applied sciences

Article An Experimental Study of a Nailed Slope: Effects of Surcharge Loading and Nails Characteristics

Mahmoud H. Mohamed 1 , Mohd Ahmed 1,*, Javed Mallick 1 and Pham V. Hoa 2

1 Civil Engineeg Department, College of Engineering, K. K. University, Abha 61421, Saudi Arabia; [email protected] (M.H.M.); [email protected] (J.M.) 2 Ho Chi Minh City Institute, Vietnam Academy of Science and Technology, Ho Chi Minh City 008428, Vietnam; [email protected] * Correspondence: [email protected]; Tel.: +966-172-418-439

Abstract: The earth nailing system is a ground improvement technique used to stabilize earth slopes. The behavior of the earth nailing system is dependent on soil and nailing characteristics, such as the spacing between nails, the orientation, length, and method of installation of nails, soil properties, slope height and angle, and surcharge loading, among others. In the present study, a three-dimensional physical model was built to simulate a soil nailed slope with a model scale of 1:10 with various soil nail characteristics. The simulated models consist of Perspex strips as facing and steel bars as a reinforcing system to stabilize the soil slope. beds in the model were formed, using a sand raining system. The performance of nailed soil slope models under three important nails characteristics, i.e., length, spacing and orientation, with varying surcharge loading were studied. It was observed that there is a reduction in the lateral movement of slope and footing settlements

 with an increase in length. It was found that the slope face horizontal pressure is non-linear with  different nail characteristics. The increase in length and inclination of the soil nails decreased the

Citation: Mohamed, M.H.; Ahmed, vertical, horizontal stress and footing settlement, while the increase in spacing of the nails increased M.; Mallick, J.; Hoa, P.V. An the vertical and horizontal stress behind the soil mass. Experimental Study of a Nailed Soil Slope: Effects of Surcharge Loading Keywords: soil nailing system; nails characteristics; soil slope; surcharge loading; nails orientation and Nails Characteristics. Appl. Sci. 2021, 11, 4842. https://doi.org/ 10.3390/app11114842 1. Introduction Academic Editor: Daniel Dias The soil nailing system is a technique for stabilizing earth slopes and it is constructed in successive phases, as first illustrated by Stocker et al. [1], from top to bottom as ex- Received: 24 April 2021 cavation proceeds. A soil-nailed slope consists of three main elements, namely, the soil, Accepted: 19 May 2021 Published: 25 May 2021 steel reinforcements bars (nails), and the facing. The elements’ composite interactions determine the deformations and stability behavior of a soil nailing system. The shear and

Publisher’s Note: MDPI stays neutral tensile strengths of the reinforcing element will increase the overall and with regard to jurisdictional claims in self-supportability of the in situ soil. The function of the facing in a soil nailing system published maps and institutional affil- is to ensure the local stability of the ground between the nails and to limit its decom- iations. pression; the facing should be flexible enough to withstand ground displacement during excavation [2]. Sharma et al. [3] have thoroughly reviewed the advancements in the soil nailing technique, different installation processes, failure modes of soil-nailed structures, design philosophies, effects of various construction parameters on the design method, and the analytical, numerical, field and lab testing procedures in the nails’ pull-out capac- Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. ity. Lazarte et al. [4] submitted state-of-the-art practice documents (NCHRP Project 24–21) This article is an open access article related to the analysis, LRF design, and construction of soil-nailed walls for highway appli- distributed under the terms and cations. The accuracy of the pull-out capacity of the nails will result in the economical and conditions of the Creative Commons safe design of the soil-nailed structure [5]. Yelti [6] analyzed and designed soil nailed walls Attribution (CC BY) license (https:// in expansive and the recommended guidelines to improve the design procedures for creativecommons.org/licenses/by/ soil-nailed walls, considering the lateral pressures generated by soil expansion. A simpli- 4.0/). fied method to determine the movement at the crest of a soil nailed wall is developed by

Appl. Sci. 2021, 11, 4842. https://doi.org/10.3390/app11114842 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, 4842 2 of 28

