fig.

4.2 (c) and Fig. 4.3 (a). For the inclination angle β = 50^o shown in Fig. 1.2, the length of the interface plate should be at least 1.370 m. On the other hand, the inside width of the soil bin of the NCTU retaining wall facility is 1 m. In order to put the interface plate into the soil bin, the width of the steel plate has to less than 1.0 m. As a result, the steel plate was designed to be 1.370 m-long and 0.998 m-wide.

4.1.2 Reinforcement with Steel Beams

To simulate the stiffness of the rock face shown in Fig. 1.1, the steel interface plate should be nearly rigid. To increase the rigidity of the 5 mm-thick steel plate, Fig.

4.2 (b) and Fig. 4.3 (b) shows 5 longitudinal and 5 transverse steel L-beams were welded to the back of steel plate. Section of the steel L-beam (30 mm × 30 mm × 3 mm) was chosen as the reinforced material for the thin steel plate. On top of the interface plate, a 65 mm × 65 mm × 8 mm steel L-beam was welded to reinforce the connection between the plate and the hoist ring shown in Fig. 4.3 (b).

4.2 Supporting System

To keep the steel interface plate in the soil bin stable during testing, a supporting system for the interface plate was designed and constructed by Zheng (2008). A top-view of the base supporting frame is illustrated in Fig. 4.4. The supporting system composed of the following three parts: (1) base supporting block;

(2) top supporting beam;and (3) base boards. These parts are discussed in following sections.

4.2.1 Top Supporting Beam

In Fig. 4.5, the top supporting steel beam is placed at the back of the interface plate and fixed at the bolt slot on the side wall of the soil bin. Details of top supporting beam are illustrated in Fig. 4.7. The section of supporting steel beam is 65 mm × 65 mm × 8 mm and its length is 1700 mm. Fig. 4.4 shows four bolt slots were drilled on each side of the U-shape steel beam on the side wall of the soil bin. Fig. 4.6 shows the top supporting beam was fixed at the slots with bolts.

4.2.2 Base Supporting Block

The base supporting block used to support the steel interface plate is shown in Fig. 4.8. The base supporting block is 1.0 m-long, 0.14 m-wide, and 0.113 m-thick.

Fig. 4.8 (b) shows three trapezoidal grooves were carved to the face of the base supporting block. Fig. 1.2 shows the foot of the interface plate could be inserted into the groove at different distance from base of the model wall. For this study, different horizontal spacing d adopted for testing includes: (1) d = 0 mm; (2) d = 50 mm; and (3) d = 100 mm. Fig. 4.5 shows 6 pieces of base boards are stacked between the base supporting block and the end wall to keep the base block stable. The base board shown in Fig. 4.9 is 1860 mm-long, 1000 mm-wide and 113 mm-thick. The surface of the top base board was cover with a layer of anti-slip material SAFETY-WALK.

Chapter 5

Backfill and Interface Characteristics

This chapter introduces the properties of the backfill, and the interface characteristics between the backfill and the wall. Laboratory experiments have been conducted to investigate the following subjects: (1) backfill properties; (2) model wall friction; (3) side wall friction; (4) interface plate friction; and (5) distribution of soil density in the soil bin.

5.1 Backfill Properties

Air-dry Ottawa sand (ASTM C-778) was used throughout this investigation.

Physical properties of the soil include Gs

= 2.65, e

max= 0.76, emin= 0.50, D60= 0.315 mm, and D10= 0.213 mm. Grain-size distribution of the backfill is shown in Fig. 5.1.

Major factors considered in choosing Ottawa sand as the backfill material are summarized as follows.

1. Its round shape, which avoids effect of angularity of soil grains.

2. Its uniform distribution of grain size (coefficient of uniformity Cu=1.48), which avoids the effects due to soil gradation.

3. High rigidity of solid grains, which reduces possible disintegration of soil particles under loading.

4. Its high permeability, which allows fast drainage of pore water and therefore reduces water pressure behind the wall.

To establish the relationship between unit weight γ of backfill and its internal friction angle φ, direct shear tests have been conducted. The shear box used has a square (60 mm×60 mm) cross-section, and its arrangement are shown in Fig. 5.2.

Chang (2000) established the relationship between the internal friction angle

φ

and unit weight

γ

of the ASTM C-778 Ottawa sand as shown in Fig. 5.3. It is obvious from the figure that soil strength increases with increasing soil density. For the air-pluviated backfill, the empirical relationship between soil unit weight

γ

and φ angle can be formulated as follows

φ = 6.43γ - 68.99 (5.1)

where

φ =angle of internal friction of soil (degree) γ =unit weight of backfill (kN/m³)

Eqn. (5.1) is applicable for γ = 15.45 ~ 17.4 kN/m³ only.

5.2 Model Wall Friction

To evaluate the wall friction angle δw between the backfill and model wall, special direct shear tests have been conducted. A 88 mm × 88 mm × 25 mm smooth steel plate, made of the same material as the model wall, was used as the lower shear box. Ottawa sand was placed into the upper shear box and vertical load was applied on the soil specimen. The arrangement of this test is shown in Fig. 5.4.

To establish the wall friction angles δw developed between the steel plate and sand, soil specimens with different unit weight were tested. Air-pluviation methods was used to achieve different soil density, and the test result is shown in Fig. 5.5.

