Chapter 3 Experimental Apparatus
3.4 Data Acquisition
A data acquisition system was used to collect and store the considerable amount of data generated during the tests. The data acquisition system was composed of the
following four parts: (1) dynamic strain amplifiers (Kyowa: DPM601A and DPM711B); (2) NI adaptor card (NIBNC-2090); (3) AD/DA card; and (4) personal computers shown in Fig. 3.8. 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 in the soil bin to simulate the constrained backfill shown in Fig. 1.1. In Fig. 4.1, the plate and its supporting system are developed 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 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 shows in Fig. 4.2 is 1.370 m-long, 0.998 m-wide, and 5 mm-thick.
The unit weight of the steel plate is 76.52 kN/m3 and its total mass is 83 kg (814 N). 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 and Fig. 4.3. For the wall height H = 0.5 m and the inclination angle β = 50o, the length of the interface plate should be at least 1.370 m. On the other hand, the inside width of the soil bin is 1.0 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 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 new supporting system for the interface plate was designed and constructed. A top-view of the base supporting frame is illustrated in Fig. 4.4. The supporting system composed of the following three parts: (1) top supporting beam; (2) base supporting block 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. 4.6. The section of supporting steel beam is 65 mm × 65 mm × 8 mm and its length is 1700 mm. Fig. 4.4 shows bolt slots were drilled on each side of the steel beam on the side wall of the soil bin. The locations of bolt slots were calculated for the interface plate at difference horizontal spacing b and inclined angle β. Fig. 4.7 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, 0.6 m-wide, and 0.113 m-thick.
Fig.4.8 shows seven trapezoidal grooves were carved to the face of the base
inserted into the groove at different distance from base of the model wall. In Fig.4.8, different horizontal spacing b adopted for testing includes: (1) b = 0; (2) b = 50 mm; (3) b = 100 mm; (4) b = 150 mm; (5) b = 250 mm; (6) b = 350 mm; and (7) b = 500 mm.
4.2.3 Base Boards
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 boards show in Fig.
4.9 is 1400 mm-long, 1000 mm-wide and 113 mm-thick. To provide adequate friction between the backfill and the base board, 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, emax= 0.76, emin= 0.50, D60= 0.40 mm, and D10= 0.22 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=1.82), 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 the 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 is shown in Fig.
5.2.
Chang (2000) established the relationship between the internal friction angle φ and unit weight γ of the 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 to replace 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 estimate 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 results are shown in Fig. 5.5.
For air-pluviated Ottawa sand, Lee (1998) suggested the following relationship:
δw = 2.33γ - 17.8 (5.2) where
δw = wall friction of angle (degree) γ = unit weight of backfill (kN/m3)
Eqn. (5.2) is applicable for γ = 15.5~17.5 kN/m3 only. The φ angle and δw angle obtained in section 5.1 and 5.2 are used for calculation of active earth pressure based 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. Lubrication layers fabricated with plastic sheets were 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).
Plastic sheets were vertically hung next to the side-wall 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 suggested by Fang et al. (2004) are illustrated in Fig. 5.7 and Fig. 5.8, respectively. The sidewall friction angle δsw is determined based on basic physics principles. In Fig. 5.8, the handle was turned to tilt the sliding plate, which the soil box on the plate starts to slide. Then measure the inclination δsw that the plate makes with the horizontal.
Fig. 5.9 shows the variation of interface friction angle δsw with normal stress σ based on the sliding block 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 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 rock face near the wall 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 densities, and the test results are shown in Fig. 5.11. For air-pluviated 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 soil unit weight γ and friction angle for different interface materials are summarized in Fig. 5.12. The internal friction angle of Ottawa sand φ, model wall-soil friction angle δw, interface-plate friction angle δi, and lubricated 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 involved for the model wall experiment 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, air-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 a 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 (2010) 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 approximately 36%.