Bridges et al. [7] who concluded that soil effective has the greatest effect on crest displacement of the wall. Centrifuge and numerical tests were conducted by Viswanadham and Rotte [8] to study the significance of slope facing on the stability and deformation behavior of soil-nailed slopes subjected to seepage. They found that soil-nailed slopes without facing experience face failure due to bearing failure at the slope surface and the nail head surface as as due to the build-up of excess at the toe region. The influence of the bending stiffness of the facing material—installed on a nailed slope surface of dense sand—on deformation and characteristics were studied by Kotake and Sato [9] by conducting tests on rigid and flexible models of footings. Several nailed soil-retaining structures were instrumented to establish a database for the evaluation of structure performance and development of reliable design methods. The material point method-based numerical model was developed by Ceccato et al. [10] to study the application of plate anchors for stabilization. The numerical model was validated with the results of some small-scale laboratory tests. Sahoo et al. [11] caried out the shaking table tests to study the seismic behavior of nailed soil slopes. They found that the model nailed slope with a nail inclination of 15◦ provided a better reinforcement action than the horizontal and 30◦ inclined nails when stabilizing soil slopes. The failure modes of the slope stabilized by a frame beam with prestressed anchors were studied by Zhang et al. [12] on a large-scale shaking table. They observed that the seismic damage of the slope stabilized by the frame beam with prestressed anchors mainly occurs at the top of the sliding mass and on the free surface of the slope. A simplified limit equilibrium method is presented by Deng et al. [13] to analyze the stability of slopes reinforced with anchor cables, considering the nonlinear Mohr–Coulomb strength criterion for shear failure of the slip surface. The seismic design of the soil nailing was carried out by Villalobos et al. [14] with varying geometrical and mechanical parameters for the nail and soil of a slope. They observed that the global factor of safety increased with soil cohesion and as well as the nail length, diameter and inclination; nail inclinations higher than 15◦ reduced the factor of safety. Yuan et al. [15] proposed a new approach for the stability analysis of soil-nailed walls and concluded that the shear strength of soil has a significant effect on the factor of safety and the reliability index of soil-nailed walls. Durguno˘gluet al. [16] presented the performance of very deep, temporary soil-nailed walls constructed in a very seismically active region. The displacement data for various projects were evaluated in terms of various design parameters of the soil-nailed walls and the excavation depth. Babu and Singh [17] studied the performance of a soil-nailed wall supporting a vertical slope under both static and seismic conditions by observing and computing the maximum lateral displacements, development of nail forces and failure modes of soil-nailed walls. Numerical analyses of the stabilizing mechanisms of loose fill slopes were carried out by Cheuk et al. [18] to study the influence of hybrid nail orientations on the behavior of the ground nailing system and concluded that the hybrid nail arrangement would limit slope movement and enhance the robustness of the system. Taule [19] applied Bishop’s Simplified Method to evaluate and rank the sensitivity of the soil properties, namely cohesion, unit weight and internal friction angle, with respect to the global factor of safety, using the Monte Carlo simulation in a soil nailing design. He showed that the internal friction angle is the most sensitive parameter, while cohesion and unit weight are less sensitive with respect to the global safety factor. Jayawickrama et al. [20] developed non-destructive test methods for evaluation and checking the integrity of installed soil nails. Villalobos et al. [21] present the re-assessment stability analysis of soil nailing design and construction in heavily weathered granite (residual soil), using a limit equilibrium sliding block method (bi-linear failure surface). They found that even after a maximum acceleration of 0.63 g of a stronger , the nailed wall did not show any damage, probably due to the use of undrained shear strength parameters. Alhabshi [22] studied the hybrid, mechanically stabilized earth and soil nail wall system and proposed the optimum length of nails required to stabilize the structure Appl. Sci. 2021, 11, 4842 3 of 28

and reduce the wall deformation. A of a combined system of soil nails and stabilization piles on soil is presented by Wu et al. [23]. Benayoun et al. [24] proposed the optimization of soil nailing parameters for soil-nailed structure design, using the genetic algorithm method. A composite –soil nailed symmetrical pit was numerically investigated by Han et al. [25] for stability and deformation characteristics. They found the critical values of inclination and spacing of the soil nails, and the diameter and embedded depth of the mixing pile for stability of the foundation pit. Despite the numerous research studies on soil nailing system behavior, laboratory modeling studies of various soil nailing system parameters are not sufficient and further parametric study under varying surcharge loading is clearly needed. The present paper studies the performance of soil-nailed slope physical models with varying nail parameters and surcharge loading. Three important nail parameters, namely, the length of the nail, the nails spacing and the angle, were selected for the study; the effect of the length, spacing and orientation of nails on the force mobilized in the nail, lateral displacement of the slope, settlement of the footing and the earth pressure at the slope face, under and behind the soil mass at various surcharging loading were observed. Four nail lengths, 0.5 H, 0.75 H, 1 H and 1.2 H in multiples of slope height (H), three nail orientations, i.e., 00, 50, and 100, and two horizontal and vertical spacings, i.e., 0.2 H and 0.4 H, were considered in the study. The surcharge pressure varied from 5.0, 10.0, 20.0, to 30.0 kPa. The results of the models without the nails were also obtained. The results for the lateral displacement and footing settlement are presented in terms of percentage of slope height.

2. Experimental Methodology The present research study was carried out by designing and developing a three- dimensional experimental model of a dry sand slope with a steel nailing system. The experimental model—its dimensions, state of stress and strain, enclosing walls—were designed so that its performance would simulate the prototype behavior.

