6.1 Earth Pressure Results
6.1.1 Earth Pressure for β = 0°
The variation of lateral earth pressure as function of active wall movement was investigated. After the loose backfill and had been placed into the soil bin as shown in Fig. 4.10, the model wall slowly moved away from the soil mass in a translation mode at a 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 are illustrated in Fig. 6.2. As the wall started to move, the earth pressure decrease, and eventually a limit 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 Fig. 6.2.
The ultimate experiment active pressure distribution is in fairly good agreement with that estimated with Coulomb and Rankine theories.
Fig. 6.3 shows a typical variation of horizontal earth pressure σh measured by different pressure transducer as a function of the wall movement, S/H (S : wall displacement, H : backfill height). In Fig. 6.3 the horizontal stress decreased with increasing active wall movements. The location for soil pressure transducer SPT1 through SPT9 is illustrated in Fig. 3.3. If the normal pressures at different depths are normalized by the soil unit weight γ and its depth z, the variation of σh/γz with S/H is shown in Fig. 6.4. In this figure, most of the data are concentrated. It seems possible that the active condition is reached at all depths simultaneously.
The variation of horizontal earth-pressure coefficient Kh as a function of wall displacement is shown in Fig. 6.5. The coefficient Kh is defined as the ratio of the horizontal coefficient component of total thrust toγH2 2. The horizontal thrust Ph
was calculated by summing the pressure diagram shown in Fig. 6.2. The coefficient Kh decreased with increasing wall movement until a minimum value was reached, then remained approximately constant. The ultimate value of Kh is defined as the horizontal active earth-pressure coefficient Ka,h. In Fig. 6.5, the active condition was reached at approximately S/H = 0.0035.
As shown in Fig. 6.2, the distribution of earth pressure at different wall movements is almost linear. Therefore, the point of application of total thrust, h/H should remained at about H/3 above the wall base. Experimental results in Fig. 6.6 show that these points are located at a distance of about 0.331 H ~ 0.359 H above the wall base.
For Test 0825, the distributions of earth pressure at different stages of wall movement are shown in Fig. 6.7. As the wall starts to move, the earth pressure decrease. The pressure distribution is approximately linear with depth. Although the distribution is not strictly linear, such an assumption would not be far from reality.
In Fig. 6.5, the earth pressure coefficient, Kh decreases with increasing wall movement and finally a constant total thrust is reached. For Test 0825, the active condition occurred at the wall movement of approximately S/H= 0.003. It may be
observed from Fig. 6.5 that Coulomb theories (δ =18.5o) provide a good estimate of the active earth pressure. In Fig.6.5 , data points obtained from Test 0809 and Test 0825, indicated that the experimental results were quite reproducible.
6.1.2 Earth Pressure for β = 50°
Fig. 6.8 shows the distribution of earth pressure at different stages of wall movement with presence of a stiff interface plate for an inclination angle β = 50o. Fig. 4.11 shows the steel interface plate was placed in the soil bin and dry Ottawa sand was pluviated behind the model wall. In Fig. 6.8, the measured stress at S/H= 0 is lower than Jaky’s solution. The measured earth pressure at-rest is clearly affected by the intrusion of the rough interface inclined at β = 50o. It is clear in Fig. 4.11(a) that, for the upper part of model wall, the interface plate is far from the SPT. It is reasonable to expect the measuredσh to be close to identical with Jaky’s prediction.
However, for the lower part of the model wall, the interface plate is quite close to the soil pressure transducers. As a result, the active earth pressure measured would be affected by the approaching of the interface plate.
Fig.6.9 shows the typical variation of lateral pressure as a function of active wall movement. The horizontal stress decreases with increasing wall movement, then reaches a constant value. Fig. 6.10 shows the relationship between normalized earth pressure σh/γz and wall movement S/H. It is clear in this figure, that σh measured at SPT1 to SPT9 decreases with the wall movement, then reach an active state.
Fig.6.11 presents the variation of lateral pressure as a function of active wall movement. As the wall starts to move, the lateral soil thrust decreases with increasing wall movement until a constant is reached, then remained approximate constant. The ultimate value of Kh is defined as the horizontal active earth-pressure coefficient Ka,h.
In Fig. 6.11, the active condition was reached at approximately S/H = 0.003.
In Fig. 6.8, as the wall starts to translate, the earth pressure start to decrease. This non-linear earth pressure distribution causes the total thrust to act at to higher location.
Fig. 6.12 shows h/H reaches a constant value which is about 0.40 H ~ 0.42 H above the base of the wall.
For Test 0815, the distribution of earth pressure at different stages of wall movement for β = 50o is shown in Fig. 6.13. As the wall started to move, the earth pressure decrease and eventually a limiting active pressure was reached. The variation of Kh with S/H for Test 0814 and Test 0815 are summarized in Fig. 6.11. It can be seen from the figure that the two sets of test data concentrate in narrow strip. It can be concluded that the experimental results are highly reproducible.
