ASSESSING EARTHQUAKE-INDUCED DISPLACEMENT IN COMPOSITE REINFORCED-SOIL RETAINING WALLS

1 Ali Tabrizi

1 Department of civil Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran

Corresponding Author: Ali Tabrizi

ABSTRACT

INTRODUCTION

Surface soils are mostly loose soils and thus feature a less bearing capacity. For this, to construct larger and heavier structures, it is necessary to increase the soil’s bearing capacity in different forms. One way of applying a greater load to the soil is to construct structures on

layers [of soil] with greater strength. On the one hand, moving down deep into the ground, we reach layers with greater strength. For this, excavation operations are performed to construct foundations beneath the ground surface and achieve a greater bearing capacity. An engineering problem arising from excavation operations is how excavated site walls could be stabilized and how safe conditions help implement structural elements at the bottom of excavated sites. In a typical situation, to stabilize excavated site walls, the walls are required to be constructed in an inclined manner with an appropriate safety factor. In populated areas of cities where construction sites suffer from space confinement due to urban population density and proximity to other structures, it is not possible to form excavated site walls in a sloped way, as excavation should be implemented by vertical or near-vertical walls. Hence, other methods should be utilized to stabilize excavated site walls. [1] The failure of excavated walls and neighboring buildings during and after excavation operations, both under static and seismic conditions, are the main problems hindering large civil projects. Unfortunately, despite recent civil engineering advancements in modern construction methods, news of damage to excavated walls and neighboring sites, as well as life and property losses are heard across various areas of Iran and other countries alike. For this, it is increasingly becoming important to safely stabilize excavated walls given the growing urban construction sites and the need for implementing deep excavation. One way to do this is to employ nailing systems that are not only safe but also incur lower costs than other methods while they can be implemented with greater ease at much less cost and time. Other excavated wall stabilization methods include composite nailing and anchoring systems, which help provide more safety and reduce changing wall locations. If optimally employed, the two methods offer appropriate angles and positions of nails and anchors. Therefore, it is critical to optimize the angles of nailing and positions of anchors under two static and seismic conditions.[4] Sabhahit et al. demonstrated that if nails were to be positioned in the lower section of the slope, their total lengths could decrease. An analysis of an earthen nailed slope with a slope angle of 70° and a rear ground slope of 20° was used to conclude that the middle section of the slope should have nails of longer length to minimize the overall reinforcement length. The authors also used the Finite Equilibrium Analysis to suggest that horizontal nails were highly regarded as optimal except that they were used for lowermost nails. [2]

The origin of soil nails comes from underground rock excavation retaining systems, which is known as a novel Austrian tunneling method. This method includes installing passive steel reinforcement systems in rocks, e.g., rock bolts on which a protective shotcrete facing is implemented. A composite system combining passive reinforcement steels and shotcrete was introduced in the early 60s in rock slope stabilization. This technique relied on the tensile strength mobilization of reinforcement steels subjected to relatively small deformation on the ground and surrounding soils. The support system is enhanced by a coherent shotcrete facing. On the other hand, soil nailing is when a combination of passive reinforcement steels and shotcrete is used instead of rocks in the soil. [3] Jiun Hung Luo and Chia Cheng Fan (2007) performed a numerical study on the optimal arrangement of earthen-nailed slopes to help stabilize the slopes. This study examined the effects of angle and geometric nail arrangements on the overall stability of the earthen slopes under varying geometric conditions using the non- linear finite element method. The stability of the earthen-nailed slopes was also determined by the safety factor.[5]

Using an experimental study, Marchal demonstrated that the nails’ angles of inclination against the failure surface of earthen masses could play a role in mobilizing tensile and shear force in the nails, and also in the overall shear strength of the nailed soils. To investigate the effects of the inclination angle of flexible nails on increasing shear strength at the moment of soil mass failure, Jewell did several direct shear laboratory experiments. It was concluded that the nails’ optimal extension perpendicular to the shearing surface to mobilize the maximum shear strength of the soil mass held an angle of 30°. [6] Shafiee (1986) employed the finite element method to conduct a study on the effects of the nails on the deformation of earthen-nailed walls. The walls in this study were analyzed using nails with horizontal angles of 0° to 30°. It was

found that the facing of the walls implemented with inclined nails of 30° saw deformations larger than horizontal nails.[7] Satyendra Mittal, Swam Saram, and Gosavi Meenal (2009) presented a quasi-static analytical technique to examine the stability of vertical and near- vertical nailed excavations. It was demonstrated that the failure surface was assumed to be a logarithmic spiral arc passing through the heel of the excavation and intersecting the ground under the right angle. Vertical and horizontal seismic forces were considered horizontal and vertical seismic coefficients, with the safety factor calculated by the anchoring equilibrium method. [8] Babu et al also studied the effects of the nails’ angles of inclination on earthen nailed walls, employing the generalized plane strain finite element method to analyze the stresses, strains, and displacements of earthen nailed walls. This study described an analytical method and the effects of the angles of inclination of the nails. This study also performed a parametric computer analysis to investigate the effects of the nails’ angles. The study demonstrated that the generalized plane strain finite element method proved to be sufficiently adaptable to both complex geometries and loading conditions, as well as non-linear material properties.[9]