2.1. Testing Tank Dimensions The dimensions of the testing tank and its material were chosen to fulfil the following criteria. • The scale factor of 10 for simulation and dimensional analysis and to handle the material easily. • The plane strain condition and minimum friction effect between the backfill soil and the sides of the testing tank. • The pressure isobars of the strip footing extend laterally to almost two times the footing width, from the center line of the footing, and extend deeply to five times the footing width. • The extent of the potential failure surface of slope stability analysis, using the slices method with no influence of tank boundaries on the tested elements: sand, nails, facing wall and the footing. • The coefficient of the material friction is controlled by using the Perspex plates. • A large ratio of width to height of the tank to minimize the effect of side wall shear stresses and consequently, reduce the active earth pressure. Considering the above criteria for the material and dimensions of the tank, an open frontal Perspex box measuring 1760 × 850 × 1000 mm was chosen as the experimental model. The loading system used in this research work is specially designed to prevent any disturbance to the experimental model and is shown in Figure1. The loading system consisted of the loading frame, loading frame base and hydraulic loading system. The box contained the nailed slope of 2250 kg of dry sand and steel bar nails. The sand used in the slope model experiments was air-dried, clean, siliceous yellow sand. The physical and mechanical properties of the sand used are given in Table1. The sand bed in the model was formed, using an automatic sand raining system to control the soil density. Appl. Sci. 2021, 11, x FOR PEER REVIEW 4 of 30

Appl. Sci. 2021, 11, 4842 mechanical properties of the sand used are given in Table 1. The4 ofsand 28 bed in the model was formed, using an automatic sand raining system to control the soil density.

Figure 1. Sand filled tank and testing loading frame with base. Figure 1. Sand filled tank and testing loading frame with base. Table 1. Soil model properties. Table 1. Soil model properties. Property Value % of clayProperty Value 0.00 % of silt 1.33 % of fine% sand of 0.00 39.17 % of medium sand 58.63 % of coarse% sand of silt 1.33 0.87 % of fine% gravelof fine sand 39.17 0.00 Effective diameter (D10) mm 0.126 Coefficient% of of uniformity medium (Cu) sand 58.63 1.99 Coefficient% of gradationof coarse (Cu )sand 0.87 1.00 Specific gravity (Gs) 2.62 3 Minimum unit weight% of ( γfinemin) (kN/mgravel) 0.0015.30 3 Maximum unit weight (γmax) (kN/m ) 17.80 Effective diameter (D10) mm 0.126 Minimum (emin) 0.472 MaximumCoefficient void ratio of (euniformitymax) (Cu) 1.99 0.712 Relative Density (Dr) (%) 48 AngelCoefficient of internal friction of gradation (φ◦) (Cu) 1.00 34 γ 3 Unit weightSpecific ( b) (kN/m gravity) (Gs) 2.6216.41 Void ratio (e) 0.597 Minimum unit weight (γmin) (kN/m3) 15.30 3 TheMaximum thickness ofunit the Perspexweight plate (γmax as) a(kN/m wall facing) in the17.80 model was 5 mm to sim- ulate the shotcreteMinimum facing withvoid a thicknessratio (emin of 140) mm. A steel0.472 rigid plate of dimensions 840 × 150 × 22 mm thick was used as a footing to give distributed load on the soil. The Maximum void ratio (emax) 0.712 properties of the facing and footing are given in Table2. The diameter of the model nails was 5 mm to simulateRelative the Density actual nail (D of diameterr) (%) of 50 mm. The48 properties of the adopted nails were asAngel follows. of internal friction (ϕ°) 34 TableUnit 2. Facing weight and footing (γb) plate (kN/m properties.3) 16.41

Void ratio (e) 0.597Bending Axial Thickness Plate Element Material Width (mm) Young’s Modulus Stiffness Stiffness (mm) (kN.mm2) (kN) The thickness of the Perspex plate as a wall facing in the model was 5 mm to simulate Footing Steel 150 22.0 21.2 × 107 188,186.6 4665.78 Facing Perspex platethe shotcrete 140 facing 5.0with a thickness 4200 of 140 mm. 0.04375 A steel rigid 0.021 plate of dimensions 840 × 150 × 22 mm thick was used as a footing to give distributed load on the soil. The properties of the facing and footing are given in Table 2. The diameter of the model nails was 5 mm to simulate the actual nail of diameter of 50 mm. The properties of the adopted nails were as follows. Young’s modulus (E) = 21.2 × 107 kPa; flexural rigidity (EI) = 6.51 × 10−3 kPa/m. Normal stiffness (EA) = 4165.9 kN/m; maximum tensile strength = 8.8 × 105 kPa. Strains at ultimate stress = 7625; maximum tensile force = 17.36 kN

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Young’s modulus (E) = 21.2 × 107 kPa; flexural rigidity (EI) = 6.51 × 10−3 kPa/m. Normal stiffness (EA) = 4165.9 kN/m; maximum tensile strength = 8.8 × 105 kPa. Strains at ultimate stress = 7625; maximum tensile force = 17.36 kN.

