Uniformity of Soil Density

To observe the distribution of soil density in the soil bin, the soil density cups were made. The soil density control cup made of acrylic is illustrated in Fig. 4.12.

and Fig. 4.13. During the preparation of soil specimen, density cups were buried in the soil mass at different elevations and different locations in the backfill as shown in

Fig. 4.14 and Fig. 4.15. After the soil had been filled up to 1.5 m from the

bottom of the soil bin, soil density cups were dug out from the soil mass carefully.

Fig. 4.16(a) shows the density cup was placed in the soil bin at desired locationand Fig. 4.16(b) shows the mass of the cup and soil in the cap was measured with an

electrical scale. The distribution of soil density with depth for sand is shown in Fig.

4.17. For the air-pluviated loose sand, the mean unit weight γ is 15.6 kN/m

², the mean relative density is Dr = 34.2 % with the standard deviation of 2.3%. For the compacted dense sand, the mean unit weight γ is 16.6 kN/m², the mean relative density is about 73.8 % with the standard deviation of 2.68 %. Das (1994) suggested that for the relative density 15 % ≤ Dr ≤ 50 % is defined as loose sand, while 70 % ≤ Dr ≤ 85 % is defined as dense sand.

Chapter 5

Test Results and Discussion

This chapter reported experimental results regarding the vertical and horizontal earth pressures in air-pluviated loose sand and vibratory compacted dense sand. The stress path during compaction was carefully investigated. Based on the experimental evidence, a rational mechanism of vibratory compaction on cohesionless soil is proposed. For all experiments, the surface of backfill was finally horizontal and the backfill was filled up to 1.5 m above the base of the model wall.

5.1 Stresses in loose sand

For comparison purposes, at the beginning of this study, experiments were conducted to investigate the stresses in an uncompacted loose backfill.

The method of air-pluviation was adopted to prepare the backfill and the relative density Dr achieved for the loose sand was 34.2 %. Fig. 5.1 illustrated stress σv showed the location of soil pressure transducers to measure the distribution of vertical and horizontal earth pressure σh with depth. SPT102, SPT105, SPT108, SPT111, and SPT114 were buried in the soil mass to measure σv. The vertical earth pressure

σ

v measured in the soil mass was illustrated in Fig. 5.2 (a). In this figure, the vertical pressure σv

increased linearly with increasing depth z and the test data were in fairly good agreement with the traditional equation

σ

v =

γ

z. In this study, unit weight γ was 15.6 kN/m³ for the loose sand. The distribution of horizontal earth pressure

σ

h with depth was illustrated in Fig. 5.2(b). In the figure, the earth pressure profile induced by the 1.5 m-thick loose backfill was

approximately linear and was in good agreement with the Jaky’s equation.

Mayne and Kulhawy (1982), Mesri and Hayat (1993) reported that Jaky’s equation was suitable for backfill in its loosest state. From a practical point of view, it was concluded that for a loose backfill, the vertical and horizontal earth pressure in the soil mass can be properly estimated with the equation

σ

v =

γ

z and Jaky’s equation, respectively.

5.2 Dynamic Behavior of the Soil compactor

The vibratory compactor was made by attaching an electric motor (Mikasa Sangyo, KJ75-2P) to a steel plate as shown in Fig. 5.4. For investigating the variation of earth pressure in the compacted sand, it was necessary to measure the forces applied to the sand by vibratory compactor. Fig. 3.8 showed the definition of x-y-z axes for this study. The photograph of the accelerometer is shown in Fig. 5.3.

In the Fig. 5.4, the accelerometer was attached to the compactor to measure its acceleration in x-direction ax. The measured acceleration in x-direction with time is illustrated in Fig. 5.5(a). In the figure, the maximum acceleration ax was about ± 23.1 m/s². The mass of the compactor was 12.1 kg. Since F = ma, the maximum force in the x-direction shown if Fig. 5.5(b) Fx was ± 280 N.

In the Fig. 5.6, the accelerometer was attached to the compactor to measure its acceleration in the y-direction. Fig. 5.7(a) showed the maximum acceleration in y-direction ay was about ± 100.3 m/s². Fig. 5.7(b) showed the maximum force in y-direction Fy was ± 1320 N.

In the Fig. 5.8, the accelerometer was attached to the compactor to measure the acceleration in z-direction. Fig. 5.9 showed the maximum acceleration in z-direction az was about ± 140.37 m/s². Fig. 5.9(b) showed the maximum dynamic force was ± 1690 N. In Fig. 5.5, 5.7 and 5.9, the acceleration az (± 140.37 m/s) and ay (± 100.3 m/s) was much stronger than ax (± 23.1 m/s). It may be observed in Fig.

was generated mainly in y and z (vertical)direction.