The soil typically features relatively high compressive strength and low tensile and shear strength. Nailing helps reinforce the soil and increases its tensile and shear strength. This technique serves as a weighted retaining wall and works as a load-bearing structure. Construction of an earthen-nailed wall includes reinforcing the soil during the excavation process using several rebars. Soil nailing offers economic viability and presents unique advantages, serving as a very suitable solution across various areas, including stabilizing slopes, increasing load-bearing capacity, and limiting deformation by minimally manipulating the natural status of the ground. This technique works by reinforcing the soil and is gaining attraction across the world, as it is widely used in stabilizing deep excavations and natural slopes. As stated above, rebars are used to reinforce the soil when excavation operations are implemented. Rebars (reinforcing bars) inherently operate in tension and mostly tend to feature a gentle downward slope while being parallel to each other. Rebars can also operate, in part, in bending and shearing, with the tension caused inside them due to the friction between the nail and the soil. If employed from a top-bottom form, a nailed soil mass is incrementally achieved. In an interactive mechanism between the soil and reinforcement materials both in a reinforced soil and in a nailing system, the mobilized frictional stress along the reinforcement materials will prevent the lateral deformation of the reinforced soil. Reinforcement materials will fail and could be removed from the soil when their anchored lengths inside a resistant zone are thought to be insufficient, with the shear stresses caused across the lengths consequently being less than the sliding resistance of the reinforced materials.

Today, nailing systems are widely used worldwide for their safety, higher speed of implementation, and lower costs, evolving as a common technique in construction and logistical projects in Iran and the world. Walls can be supported and stabilized using nailing systems and a combination of nailing and other techniques. Using composite systems helps reduce wall stability dependence on soil types. In this connection, the combined nailing and anchoring systems could be widely used due to their environmentally friendly, easy installment, and low wall displacement properties.

Earthen structures do not feature regular and plain forms as soil masses are not homogenous or elastic, requiring complex mathematical methods to measure stresses and displacement. Over the past decades, numerical techniques have replaced mathematical methods and developed recently due to technological and computer science advancements. As stated, the goal of the present study was to evaluate earthquake-caused displacement in composite reinforced-soil retaining walls.

CHARACTERISTICS OF THE AREA UNDER STUDY

This study used the characteristics of an area taken from the article “Soil Nailing Simulation” on Plaxis Practice to help model soil masses and wall nailing.[10]

Figure 1: Area Under Study

The soil mass in the studied area is composed of a gravel soil layer with specifications listed in Table 1 below and a very hard layer starting 22.5 m deep in the ground.

Table 1. Soil mass specifications

In this area, a 10 m wide excavated site consisting of 5 layers, each measuring 2 m thick was implemented. After each layer of drilling, first the nails and then the wall (the shotcrete coating) were embedded, which continued until the end of the excavation operation. Tables 2 and 3 provide the specifications of the wall and the nailing.

Also, the 2D nailing plane strain modeling requires the equivalence of bending and axial stiffness of the nails. The specifications required for the equivalence process are listed in Table 2 below.

Table 2: Wall specifications

Table 3: Nailing specifications

Here, t is the thickness and H is the total height of the wall, while d, L, and S v represent the diameter, length, and horizontal spacing of the nails. Also, the angle of the nails is horizontal, and the D DH is the diameter of the drill hole.

This study employed a 2D geometric plane strain model for the numerical finite elements analysis and modeling, and a 15-node element for meshing. It should be pointed out that due to the model’s geometric symmetry, only half of the model (the right side of the model) was considered in the modeling. An equivalent elastic beam was used for the nailing modeling, and the nailing specifications required for the equivalence are given in Table 2. Also, for the wall modeling (shotcrete coating), the beam with the elastic behavioral model, whose specifications are given in Table 3, was used (Fig. 2).

Concerning Rayleigh’s damping coefficients (α (and) β), a value of 0.01 was considered for the seismic analysis. Also, for the seismic analysis of the earthquake simulation, a horizontal dynamic prescribed displacement of 0.01 was applied to the lower boundary of the soil mass (Fig. 2).

Figure 2: Geometric model

Medium-sized 15-node elements were used for the model’s meshing (based on the sensitivity analysis). Then, considering the range of distributed lateral displacement at the end of the excavation operation (static conditions), as exhibited in Figure 3, the meshes were arranged in rectangular clusters, as exhibited in Figure 4.