2.2. Testing Procedure The testing of the experimental model was carried out in the following steps to match the true construction sequence as closely as possible to that in the field. This is due to the excavation of the soil, the construction of the slope soil nailing system and the subsequent placement of the surcharge load. • The tank is cleaned, which has movable rear doors fixed with an opening to pass the tube containing the nails. The rest of the doors, in the rear and front sides, are in a closed position. • The sand spreader forms the first layer of the sand and it is leveled, or compacted and leveled, as desired, to get the required predetermined density as was previously explained. This layer is a base sand layer, and its thickness was 150 mm. • The lower middle nails with tubes are fixed in their positions. • The hopper of the sand spreader forms the second layer and is leveled, or compacted and leveled, again, to reach the required density. • In each layer, the horizontal and vertical pressure cells are installed in its predeter- mined positions. • The above three steps are repeated until the tank is filled up. • When the tank is filled with sand, the model is ready to begin the test. To simulate the actual behavior of the prototype model, the test was divided in two stages. The first stage was the excavation stage to make sand slope and the second was the loading stage. This was done as follows and is depicted in Figure2. • The first layer of the sand, 140 mm thick, is excavated. • The first paneled face is placed, which includes pressure cells flush with the middle of the panel, and this panel is held with two polyethylene strips (sticky tape) at the sides of the box to prevent sand spilling from the gap between the edges of the slope face unit and the box sides. • The first row of the strain gauge fitted nails is installed in its position, tight to the nail face with nuts by pushing the nail into the sand. • Dial gauges are installed to record the displacements of the facing due to excavation the second layer. • In the case of inclined nails, the nails are hammered at the required inclined angle by means of a wooden plate with 20 mm thickness a 12 mm metal tube aligned at the predetermined holes as shown in Figure3. • Another four layers of the sand, 140 mm thick, are excavated and the facing panels are installed as before. At the third and fifth layers, a row of nails and pressure cells are installed. • In each stage, displacement of the face, tensile force in the nails, and pressure (hori- zontal and vertical) are recorded. • As the excavation is completed to the final depth of 700 mm, the rigid footing is placed at the required location from the nailed slope crest at the top surface and leveled by a water bulb level and then loaded to the required pressure. • LVDTs are installed to measure the settlement of the footing. The electrical strain gauge reading is recorded simultaneously with the LVDTs and pressure cells in each loading case. Horizontal stresses on the wall face, pressure distribution under the reinforced mass, and the horizontal pressure behind the reinforced mass are measured by means of 5 soil pressure transducers, namely, 1, 2, 3, 4, 5, and 6 miniature strain gauge cells and local pressure cell transducers, namely, 2 L, 3 L, 4 L, 5 L, 7 L, 8 L which were designed, manufactured, and calibrated by the authors. Appl. Sci. 2021, 11, x FOR PEER REVIEW 6 of 30 Appl. Sci. 2021, 11, x FOR PEER REVIEW 6 of 30

reinforced mass, and the horizontal pressure behind the reinforced mass are meas- reinforced mass, and the horizontal pressure behind the reinforced mass are meas- ured by means of 5 soil pressure transducers, namely, 1, 2, 3, 4, 5, and 6 miniature ured by means of 5 soil pressure transducers, namely, 1, 2, 3, 4, 5, and 6 miniature strain gauge cells and local pressure cell transducers, namely, 2 L, 3 L, 4 L, 5 L, 7 L, 8 Appl. Sci. 2021, 11, 4842 strain gauge cells and local pressure cell transducers, namely, 2 L, 3 L, 4 L, 5 L, 7 L, 8 6 of 28 L which were designed, manufactured, and calibrated by the authors. L which were designed, manufactured, and calibrated by the authors.

Figure 2. Construction stages of the slope-nailed system. Figure 2.Figure Construction 2. Construction stages of stages the slope of the-nailed slope-nailed system. system.