Fz is the vertical force the vibratory compactor applied on the soil surface. The Fz included the static dead load of the compactor W and the dynamic vertical force Fz,dynamic.

Fz = W ± Fz,dynamic (5.1)

Where W = mg = 12.1 kg × 9.81 m/s² = 119 N. It should be mentioned that only positive force (compression) can be applied at the soil-compactor interface as shown in Fig 5.9(b). As a result, in Fig. 5.10, the total force (static + dynamic) Fz

was about 1819 N. Assuming the distribution of contact pressure between the base plate (0.225 m × 0.225 m) and soil is uniform, the peak cyclic vertical stress σz

applied on the surface of soil would be about 35750 N/m².

5.3 Vertical and Horizontal Stresses in Sand during Compaction

To obtain the expected dense condition, the loose backfill was placed and compacted in five lifts as shown in Fig. 5.1. Each lift in Fig. 4.11 was divided into six lanes, and each 1.5 m long lane was compacted with the vibratory compactor for 70 seconds. Fig. 5.11 showed the vertical pressure σv profile after the vibratory compaction. In the figure, the measured vertical stresses increased with increasing depth. It is clear in the figure that the vertical overburden pressure σv can be properly estimated with the equation

σ

v =

γ

z. As compared with the

σ

v for loose sand,

σ

v measured in dense sand was slightly greater because the compacted backfill had a slightly higher unit weight. It is clear in the figure that the compaction process did not result in significant residual stress in the vertical direction. It may be concluded that the effect of vibratory compaction on the vertical pressure σv was insignificantly.

The distributions of horizontal earth pressure against the nonyielding wall after the compaction of soil from lift 1 to lift 5 were shown in Fig. 5.12 (a) to (e).

The test results reported by Chen and Fang (2008) were also plotted in Fig. 5.12.

Each compacted lift is 0.3 m-thick after compaction. The variation of lateral earth pressure was monitored by the soil pressure transducer mounted on the wall.

Before compaction, the earth pressure at-rest can be properly estimated with Jaky’s equation. However, after vibratory compaction, it is clear in Fig. 5.12 (d) that an extra horizontal stress

Δσ

h,ci was induced by compaction. The compaction-influenced zone indicated in Fig. 5.12 (d) extended from the compacted surface to the depth of approximately 0.7 m. In Fig. 5.12 (c) to (e), the compaction-influenced zone rose with rising compaction surface. It was interesting to note in Fig. 5.12 (e) that, below the compaction-influenced zone the horizontal stresses converged to the earth pressure at-rest based on Jaky’s equation. The lateral stress measured near the top of backfill was almost identical to the passive earth pressure estimated with Rankine theory. It should be emphasized that the influence of vibratory compaction on the horizontal earth pressure σh in the soil mass was quite significant.

5.4 Stress Paths for Filling and Compaction of Backfill

The stress path (σv versus σh) for a soil element under the filling and compaction of the backfill for Test 0812 was shown in Fig. 5.13. Chen and Fang (2008) reported that the compaction process would not result in residual stress in the vertical direction. On the other hand, horizontal earth pressure near the top of the wall increased significantly due to compaction. The test data shown in Fig. 5.13 (a) to (e) were measured by SPT2, SPT5, SPT8, SPT11, and SPT14 respectively. In Fig. 5.13, the stress path F represented the stress variation due to the filling of the 0.3 m-thick Ottawa sand. Stress path C represents the stress variation due to the

Fig. 5.13(a) that at SPT2, compaction of lift1 caused theσh to increase as shown in stress path C1. The compaction of lift 3 to lift 5 gradually brought the σh back to an at-rest stress condition indicated by the K0-line. The Rankine passive pressure (Kp-line) was apparently the upper bound of the induced lateral earth pressure. The path C2 in Fig. 5.13(b), path C3 in Fig. 5.13(c), path C4 in Fig. 5.13(d), and path C5 in Fig. 5.13(e) indicated that the variation of lateral stress was mainly caused by the compaction of backfill near the pressure-transducer, not soil filling. Based on the test results of Test 0804. 0805, 0806, 0810, similar stress variation of stress path could be shown in Fig. 5.14. It appeared the test results were quite reproducible.

5.5 Dynamic Stress Paths during Compaction

The dynamic stress paths (σh vs. σv) due to vibratory compaction were investigated in this study based on soil pressure transducer measurements. In Fig.