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 to Fig. 5.21, interface plate was placed with the inclination angle
β = 90° and the horizontal spacing b = 150 mm, 250 mm, 350 mm, and 500 mm. In Fig. 5.22 to Fig. 5.24, interface plate was placed with the inclination angle β = 80°, 70°, 60°, and b = 150 mm. A layer of 100 mm-thick Ottawa sand was placed in the soil bin as a soil blanket. The bottom density cup was then put on the surface of soil blanket. Locations of the density cups buried in the fill are illustrated in Fig.5.18 to Fig.5.24. Ottawa sand was placed layer by layer into the soil bin up to 0.5 m thick.
After the soil has been placed in the soil bin to the top, soil cups were dug out of the backfill carefully. Soil density is determined by dividing the mass of soil in the cup by the inside volume of the cup. The distributions of relative density of loose sand measured at different elevations with the plate inclination angle β = 90° are shown in Fig. 5.25. Test result for b = 150 mm are also shown in Fig. 5.25. In the figure, the mean relative density is 35.6%, with a standard deviation of relative density was 1.39%. From a practical point of view, it may be concluded from these data that the soil density in the soil bin is quite uniform. The relative density of the Ottawa sand in the soil bin is independent of the interface plate inclination and location.
Chapter 6 Test Results
This chapter reports the experimental results of the lateral earth pressure on a retaining wall with a constrained cohesionless backfill. Test conditions for the interface plate located at the horizontal spacing b = 150 mm, 250 mm, 350 mm, 500 mm and 2000 mm are illustrated in Fig. 1.3 to Fig. 1.7, respectively. The height of backfill H is 0.5 m and the air-pluviation method was used to prepare the loose backfill. The loose Ottawa sand has a relative density Dr = 35.6 % and a unit weight γ = 15.6 kN/m. Based on direct shear tests by Ho, (1999) the corresponding internal friction angle φ for the loose backfill would be 31.3o. The γ and φ values are used to calculate earth pressures based on the Jaky and Coulomb theories. The testing program for this study is summarized in Table 6.1.
6.1 Horizontal Earth Pressure with Faraway Plate
The variation of horizontal earth pressure against the wall as function of active wall movement was investigated. After the loose backfill was placed into the soil bin as shown in Fig. 6.1 (a) and (b). The model wall slowly moved away from the soil mass in a translation mode at the constant speed of 0.015 mm/s. No compaction was applied to the loose backfill.
Distributions of horizontal earth pressure σh measured at different stages of wall displacements S/H (S: horizontal wall displacement, H: backfill height) for Test 0119-1 and Test 0427-2 are illustrated in Fig. 6.2 and Fig. 6.3. As the wall started to move, the earth pressure decrease, and eventually a limiting active pressure was reached. The pressure distributions are essentially linear at each stage of wall movement. Active earth pressures calculated with Rankine and Coulomb theories
are also indicated in the figure. The ultimate experiment active pressure distribution at S/H = 0.004 is in fairly good agreement with that estimated with Coulomb and Rankine theories.
The variation of horizontal earth-pressure coefficient Kh as a function of wall displacement is shown in Fig. 6.4. The coefficient Kh is defined as the ratio of the horizontal component of total soil thrust Ph toγH2 2. The horizontal soil thrust Ph
was calculated by summing the pressure diagram shown in Fig. 6.2 and Fig. 6.3. In Fig. 6.4 the coefficient Kh decreased with increasing wall movement S/H until a minimum value was reached then remained approximately a constant. The ultimate value of Kh is defined as the horizontal active earth-pressure coefficient Ka,h. In Fig.
6.4, the active condition was reached at approximately S/H = 0.004.
In Fig. 6.4, it may not be an easy task to define the point of active wall movement Sa. For a wall that moved away from a loose sandy backfill in a translational mode, Mackey and Kirk (1967) concluded the wall displacement required to reach an active state is Sa = 0.004 H. The Sa values recommended by Mackey and Kirk (1967), Bros. (1972), Fang and Ishibashi (1986) Fang et al. (1997) illustrated in Fig. 6.4. In this study the active wall movement is assumed to be Sa = 0.004 H.