FigureFigure 3.3. ConstructionConstruction ofof thethe inclinedinclined nail.nail. Figure 3. Construction of the inclined nail. 3.3. Results and Discussion 3. Results and Discussion InIn thethe presentpresent study,study, thethe experimentalexperimental modelsmodels withwith aa soilsoil slopeslope ofof 700700 werewere preparedprepared In the present study, the experimental models with a soil slope of 700 were prepared withwith fourfour nailsnails lengths,lengths, 0.50.5 H,H, 0.750.75 H,H, HH andand 1.21.2 H,H, inin multiplesmultiples ofof slopeslope heightheight (H),(H), threethree with four nails lengths, 0.5 H,◦ 0.75◦ H, ◦H and 1.2 H, in multiples of slope height (H), three nailnail orientations,orientations, i.e.,i.e., 00°,, 55°,, 1010°, and two horizontalhorizontal andand verticalvertical spacings,spacings, i.e.,i.e., 0.20.2 HH andand nail orientations, i.e., 0°, 5°, 10°, and two horizontal and vertical spacings, i.e., 0.2 H and 0.40.4 H. The horizontal horizontal nails nails were were used used with with equal equal horizontal horizontal and and vert verticalical spacing spacing,, i.e., i.e., 0.4 0.4 H. The horizontal nails were used with equal horizontal and vertical spacing, i.e., 0.4 0.4H, Hfor, forthe the parametric parametric study study besides besides the the inclined inclined nail nail slope slope behavior. behavior. The The results ofof thethe H, for the parametric study besides the inclined nail slope behavior. The results of the modelsmodels withoutwithout thethe nailsnails werewere alsoalso obtained.obtained. TheThe displacementdisplacement ofof thethe slope,slope, forceforce inin thethe models without the nails were also obtained. The displacement of the slope, force in the nail,nail, settlementsettlement ofof thethe footingfooting andand thethe earthearth pressurepressure inin thethe backfillbackfill soilsoil duedue toto thethe nailingnailing nail, settlementparameters of the (nail footing length, and inclination the earth and pressure spacing) in the were backfill measured soil due and to the the obtained nailing results are discussed below. The lateral displacement of the nailed slope facing were recorded with 3 dial gauges at three measurements points, A, B and C, at distances of Z = 70, 350, and 630 mm from the top surface. These distances are expressed as 0.1 H, 0.5 H, and 0.9 H. Pressure cells were mounted flush with the back of the slope face in special arrangement to Appl. Sci. 2021, 11, x FOR PEER REVIEW 7 of 30

parameters (nail length, inclination and spacing) were measured and the obtained results are discussed below. The lateral displacement of the nailed slope facing were recorded with 3 dial gauges at three measurements points, A, B and C, at distances of Z = 70, 350, and 630 mm from the top surface. These distances are expressed as 0.1 H, 0.5 H, and 0.9 H. Pressure cells were mounted flush with the back of the slope face in special arrange- Appl.ment Sci. 2021to ,measure11, 4842 the horizontal pressure as shown in Figure 4 at points A, B, and C. The7 of 28 readings were measured after each increment of footing pressure from 5.0, 10.0, 20.0, to 30.0 kPa. measure the horizontal pressure as shown in Figure4 at points A, B, and C. The readings were measured after each increment of footing pressure from 5.0, 10.0, 20.0, to 30.0 kPa.

FigureFigure 4. 4.ExperimentalExperimental models models with with different different nail parameters. nail parameters H—Excavation. H height;—Excavation B—Footing width;height; Sv—Nail B—Footing vertical spacing; Sh—Nail horizontal spacing; Ln—Nail length; q—Surcharge; δ—Inclination of the nail; X—Distance of footing width; Sv—Nail vertical spacing; Sh—Nail horizontal spacing; Ln—Nail length; q—Surcharge; δ— from crest; θ—Slope angle; RD—Relative density of the sand. Inclination of the nail; X—Distance of footing from crest; θ—Slope angle; RD—Relative density of the sand. 3.1. Length of Nails 3.1.1. Lateral Movement of the Soil Nailing Slope 3.1. Length of Nails The lateral movement of the slope face with and without the nailing system during the loading stages is shown in Figure5. The figure depicts that, in general, the lateral 3.1.1. Lateral Movementmovement of the Soil of the Na slopeiling in the Slope middle third is higher than the top and bottom third and it has the lowest value at the toe of the slope. The maximum lateral displacement of the slope The lateral movementis in the of top the upper slope portion face when with the and length without is more than the the nailing slope height system or at during least equal the loading stages is shownto the slope in height,Figure but 5. it shiftsThe tofigure the middle depicts of the that slope, whenin general, the nail length the lateral is reduced movement of the slopeto in the the slope middle height. Thethird maximum is higher displacement than the with top different and bot nailtom lengths third is observed and it at the middle third of the slope, except with the nail length of 1.20 H wherein the maximum has the lowest value at horizontalthe toe of movement the slope. is at The theupper maximum third of thelateral slope. displacement of the slope is in the top upper portionFigure when6 showsthe length the relation is more between than the the nail slope length height and horizontal or at least movement equal at to the slope height, butdifferent it shifts nail to lengths the middle at the center of the of the slope slope (atwhen point the B). Innail general, length the presenceis reduced of nails decreases the lateral movement. The installation of nails mobilizes friction stresses around to the slope height. Thethe maximum sand and the displacement surface of the nail. with These different friction stresses nail lengths prevent lateral is observed movement. at By the middle third of theincreasing slope, except the length with of the the nail, nail the length total value of of 1.20 the shearH wherein stresses between the maximum the sand and horizontal movement isnail at increases. the upper The lateralthird movement of the slope. decreases rapidly when the nail length increases from 0.3 H to 0.75 H; however, further increases in the nail length, for example, up to 1.2 H, will Figure 6 shows thenot relation help in decreasing between the the lateral nail movement length ofand the slope.horizontal This may movement be attributed at to thedif- fact ferent nail lengths at thethat center an increase of inthe the slope nail length (at point is effective B). upIn to general, a certain limit,the i.e.,presence when the of nail nails length decreases the lateral movement.lies in a stable The zone installation (inside the surface of nails of failure). mobilizes friction stresses around the sand and the surface3.1.2. of Footing the nail. Settlement These friction stresses prevent lateral movement. By increasing the length of theThe nail, foundation the total settlements value of were the measured shear stresses at three pointsbetween on the the footing sand and and then nail increases. The lateralthe average movement value was dec presented.reases rapidly The footing when settlements the nail were length measured increases by means of three LVDTs. The footing settlements were measured at each surcharge load increment. from 0.3 H to 0.75 H; however,Figure7 presents further the footing increases settlement in the in termsnail oflength the fraction, for example of the slope, heightup to (S/H), 1.2 H, will not help in decreasingi.e., vertical the settlement/slope lateral movement height, for differentof the slope. nail lengths This at differentmay be footing attributed pressures. to the fact that an increaseIt is clear in the from nail the figurelength that is the effective footing settlement up to a certain decreases limit, from 12% i.e., to when 51% with the the nail length lies in a stable zone (inside the surface of failure). Appl. Sci. 2021, 11, 4842 8 of 28