5.13(a) the stress path F1 represented the stress path due to the Filling of Lift 1.

The F1 stress path basically followed the K0-line as expected. The stress path C1 represented the Compacting of Lift 1. It should be mentioned that the loose backfill was placed and compacted in five Lifts, from Lift 1 to Lift 5 as shown in Fig.

5.15(d). Each compacted lift had a thickness of 0.3 m.

In Fig. 5.15(a) showed the soil surface of each lift was divided into six lanes parallel to the face of the model wall. Lane f compacted first and Lane a was compacted last. Each lane was densified with a pass having duration of 70 seconds.

In Fig. 5.13(a), the stress path C1 was approximated with a straight lone.

However the dynamic stress path from point A to point B was much more complicated than a straight line. As illustrated in Fig. 5.15, the dynamic stress paths in the sandy backfills were discussed in three conditions: (1) compaction approaching SPT in x-direction; (2) compaction passing SPT in y-direction; and (3) compaction rising in z-direction.

5.5.1 Compaction Approaching SPT in x-direction

Fig. 5.16 showed the dynamic stress paths due to compaction of Lift 1 from lane f to lane a. Each lane was compacted with a pass of 70 seconds.

To avoid confusion due the large amount of test data obtained, only the dynamic stress path measured from t = 34.5 to 35.5 s (duration = 1 second) was plotted in Fig. 5.16. In Fig. 5.16(a) the legend C1-f-center represented the Compaction of Lift 1 , on Lane f, at the center part of the lane. In this figure, the horizontal stress σh and vertical stress σv were measure by SPT2 and SPT102, respectively, as illustrated in Fig. 5.1. Since Lane f was about horizontally 1.25 m away from the SPT, the dynamic stress path illustrated in Fig. 5.16(a) was insignificant. As the vibratory compactor moved from Lane f towed Lane a, the compaction-induced stresses increased.

In Fig. 5.16(f), the dynamic stress path due to the 1-second compaction on Lift 1 at the center part of Lane a was quite apparent. The stress paths were bounded by the at-rest k0-line and passive kp-line. The shape of the stress path was quite different from the stress paths proposed by Broms(1971), and Duncan and Seed(1986).

The dynamic stress path due to the compaction on Lift 2, 3, 4, and 5 were illustrated in Fig/ 5.17, 5.18, 5.19 and 5.20, respectively. In three figures, with the approaching of compaction toward the earth pressure transducers , the stress paths became more significant. No stress beyond the kp-line had been observed in the experiments.

5.5.2 Compaction Passing SPT in y-direction

The stress paths due to the compaction on Lane a of Lift 1 were shown in Fig. 5.21. As illustrated in Fig. 5.15(b), only the stress path due to the

Center-L375; and (5) Center-L750 were reported. Center-R750 represented a location 750 mm to the right of the centerline of the model wall.

In Fig. 5.21(a), the measured stress path was not obvious, because the point of compaction was 750 mm to the right of SPT2 and SPT102. As the compaction moved toward the SPT in y-direction, the stress path became move apparent in Fig. 5.21(b). In Fig. 5.21(c), the compaction-induced stresses were most significant. The stress path was definitely not a straight line. As the point of compaction passed and moved away from the SPT, the effects compaction became less obvious.

The dynamic stress path due to the passing of compactor on Lane a of Lift 2, 3, 4 and 5 were indicated in Fig. 5.22, 5.23, 5.24 and 5.25, respectively. In three figures, as the compactor moved toward the SPT in y-direction, the stress paths became more apparent. No stress below the K0-line had been observed.

5.5.3 Compaction Rising in z-direction

Fig. 5.26 showed the dynamic stress paths measured at SPT2 and SPT102 due to compaction on the center part of Lane a of Lift 1 to Lift 5. In Fig.

5.26(a), since the vibratory compaction was only about 0.15 m right above the pressure transducers, the compaction-induced stress path was quite obvious. In Fig. 5.26(b), (c) and (d), the thickness of the overburden soil increased, and the compaction induced stress path became less significant.

In Fig. 5.26(d), the compaction of Lift 5 draged the stress path to a point below the K0-line. The stress paths due to compaction measured with SPT5 and SPT105, SPT8 and SPT108, SPT11 and SPT111, and SPT14 and SPT114 were shown in Fig. 5.27, 5.28, 5.29 and 5.30 respectively In Fig.