Das (2004) stated that, in the actual design of retaining walls, the wall friction angle δ is generally assumed to be between φ/2 and 2φ/3. Potyondy (1961) investigated the skin friction between various soils and construction materials. It was concluded that, among several other factors, the interface friction was influenced by the roughness of the wall material. For this study, the model-wall surface was made of smooth steel, as a result the wall friction angle was assumed to be δ = φ/2 = 15.65°. The wall friction angle mentioned above was assumed for calculation of earth pressure for the Coulomb theory in the following sections. It may be observed in Fig. 6.4 that the Coulomb theory (δ = φ/2) provide a good estimate of the active soil thrust. The wall friction calculated with Equation 5.2 is δ = 18.5°. For comparison purposes, the K determined with δ = 18.5° is also illustrated in Fig.
6.4.
In Fig 6.2 and Fig. 6.3, the distribution of earth pressure with depth at different wall movements is nearly linear. As a result, the point of application of the total soil thrust should act at about H/3 above the wall base (h/H = 0.333). The vertical distance between the point of application of the total soil thrust and wall base is designed as h. Test results in Fig. 6.5 shows that the points of application of soil thrust are located at about 0.33 H ~ 0.36 H above the wall base.
6.2 Horizontal Earth Pressure for b = 150 mm
Fig. 6.6 (a) and (b) show the steel interface plate was placed in the soil bin for b = 150 mm and β = 90°. It is clear in the figures that only a thin layer of soil was sand which between the wall and the interface plate. The distributions of earth pressure at different stages of wall movement are illustrated in Fig. 6.7 and Fig. 6.8. The measured σh was significantly lower than Jaky’s solution at S/H = 0. At the wall movement S/H = 0.004, the active earth pressure is significantly less than that of Coulomb’s solution. In Fig. 6.6(a), the interface plate constrained the backfill so the active soil wedge cannot develop fully. It is reasonable to expect the measured σh to be less than Coulomb’s prediction.
Fig. 6.9 (a) and (b) show the steel interface plate was placed in the soil bin for b = 150 mm and β = 80°. The distributions of earth pressure at different stages of wall movement are illustrated in Fig. 6.10 and Fig. 6.11. The measured σh was slightly lower than Jaky’s solution at S/H = 0. At S/H = 0.004, the measured σh was lower than Coulomb’s solution. It may be observed in Fig. 6.9, with the β angle decreasing from β = 90° to β = 80°, the horizontal distance between the model wall and interface plate was increased. The amount of soil mass between the wall and the inclined plate increased.
Fig. 6.12 (a) and (b) show the inclined plate was standing in the soil bin with b =
150 mm and β = 70°. The distributions of earth pressure at different stages of wall movement are shown in Fig. 6.13 and Fig. 6.14. The stress measured at S/H = 0 was lower than Jaky’s solution near the bottom of the wall. However, the active earth pressure in Fig. 6.13 and Fig. 6.14 was close to Coulomb’s solution. It was clear in Fig. 6.12 (a) with β angle decreased from 80° to 70°, the interface plate did not intrude the active soil wedge. It is possible for the active soil wedge to develop fully in the backfill. As a result, the measured active earth pressure was close to Coulomb’s solution.
The steel interface plate with b = 150 mm and β = 60° is shown in Fig. 6.15 (a) and (b). The distributions of earth pressure at different stages of wall movement are shown in Fig. 6.16 and Fig. 6.17. The measured σh at S/H = 0 was close to Jaky’s solution, and the active pressure distribution was close to Coulomb’s solution. Fig.
6.15 (a) shows the interface plate was relatively far from the wall face, thus the measured lateral stress was not be strongly affected by the existence of the steel interface plate.
Fig. 6.18 to Fig. 6.21 presents the variation of horizontal earth pressure coefficient Kh as a function of wall movement for β = 90°, 80°, 70° and 60°. As the wall started to move, the lateral soil thrust decreased with increasing wall movement
Fig. 6.18 to Fig. 6.21 presents the variation of horizontal earth pressure coefficient Kh as a function of wall movement for β = 90°, 80°, 70° and 60°. As the wall started to move, the lateral soil thrust decreased with increasing wall movement