increase in the nail length from half of the slope height to a nail length of more than the slope height, with respect to the footing settlement on the slope without nailing. The decrease in footing settlement is not large under a lower footing pressure range, but a large Appl. Sci. 2021, 11, x FOR PEER REVIEWdecrease in the footing settlement is observed with a higher footing pressure. This may be8 of 30 due to the fact that the lateral displacement of the facing slope decreases with the increase in nail length, and this will also result in a lower footing settlement. It can be inferred that the soil nailing system can sustain more surcharge load without failure.

Figure 5. Lateral movement of the slope at different nail lengths. Figure 5. Lateral movement of the slope at different nail lengths. Appl. Sci. 2021, 11, x FOR PEER REVIEW 9 of 30

Appl.Appl. Sci. Sci.2021 2021, ,11 11,, 4842 x FOR PEER REVIEW 9 ofof 2830

Figure 6. Effect of nail length on the horizontal movement of the middle of the slope.

3.1.2. Footing Settlement The foundation settlements were measured at three points on the footing and then the average value was presented. The footing settlements were measured by means of three LVDTs. The footing settlements were measured at each surcharge load increment. Figure 7 presents the footing settlement in terms of the fraction of the slope height (S/H), i.e., vertical settlement/slope height, for different nail lengths at different footing pres- sures. It is clear from the figure that the footing settlement decreases from 12% to 51% with the increase in the nail length from half of the slope height to a nail length of more than the slope height, with respect to the footing settlement on the slope without nailing. The decrease in footing settlement is not large under a lower footing pressure range, but a large decrease in the footing settlement is observed with a higher footing pressure. This may be due to the fact that the lateral displacement of the facing slope decreases with the increase in nail length, and this will also result in a lower footing settlement. It can be inferred that the soil nailing system can sustain more surcharge load without failure. FigureFigure 6.6. EffectEffect ofof nailnail lengthlength onon thethe horizontalhorizontal movementmovement ofof thethemiddle middle of of the the slope. slope.

3.1.2. Footing Settlement The foundation settlements were measured at three points on the footing and then the average value was presented. The footing settlements were measured by means of three LVDTs. The footing settlements were measured at each surcharge load increment. Figure 7 presents the footing settlement in terms of the fraction of the slope height (S/H), i.e., vertical settlement/slope height, for different nail lengths at different footing pres- sures. It is clear from the figure that the footing settlement decreases from 12% to 51% with the increase in the nail length from half of the slope height to a nail length of more than the slope height, with respect to the footing settlement on the slope without nailing. The decrease in footing settlement is not large under a lower footing pressure range, but a large decrease in the footing settlement is observed with a higher footing pressure. This may be due to the fact that the lateral displacement of the facing slope decreases with the increase in nail length, and this will also result in a lower footing settlement. It can be inferred that the soil nailing system can sustain more surcharge load without failure.