Figure 3: Meshing

Figure 4: Meshing

Following the meshing, the modeling was completed using the finite element method, and initial conditions had to be applied to the model before the computations. This was aimed at solving the model to arrive at an initial equilibrium and achieve a pre-computation initial status. To apply the initial conditions to the model, initial stresses could be generated by applying the total soil weight of the model and the lateral earth pressure coefficient at rest ( K O). These stresses included the initial effective vertical and horizontal earth stresses. It should be stated that the initial effective horizontal stress was associated with the initial effective vertical stress by the lateral earth pressure coefficient at rest. Here, the default value of this coefficient, which is based on the 1− 𝑠𝑖𝑛∅ formula, was used.

To simulate the steps of the excavation operation, five Plastic computational phases were considered which were as follows:

• Phase 1: Drilling, nailing, and installing the wall (shotcrete coating) of the first layer

• Phase 2: Drilling, nailing, and installing the wall (shotcrete coating) of the second layer

• Phase 3: Drilling, nailing, and installing the wall (shotcrete coating) of the third layer

• Phase 4: Drilling, nailing, and installing the wall (shotcrete coating) of the fourth layer

• Phase 5: Drilling, nailing, and installing the wall (shotcrete coating) of the fifth layer

On the other hand, to calculate the safety factor of the wall’s stability during the excavation operation, a computation phase (Phi/c-reduction) was considered following each of the phases.

FINDINGS

To analyze the sensitivity of the strength-reduction factor of the nailing in the relevant modeling, the [factor’s] value was changed from 1 to 0.6 to examine the maximum lateral displacement of the wall and the safety factor of the wall’s stability/the strength-reduction factor after the completion of the excavation operation under static conditions.

The following diagrams show that increasing the value of the strength-reduction factor (increasing interface element rigidity) after the completion of the excavation operation under static conditions will decrease the maximum lateral displacement of the wall and increase and the safety factor of the wall’s stability.

Figure 5: Effects of Rinter (strength-reduction factor) on the maximum lateral displacement of the wall after the completion of the excavation operation

Using Geogrid Structural Elements for Nailing

Modeling nailing using geogrid structural elements helps examine the maximum lateral displacement of a wall, the safety factor of a wall, and the maximum axial-tensile force of nails during the excavation stages under static conditions. This is followed by comparing these results with those of nailing modeling using beam structural elements. To validate the numerical model and the software used, these results were matched with those of the article “Soil Nailing Simulation” on Plaxis Practice (Diagrams 6-11).

Figure 6: Maximum lateral displacement of the wall during the excavation operation

Figure 7: Safety factor of the wall’s stability during the excavation operation

Figure 8: Maximum axial-tensile force of the nails during the excavation operation

Figure 9: Maximum lateral displacement of the wall during the excavation operation in nailing modeling with the beam and the geogrid

Figure 10: Safety factor of the wall’s stability during the excavation operation in nailing modeling with the beam and the geogrid

Figure 11: Maximum axial-tensile force of the nails during the excavation operation in nailing modeling with the beam and the geogrid

Figure 12: Distribution of the axial-tensile force along the lower nail of each layer after the completion of the excavation operation in the nailing modeling with the beam and the geogrid

As shown by Diagrams 6 to 11, as the excavation operation continued, the maximum lateral displacement of the wall and the maximum axial-tensile force of the nails increased, whereas the safety factor of the wall’s stability decreased. It was also noted that the results corresponded relatively well with those of the article “Soil Nailing Simulation” on Plaxis Practice.

The diagrams also demonstrated that using the geogrid structural element rather than the beam structural elements increased the maximum lateral displacement of the wall and the maximum axial-tensile force of the nails while decreasing the safety factor of the wall’s stability during the excavation process, which was due to bending non-stiffness in the beam structural element.

Diagram 12 showed that bending stiffness significantly increased the safety factor of the wall’s stability during the excavation operation; however, following the excavation operation, [bending stiffness] did not have such a marked effect on increasing the factor any longer. This indicated that bending stiffness played a major role in the wall’s stability during the excavation operation; however, the effect of stiffness on wall stability should be ignored when using the geogrid during excavations.

Also, the effect of bending moment and the maximum shear force of nailing close to walls are factors to be ignored in nailing modeling with geogrids as the two factors may cause wall failure.

Anchoring can be modeled by a combination of a pre-stressed node-to-node anchor (non- anchored section) and a geogrid (anchored section) with specifications listed in Table 4. The geogrid helps simulate the mortar-anchored section while the node-to-node anchor stimulates the prestressed anchor rod.

In sum, to model the anchor section of the geogrid structural element, the equivalent elastic geogrid was used, the specifications of which are given in Table 4.

Table 4: Specifications of the node-to-node anchors (non-anchored section)

L 1 and L 2 represent the non-anchored and anchored section lengths, respectively, as EA, L spacing , and F prestress represent the stiffness, horizontal spacing, and prestressed force of node-to-node anchors (non-anchored sections), respectively.