5.28(b), the 1-second dynamic stress path due to the compaction on the center part of Lane of Lift 4 was beyond the C4 stress path. It is possible

that the dynamic stress path may not be restrained and described by the simplified straight-line stress path

5.6 Comparison among Lifts and Tests

Fig. 5.31(a) to (e) showed the stress paths due to the 1-second compaction at the center of Lane a for Lift 1 to Lift 5. It was observed in these figures that the shape and the size of the dynamic stress paths obtained at five different lifts were quite similar. The dynamic stress path had the shape of a comet. The comet moved between the K0-line and Kf-line.

Fig. 5.32 showed similar experimental results were obtained from Test 0805.

5.7 Comparison of Theoretical and Experimental Stress Paths

Fig. 5.33 showed the theoretical stress path of hysteretic model proposed by Broms (1971). For a soil element existed at some depth of backfill, the initial vertical stress due to the overburden soil was σvi. The initial horizontal stress was σhi = K0σvi, which was represented by the point A in Fig. 5.33. When a heavy compactor was positioned immediately above the soil element, following the K0-line, an increase of the vertical stress resulted in an horizontal stress increase based on the assumption of no lateral yield. The stress state can be expressed as σhm = K0 σvm (point B). As the heavy compactor moved off the fill, a subsequent decrease in σv (unloading) resulted in no σh decrease until a limitation (Kr-line) was reached (point C). the assumption was made that the maximum horizontal stress induced by compaction σhm sustained until the vertical stress is reduced below a critical value at point c. After that, further σv unloading resulted in a

vertical stress σvi was reached. Broms (1971) assumed that Kr = 1/K0.

The experiment stress paths due to the filling of backfill of Lift 2 (F2) and the compaction of Lift 2 (C2) were shown in Fig. 5.33. It is interesting to note that the starting point A and ending point D lased on Brown’s theory, was similar to the starting point A and ending point E of the stress path C2. It was indicated that compaction would result in an increase of stress only in the horizontal direction, but not in the vertical direction.

The dynamic stress path due to on-cycle of compaction at the center part of Lane A was also illustrated in Fig. 5.33. It was obvious that the comet-shaped dynamic stress path was quite different from the stress path proposed by Broms. It should be mentioned that the stress path AB in Fig. 5.33 indicated the heavy compactor generally 5~15 ton applied a large static vertical pressure σv on the surface of fill.

However, stress path BC represented the removal of the heavy compactor. The mass of hand-operated square-plate compactor used in this study was only 12.1 kg (W= 119 N). Fig. 5.9 showed the peak dynamic force applied on the surface of fill was Fx = ± 280 N, Fy = ± 1320 N , and FZ = 1690 N. The vibratory compaction was 3-dimentional and was controlled by the cyclic loading instead of the dead-load of the compactor. This was probably the main reason why the dynamic stress path due to vibratory compaction was so different from Broms’ finding.

Chapter 6

CONCLUSIONS

This paper studied variation of earth pressure and dynamic stress path in compacted sand. Based on the experiment results, the following conclusions were drawn.

1. For a loose backfill, the horizontal earth pressure in the soil mass was in good agreement with Jaky’s solutions. The vertical earth pressure in soil was near to the equation

σ

_v =

γ

z.

2. After compaction, the lateral stress measured near the top was almost identical to the passive earth pressure estimated with Rankine theory. The effect of vibratory compactiom on the vertical pressure was insignificant.

3. After compaction, the thickness of the compaction-influenced zone rose with the elevation of the compaction surface. Below the compaction-influenced zone, the horizontal stresses converged to the earth pressure at-rest based on Jaky’s equation.

4. As the area of the compaction approached the soil pressure transducer ( SPT ) in x-direction ( perpendicular to the wall face), the dynamic stress path became more obvious when the compactor moved to the lane near the wall.

5. As the area of compaction passed the SPT in y-direction (parallel to the wall surface), the maximum dynamic stress path was obvious when the compactor was right in front of the SPT.

6. For a SPT at a lower elevation, when the area of compaction rose with the elevation of the lift surface, the compaction-induced stress path became less significant.

7. The dynamic stress path of a soil element under vibratory compaction had the shape of a comet. The shape size of the dynamic stress paths obtained at five different lifts was quite similar. The stress paths were bounded by the at-rest K0-line and passive Kp-line.

8. The measured dynamic stress path was quite different from the stress path proposed by Broms (1971). The stress path reported by Broms was induced by a static heavy compactor. The vibratory compactor used in this study vibrated and generated cycle force in three direction: Fx, Fy, and Fz. This was probably the main reason why the dynamic stress path due to vibratory compaction was so different from Broms’ finding.

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