Figure 7. Effect of nail lengths on the settlement of the footing. Figure 7. Effect of nail lengths on the settlement of the footing. 3.1.3. Force in the Nail 3.1.3. TheForce axial in the strains Nail in the nails were measured by means of electrical resistance strain gauges.The Eachaxial nailstrains was in instrumented the nails were with measured strain gauges by means on its of upper electrical and lowerresistance faces strain along gauges.its whole Each length. nail was The instrumented distribution ofwith the strain nail tensile gauges force on its at upper different and levelslower offaces the along slope itswith whole the naillength. lengths Theis distribution shown in Figure of the8. nail From tensile these force figures, at itdifferent is seen thatlevels in allof cases,the slope the withdistribution the nail islength non-uniforms is shown and in the Figure forces 8.are From tensile. these The figures, minimum it is seen tensile that force in all occurs cases, at the end of the nails, whereas the maximum tensile force is at the middle third of the nail. The tensile force increases with the increase in the surcharge loading and increasing length. It is also clear that the lower nails have lesser tensile force, as compared with the upper nails, and the middle nails have the maximum tensile force at all loading stages. This may be because the maximum horizontal displacement is at mid height of the slopes, which result in maximum mobilization of the nail tensile force at this level. Figure9 presents the presence of the maximum tensile force in nails of various lengths at different levels. Figure9 shows that there is a linear increase in the maximum tensile forces with an increase in the nail length for the middle nails. However, for the upper and lowerFigure nails, 7. Effect maximum of nail length tensiles on forces the settlement first decrease of the footing with the. increase in nail length, i.e., up to a nail length of three fourths of the slope height, and then the nails’ maximum tensile forces3.1.3. Force increase in the by Nail further increasing the nail length. This may be due to disturbance of the soilThe under axial thestrains footing in the and nails around were the measured nail during by themeans loading of electrical stages in resistance the upper strain and lowergauges. part, Each but nail in thewas middle instrumented portion with of slope, strain the gauges soil moves on its only upper under and steadylower faces expansion. along its whole length. The distribution of the nail tensile force at different levels of the slope with the nail lengths is shown in Figure 8. From these figures, it is seen that in all cases, Appl. Sci. 2021, 11, x FOR PEER REVIEW 10 of 30

the distribution is non-uniform and the forces are tensile. The minimum tensile force oc- curs at the end of the nails, whereas the maximum tensile force is at the middle third of the nail. The tensile force increases with the increase in the surcharge loading and increas- ing length. It is also clear that the lower nails have lesser tensile force, as compared with the upper nails, and the middle nails have the maximum tensile force at all loading stages. This may be because the maximum horizontal displacement is at mid height of the slopes, Appl. Sci. 2021, 11, 4842 10 of 28 which result in maximum mobilization of the nail tensile force at this level.

(Axial tensile force × 10−2 kN)

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FigureFigure 8. Distribution 8. Distribution of of the the nail nail force force at differentdifferent levels levels and and nail nail lengths. lengths.

Figure 9 presents the presence of the maximum tensile force in nails of various lengths at different levels. Figure 9 shows that there is a linear increase in the maximum tensile forces with an increase in the nail length for the middle nails. However, for the upper and lower nails, maximum tensile forces first decrease with the increase in nail length, i.e., up to a nail length of three fourths of the slope height, and then the nails’ maximum tensile forces increase by further increasing the nail length. This may be due to disturbance of the soil under the footing and around the nail during the loading stages in the upper and lower part, but in the middle portion of slope, the soil moves only under steady expansion.

FigureFigure 9. 9. EffectEffect of nailnail length length on on maximum maximum tensile tensile force force in the in nail the at nail different at different levels. levels.

3.1.4. Horizontal Stresses on the Slope Face Figure 10 presents the distribution of the horizontal stresses on the slope face with different nail lengths. The figure shows that the minimum horizontal stresses at the slope face occur at the bottom and upper levels, whereas the maximum horizontal stresses are at the mid height of the slope; the footing pressure increases the horizontal stresses at the slope face. Appl. Sci. 2021, 11, 4842 11 of 28

3.1.4. Horizontal Stresses on the Slope Face Figure 10 presents the distribution of the horizontal stresses on the slope face with different nail lengths. The figure shows that the minimum horizontal stresses at the slope Appl. Sci. 2021, 11, x FOR PEER REVIEWface occur at the bottom and upper levels, whereas the maximum horizontal stresses12 are of 30

at the mid height of the slope; the footing pressure increases the horizontal stresses at the slope face.

FigureFigure 10 10.. DistributionDistribution of of the the slope slope face face horizontal horizontal stressesstresses atat different different nail nail lengths. lengths.