CONCLUSION

In the nailing modeling with the beam structural element, it was found that as the excavation operation continued under static conditions, the maximum lateral displacement of the wall, the maximum axial-tensile force, the maximum bending moment, and the maximum sheer force of the nails increased, whereas the wall’s stability safety factor decreased. In the nailing modeling with the geogrid structural element, it was found that as the excavation operation continued under static conditions, the maximum lateral displacement of the wall and the maximum axial- tensile force of the nails increased, while the wall’s stability safety factor decreased. By comparison, the performance of the nailing modeled with two beam and geogrid structural elements under static conditions showed that using the geogrid structural element instead of the beam structural element could increase the maximum lateral displacement of the wall and the maximum axial-tensile force of the nails while decreasing the safety factor of the wall’s stability during the excavation operation. This was later found to be due to the bending non- stiffness of the beam structural element. It was also noted that bending stiffness significantly increased the safety factor of the wall’s stability during the excavation operation; however, following the excavation operation, it did not have such a marked effect on increasing the factor any longer. This indicated that bending stiffness played a major role in wall stability during excavation operations; however, the effect of stiffness on wall stability should be ignored when using the geogrid during excavations.

As shown by parametric studies, following excavation operations under static conditions, it is shown that the safety factor of the wall’s stability increased with the increase of the nails’ angles from 0° to 25° before decreasing after 25°. Also, the maximum lateral displacement of the wall in the nailing with an angle of 5° held the lowest value. As a consequence, the optimal angles of the nailing to reduce the maximum lateral displacement of the wall and to increase the safety factor of the wall’s stability were 5° and 25°, respectively. However, the safety factor of the wall’s stability and the maximum lateral displacement of the wall (in composite nailing and anchoring systems), with the anchors positioned at the low end of the middle layer, held the highest and the lowest values, respectively. Thus, the optimal positioning of the anchor was at the low end of the middle layer.

Under seismic conditions (following the simulation of the 1990 Upland Earthquake), parametric studies showed that the safety factor of the wall’s stability increased with increasing the angle of the nails from 0° to 25° before decreasing after 25°. Also, the maximum lateral displacement of the wall in the nailing with an angle of 10° held the lowest value. This suggested that the optimal angles to reduce the maximum lateral displacement of the wall and to increase the safety factor of the wall’s stability were 10° and 25°, respectively. The safety factor of the wall’s stability and the maximum lateral displacement of the wall (in composite nailing and anchoring systems), with the anchors positioned at the low end of the middle layer, held the highest and the lowest values, respectively. Thus, the optimal positioning of the anchor was at the low end of the middle layer.

According to the optimal lengths of the nails and the anchors, as well as the optimal horizontal and vertical spacing of the nails and the anchors, it is recommended to provide optimal axial and bending stiffness for nails.

REFERENCES

1. Elias, V. and Juran, I., 1991, Soil Nailing for Stabilization of Highway Slopes and Excavations, Report FHWA-RD-89-198, Federal Highway Administration, U.S. Department of Transportation, Washington, DC, U.S.A.

2. Sabhahit, N., Basudhar, P.K. and Madhav, M.R., 1995, A generalized procedure for the optimum design of nailed soil slopes, Int J Numer Anal Meth Geomesh.

3. Lang, T.A., 1961, Theory and practice of rockbolting, Transactions of American Institute of Mining, Metallurgical, and Petroleum Engineers, 220, pp. 333-348.

4. J.A.R., Palmeira, E.M. and Zirlis, A.C., 1995, EXPERIENCE WITH SOIL NAILING IN BRAZIL: 1970-1994, PROCEEDINGS OF THE INSTITUTION OF CIVIL ENGINEERS: GEOTECHNICAL ENGINEERING, 113(2), pp. 93-106.

5. Fan, C.C. and Luo, J.H., 2007, Numerical study on the optimum layout of soil-nailed- slopes.

6. Jewell, R.A., 1980, Some effects of reinforvement on the mechanical behavior of soil, Doctor of Philosophy Thesis, Cambridge University.

7. Shafiee, S., 1986, Simulation Numérique de Comportement des Sols Cloues; Interaction Sol-Renforcement et Comportement de L’ouvrage, Ph.D. Dissertation, ENPC, Paris

8. Meenal, G., Saran, S. and Mittal, S., 2009, Pseudo-Static Analysis of Soil Nailed Excavations, Geotechnical and Geological Engineering, 27(4), pp. 571-583

9. Babu, G.L.S. and Singh, V.P. (2009), Plaxis Practice-Simulation of soil nail structures using Plaxis 2D, Plaxis Bulletin.

10. Plaxis, PLAXIS 2D: Reference Manual, Plaxis BV, Delft, The Netherlands.