The paper presents a one-meter-height rigid facing panel, supported rigidly at the top and bottom to simulate nonyielding retaining wall system. A set of load cells is used to measure the horizontal force at the top and bottom of the facing panel, which is converted to equivalent horizontal earth pressure acting at the back of the wall. Another set of load cells is used to measure the vertical load at the bottom of the wall facing, both at the toe and the heel. Uniformly graded sand was used as backfill soil. The measured wall responses were used to calibrate a numerical model that used to predict additional wall parameters. Results indicated that the measured horizontal earth force is about three times the value calculated by classical at-rest earth pressure theory. In addition, the location of the resultant earth force is located closer to 0.4 H, which is higher compared to the theoretical value of H/3. The numerical model developed was able to predict the earth pressure distribution over the wall height. Test set up, instrumentation, soil properties, different measured responses, and numerical model procedures and results are presented together with the implication of the current results to the practical work.

Earth pressure distribution behind retaining wall systems is a soil-structure interaction problem. Therefore, determination of earth pressure distribution at the back of the wall should be done interactively with the deflection of the wall. However, this is not the case in the current design practice. Practically, the hydrostatic earth pressure distribution behind the wall is adopted according to the at-rest, active, or passive earth pressure theories for both internal and external stability analyses. Furthermore, triangular distribution is typically assumed for of the lateral earth pressure for at-rest, active or passive conditions. This assumption can be true for walls that are free to move laterally or rotate around the toe with sufficient movement to initiate the sliding wedge (i.e., active or passive state). However, this is not the case for nonyielding walls that do not develop the limiting static active or passive earth pressure, because the movements are not sufficient to fully mobilize the backfill soil shear strength. Typically, all underground basements walls, tunnels, bridge abutments, culverts, and piles are examples of nonyielding structures that are in contact with soil. These structures usually undergo relatively very small movement which is insufficient to initiate the sliding wedge behind the wall and to relieve the pressure to its active or passive state. Examples of nonyielding walls are schematically shown in Figure

Schematic views of structures with nonyielding retaining walls.

Bridge abutment

Building basement

Underground tunnel system

This paper presents experimental and numerical models developed to study the vibratory compaction-induced lateral stresses acting against vertical nondeflecting walls. The experimental model provided reliable quantitative results for values of earth pressure at rest (

Using the so-called “local arching” effect of the soil, Terzaghi [

Coefficient of earth pressure at rest,

In (

Cherubini et al. [

Despite its practical significance and attractive simplicity, Jaky’s formula and its derivative (i.e., (

An important aspect of vibratory compaction, which is not generally appreciated, is the increase of the lateral stresses in the soil due to vibratory compaction. Sand backfills are usually normally consolidated prior to compaction with earth pressure coefficient (

Quantitative studies of the at-rest earth pressure distribution behind rigid retaining walls have been conducted by Mackey and Kirk [

Typical experimental model and instrumentations on nonyielding wall on RMC shaking table.

Top instrumentation

Bottom instrumentation

A set of 1/3 scale model tests were carried out at the Royal Military College of Canada using the shaking table test facility. The physical models were 1 m high (H), 1.4 m wide, (W) and 2.4 m depth (D), as shown in Figure

Experimental model setup, arrangement, and instrumentations.

The total horizontal force transmitted to the rigid facing panel wall was measured by load cells attached to the rigid reaction beam used to restrain the facing panel in the horizontal direction (Figures

Artificial silica-free synthetic olivine sand was used as retained soil. The soil properties are summarized in Table

Backfill sandy soil properties.

Soil property | From direct shear tests | Back-calculated from direct shear box test simulations using FLAC |
---|---|---|

Bulk unit weight (kN/m^{3}) | 15.7 | — |

Peak friction angle | 51° | 58° |

Residual friction angle, | 46° | 46° |

Dilation angle, | 15° | 15° |

Cohesion, | 0 | 0 |

Shear modulus (MPa) | — | 7 |

Bulk modulus (MPa) | — | 6 |

The numerical simulations were carried out using the program FLAC [

FLAC numerical model of nonyielding wall retaining sand backfill.

A no-slip boundary at the bottom of the sand backfill was assumed to simulate the rough boundary in the physical tests (i.e., a layer of sand was glued to the bottom of the shaking table containing box). The vertical boundary at the right side of the model was designed as rigid wall to simulate the back wall of the strong box in the shaking table tests. The model wall facing toe boundary condition was modelled with two-noded one-dimensional beam elements with three plastic hinges (Figure ^{3} and linear elastic material properties. The material parameters adopted for the facing elements values are shear modulus,

The interface between the backfill soil and the facing panel was modelled using a thin (15 mm thick) soil column directly behind the facing panel (Figure

Directions and locations of forces used for static earth pressure analysis are shown in Figure

Force diagram used for the analysis of construction stages in both experimental and numerical models.