For air-pluviation Ottawa sand, Lee (1998) suggested the following relationship:

δw = 2.33γ - 17.8 (5.2)

Eqn. (5.2) is applicable for γ = 15.5~17.5 kN/m³ only. The φ angle and δ angle

on Coulomb, and Rankine’s theories.

5.3 Side Wall Friction

To constitute a plane strain condition for model wall experiments, the shear stress between the backfill and sidewall should be eliminated. A lubrication layer fabricated with plastic sheets was equipped for all experiments to reduce the interface friction between the sidewall and the backfill. The lubrication layer consists of one thick and two thin plastic sheets as suggested by Fang et al. (2004).

All plastic sheets had been vertically placed next to both side-walls as shown in Fig.

5.6.

The friction angle between the plastic sheets and the sidewall was determined by the sliding block tests. The schematic diagram and the photograph of the sliding block test by Fang et al. (2004) are illustrated in Fig. 5.7 and Fig. 5.8. The sidewall friction angle

δ

_sw is determined based on basic physics principles. Fig. 5.9 shows the variation of interface friction angle

δ

_sw with normal stress σ based on the plastic sheet lubrication tests. The friction angle measured was 7.5°. With the plastic – sheet lubrication method, the interface friction angle is almost independent of the applied normal stress. The angle of wall friction for smooth concrete is about φ/2 to 2φ/3, with the φ = 31.3° for loose sand, the wall friction angle should be δ = 15.7°~20.9°. The shear stress between the acrylic side-wall and backfill has been effectively reduced with the plastic-sheet lubrication layer.

5.4 Interface Plate Friction

To evaluate the interface friction between the interface plate and the backfill special, direct shear tests were conducted as shown in Fig. 5.10. In Fig. 5.10(b), a 80

mm × 80 mm × 15 mm steel plate was covered with a layer of anti-slip material

“SAFETY-WALK” to simulate the surface of the interface plate. The interface-plate was used to simulate the inclined rock face near the wall as shown in Fig. 1.1. Dry Ottawa sand was placed into the upper shear box and vertical stress was applied on the soil specimen as shown in Fig. 5.10(a).

To establish the relationship between the unit weight γ of the backfill and the interface-plate friction angleδi, soil specimens with different unit weight were tested. Air-pluviation methods was used to achieve different soil density, and the test result is shown in Fig. 5.11. For air-pluviation Ottawa sand, Wang (2005) suggested the following empirical relationship:

δ i = 2.7γ- 21.39 (5.3)

where

δi = interface-plate friction angle (degree) γ = unit weight of backfill (kN/m³) Eqn. (5.3) is applicable for γ = 15.1 ~16.36 kN/m³ only.

The relationships between backfill unit weight γ and different friction angles are illustrated in Fig. 5.12. The internal friction angle of Ottawa sand φ, model wall-soil friction angle δw, interface-plate friction angle δi, and sidewall friction angle δsw as a function of soil unit weight γ are compared in the figure. It is clear in Fig. 5.12 that, with the same unit weight, the order of the four different friction angles is φ＞δi ＞δw ＞δsw.

5.5 Control of Soil Density

5.5.1 Air-Pluviation of Backfill

To achieve a uniform soil density in the backfill, dry Ottawa sand was

deposited by air-pluviation method into the soil bin. The air-pluviation method had been widely used for a long period of time to reconstitute laboratory sand specimens.

Rad and Tumay (1987) reported that pluviation is the method that provides reasonably homogeneous specimens with desired relative density. Lo Presti et al.

(1992) reported that the pluviation method could be performed for greater specimens in less time. As indicated in Fig. 5.13, the soil hopper that lets the sand pass through a calibrated slot opening at the lower end was used for the spreading of sand. A picture showing air-pluviation of the Ottawa sand into soil bin is indicated in Fig.

5.14. Air-dry Ottawa sand was shoveled from the soil storage bin to the sand hopper, weighted on the electric scale, then pluviated into the soil bin. As indicated in Fig.

5.15, four types of slot openings (5 mm, 7 mm, 10 mm and 15 mm) were adopted by Ho (1999), and the drop height of soil varied from 0.25 m to 2.5 m.

Das (1994) suggested that the granular soil with a relative density of 15% ~ 50% is defined as loose. In this study, the drop height of 1.0 m and the slot opening of 15 mm were selected to achieve the loose backfill with a relative density of 35%.

5.5.2 Distribution of Soil Density

To investigate the distribution of soil density in the soil bin, soil density measurements were made. The soil density control cup made of acrylic is illustrated in Fig. 5.16 and Fig. 5.17. For the air-pluviated backfill, the density cups were used to measure the soil density at different elevations and locations.

In Fig. 5.18, a layer of 100 mm-thick Ottawa sand was placed in the soil bin as a soil blanket. Four density-control cups were then put into the soil bin on the surface of soil blanket. Locations of the cups are illustrated in Fig.5.18. Then Ottawa sand was placed layer by layer into the soil bin up to 0.5 m thick.

In Fig. 5.18, a layer of 100 mm-thick Ottawa sand was placed in the soil bin as a soil blanket. Four density-control cups were then put into the soil bin on the surface of soil blanket. Locations of the cups are illustrated in Fig.5.18. Then Ottawa sand was placed layer by layer into the soil bin up to 0.5 m thick.

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