6.1.3 Earth Pressure for β =60°
Fig. 6.14 shows the earth pressure distributions corresponding to different stages of wall displacements for the interface inclination angle β = 60°. At S/H = 0, the measured σh was significantly lower than Jaky’s solution, especially the σh
measured near the base of wall. It may be observed in Fig. 4.12 (a), with increasing β angle, the horizontal distance between the model wall and interface plate was reduced.
Fig.6.15 shows the typical variation of lateral pressure as a function of active wall movement. The horizontal stress decreases with increasing wall movement, then reaches a constant value. Fig. 6.16 shows the relationship between normalized earth pressure σh/γz and wall movement S/H.
For β = 60°, the variation of earth pressure Kh with wall movement is shown in Fig. 6.17. The earth-pressure coefficient value Kh decreased with increasing wall movement until a constant value is reached. In Fig. 6.17 the active condition was reached at approximately at S/H = 0.003. Referring to Fig. 6.14, at S/H = 0.003 the active earth pressures measured near the base portion of the wall is much lower than Coulomb’s prediction. The measured active earth pressure is clearly affected by the interface plate inclined at β = 60°. It is reasonable to expect the point of application of the active thrust would be located at a position higher than h/H = 0.333. Fig. 6.18 shows the experiment points of application the active thrusts were located at about 0.40 H ~ 0.43 H above the wall base.
For Test 0818, Fig. 6.17 shows the pressure distribution at various movement stages. The measured active earth pressure was lower than Coulomb’s solution especially the pressure measured near the base of wall. This is most probably because the active earth pressure is affected by the intrusion of the inclined interface plate.
6.1.4 Earth Pressure for β =70°
The pressure distributions at various wall movements for β =70° are shown in Fig.
6.20. At S/H = 0, the measured earth pressure at rest was lower than Jaky’s prediction, especially at the lower part of the model wall. This is because the interface plate is very close to the soil pressure transducers as shown in Fig. 4.13.
Fig. 6.21 shows the variation of horizontal earth pressure σh measured by different pressure transducer as a function of the wall movement. It is clear from the data shown in Fig. 6.21 that the horizontal stress decreases with increasing active wall movements. The variation of σh/γz with S/H is shown in Fig. 6.22.
Fig. 6.23 shows the variation of Kh with active wall movement for β = 70°. The coefficient Kh decreases with increasing wall movement. The wall movement needed for Kh to reach an active state is about S/H = 0.0035.
The variation of the location of to the active soil thrust with wall movement is shown in Fig. 6.24.Without the interface plate (β = 0°), the point of application h/H of the earth resultant is located at about 0.33H above the base of the wall. With the interface angle β = 70°, the earth pressure does not increase linearly with depth. This active earth pressure distribution shown in Fig. 6.20 causes the location of the total thrust to rise to a higher location. Experimental result in Fig. 6.24 shows the point of application of the active thrust was located at about 0.41 H ~ 0.43 H above the wall base.
Fig. 6.25 illustrates the distributions of earth pressure at different stages of wall movement for Test 0824. The active earth pressure measured near the base of the wall was much lower than Coulomb solution. In Fig. 6.23 and Fig. 6.24, data points obtained form Test 0822 and Text 0824 indicate that experimental results were in good agreement.
6.1.5 Earth Pressure for β =80°
Fig. 6.26 shows the variation of the earth pressure distributions with depth at various wall movements. At S/H = 0, the measured at-rest pressure distribution is not linearly with depth. and it is significantly less than the Jaky solution. Fig. 4.14 shows, for β = 80°, the interface plate was quite close to the wall surface. The amount of backfill sand withed between the rock face and the wall was very little. In this figure, the earth pressure slightly decreased with the active wall movement.
Fig.6.27 presents the variation of lateral pressure as a function of active wall movement. As the wall starts to move, the earth pressure decrease, and eventually a active pressure is reached. Fig. 6.28 shows the relationship between normalized earth pressure σh/γz and wall movement S/H.
In Fig. 6.29, the horizontal earth pressure coefficient Kh decrease with increase wall movement, then a constant value Ka,h is observed. The constant value Ka,h is significantly lower than the value estimated with the Coulomb’s theory.
The location of total soil thrust versus the wall movements is shown in Fig. 6.30.
Experimental results show that these points are located at a distance of about 0.42 H
~ 0.43 H above the wall base. This is most probably because the measureσh
distribution is significantly affected by the presence of the nearby rock face.
For Test 0826, the earth pressure distributions corresponding to different stages of wall displacement for β = 80° are shown in Fig. 6.31. In this figure, the distribution of lateral earth pressure are non-linear with depth. This is probably because the interface plate is very close to the soil pressure transducers on the wall surface. The wall movement needed for the horizontal stress to reach a constant value is about S/H = 0.004. Similar variation of Kh with can be observed for Test 0825.and Test 0826.