Experimental

Numerical

Variation of horizontal toe load, vertical toe load, and normalized earth pressure resultant elevation with the backfill height during construction stages.

Horizontal load

Vertical load

Resultant elevation

Variation of the vertical toe load with backfill height at different construction stages is shown in Figure

The elevation of the resultant lateral earth force above the foundation of nonyielding wall, normalized to the backfill height is shown in Figure

Figure ^{3},

Variation of horizontal earth force with the backfill height during construction stages at different overconsolidation ratio.

Figure

Variation of horizontal earth force, normalized to the theoretical calculated value, with the backfill height, at different overconsolidation ratio.

The construction of the model wall was finalized with the compaction of the last soil lift using the vibration procedures used previously with all soil lifts. Results presented in this paper were measured after the model was vibrated for the compaction of last soil lift. This is considered the first time when the model is fully vibrated (i.e., end of construction vibration). It was decided to vibrate the model wall two times in addition to the first time in order to report the effect of further vibrations on the resulted wall response. Figure

Effect of second and third vibration on the measured vertical and horizontal earth forces on nonyielding wall.

Calibration of the numerical model was focused on achieving a good agreement between the calculated and measured horizontal wall force at top and bottom, vertical force, and the location of the lateral earth force resultant at different construction stages. It should be noted that the soil backfill in experimental model was constructed in 8 layers, which is replicated in the numerical model. During the construction of the numerical model, there were two options that could be used alternatively in order to compact each sand layer. The first option is to vibrate each layer using the prespecified horizontal motion that used in the experimental model. This method was found to be time consuming, and the final construction of the model took about 24 hours to execute in a personal computer. Alternatively, after the placement of each sand layer, a horizontal stress condition equivalent to

Figure

Predicted and measured horizontal load versus backfill height during construction stages.

Top horizontal load

Bottom horizontal load

Total horizontal load

Predicted and measured vertical toe load and normalized resultant elevation versus backfill height during construction stages.

Vertical load

Resultant elevation

Values of horizontal forces shown in Figure

Experimental, numerical, and theoretical predicted lateral earth pressure resultant and point of application versus backfill height.

Earth pressure resultant

Resultant elevation

The earth pressure distributions on the wall at different backfill heights are shown in Figure

Numerical and theoretical prediction of lateral earth pressure distribution versus backfill height during construction stages.

The current study presents experimental and numerical investigation of at-rest lateral earth pressure resulted due to overconsolidated sandy soil adjacent to nonyielding walls. For this purpose, scaled model walls were constructed and specially instrumented to measure the lateral earth force. The sandy soil was compacted by vibration in order to increase the overconsolidation ratio. In addition, a numerical model has been developed to simulate nonyielding wall and validated using the measured wall responses. Based on the results presented in this study, the following points could be summarized.

For nonyielding wall systems with nearly smooth back, the vertical load transfer to the footing of the wall is approximately equivalent to the facing self weight. This value expected to be larger in cases of walls with rough back.

Overconsolidation ratio of sandy soil increases with repeated vibration compaction, and as a result, the horizontal effective stress increases significantly.

Jaky’s formula is proven to significantly underestimate the at-rest lateral earth pressure coefficient for overconsolidated sand.

Overconsolidation ratio of sandy soil is an important factor that affects the at-rest lateral earth force. Including a suitable overconsolidation ratio in the modified Jaky’s formula produced realistic at-rest earth pressure coefficient.

The resultant of at-rest lateral earth pressure is measured to be located closer to 0.4 H (H is the backfill height), from the footing of the wall, which is above the 0.3 H assumed by the classical earth pressure theory.

The location of the earth pressure resultant measured in the current study indicated that the hydrostatic distribution for at-rest condition assumed by the classical earth pressure theories is not valid for overconsolidated sand.

The numerical model developed in this study predicts wall responses that agree well with the measured responses.

The earth pressure distribution predicted numerically shows that the increase of the earth pressure due to vibration at the wall top is more significant compared to the wall bottom.

The author is grateful for funding provided by the office of research and graduate studies, American University of Sharjah, UAE (Travel Grant, FRG11-III-14). The many discussions with Dr. Kianoosh Hatami, University of Oklahoma, and Dr. Richard Bathurst, Royal Military College of Canada (RMC), on the numerical and experimental models are also gratefully acknowledged.