Figure 11 represents the influence of the nail length on the horizontal stresses at the slope face at the middle of the slope without surcharge loading and at a footing pressure of 30.0 kPa. It is clear from the figure that the percentage increases in horizontal stresses at the slope face range from 19.2% to 30.3% with the inclusion of nails and with the in- crease in nail length. This may be due to small, lateral displacements of the slope face with longer nails, producing larger horizontal stresses at the slope face. Appl. Sci. 2021, 11, 4842 12 of 28

Figure 11 represents the influence of the nail length on the horizontal stresses at the slope face at the middle of the slope without surcharge loading and at a footing pressure of 30.0 kPa. It is clear from the figure that the percentage increases in horizontal stresses at

Appl. Sci. 2021, 11, x FOR PEER REVIEWthe slope face range from 19.2% to 30.3% with the inclusion of nails and with the increase13 of 30 in nail length. This may be due to small, lateral displacements of the slope face with longer nails, producing larger horizontal stresses at the slope face.

FigureFigure 11. 11. InfluenceInfluence of of nail nail length length on on the the slope slope face face horizontal horizontal stresses stresses at at mid mid height height of of slope slope..

3.1.5.3.1.5. Vertical Vertical Stress Stress under under Nailed Nailed Soil Soil Mass Mass FigureFigure 12 12 presents presents the the distribution distribution of of the the vertical vertical stresses stresses under under the the nailed nailed soil soil mass mass withwith different different nail length lengthss under differentdifferent surchargesurcharge loadingloading at at three three selected selected points, points D,, D, E, E,and and F (pointF (point D isD nearis near the the toe), toe) at a, levelat a level of 150 of mm 150 from mm thefrom bottom the bottom of the tankof the at tank various at variousdistance distance ratios (T/H), ratios (T/H), i.e., distance i.e., distance from slopefrom slope toe/slope toe/slope height. height. From From these these figures, figures, it is itseen is seen that that the magnitude the magnitude of the of vertical the vertical stresses stresses under under the nailed the nailed soil mass soil is mass at a greater is at a greaterdistance distance from the from slope the face;slope increaseface; increase in the in surcharge the surcharge load load leads leads to an to increase an increase inthe in thevertical vertical stresses stresses under under the the nailed nailed soil soil mass, mass especially, especially at at a a farfar pointpoint from the slope face face becausebecause it it lies lies almost almost directly directly under under the the footing footing width. width. This Thismay maybe attributed be attributed to the topres- the encepresence of nails of nails in the in thesoil soilmass mass,, making making the the slope slope behave behave asas a acoherent coherent mass. mass. The The figures figures alsoalso show show that thethe observedobserved distribution distribution of of vertical vertical stresses stresses under under the the nailed nailed soil masssoil mass with withdifferent different nail lengthsnail length is similar,s is similar and, the and effect the effect is small is small on vertical on vertical stresses stresses under under the nailed the nailedsoil mass soil withmass different with different nail lengths. nail lengths. 3.1.6. Horizontal and Vertical Stress behind the Nailed Soil Mass Figures 13 and 14 present the distribution of the horizontal and vertical stresses behind the soil mass with different nail lengths and with different footing loadings. From the figures, it is seen that the maximum horizontal and vertical stresses behind the soil mass occur at the lower measured point, whereas the minimum is at the upper measured point. There is no significant effect of the nail length on the horizontal and vertical stresses behind the nailed soil mass. Due to the application of the footing pressure, the soil starts to move, tensile stresses in the soil are transferred to the nails, and the nails hold the soil mass in position. The soil mass behind the nails behaves as a gravitational wall, and horizontal pressure develops in the soil mass, increasing at the lower part almost similarly to the hydrostatic pressure. Appl.Appl. Sci. Sci. 20212021, 11, ,11 x ,FOR 4842 PEER REVIEW 14 of13 of30 28

FigureFigure 12. 12. DistributionDistribution of ofvertical vertical stresses stresses under under the the soil soil mass mass at atdifferent different nail nail length length.. Appl. Sci. 2021, 11, x FOR PEER REVIEW 15 of 30

3.1.6. Horizontal and Vertical Stress behind the Nailed Soil Mass Figures 13 and 14 present the distribution of the horizontal and vertical stresses be- hind the soil mass with different nail lengths and with different footing loadings. From the figures, it is seen that the maximum horizontal and vertical stresses behind the soil mass occur at the lower measured point, whereas the minimum is at the upper measured point. There is no significant effect of the nail length on the horizontal and vertical stresses behind the nailed soil mass. Due to the application of the footing pressure, the soil starts to move, tensile stresses in the soil are transferred to the nails, and the nails hold the soil mass in position. The soil mass behind the nails behaves as a gravitational wall, and hor- Appl. Sci. 2021, 11, 4842 izontal pressure develops in the soil mass, increasing at the lower part14 almost of 28 similarly to the hydrostatic pressure.

Figure 13. Distribution of horizontal stresses behind the soil mass at different nail lengths. Figure 13. Distribution of horizontal stresses behind the soil mass at different nail lengths. Appl.Appl. Sci. Sci.2021 2021, 11, 11, 4842, x FOR PEER REVIEW 1516 ofof 2830

FigureFigure 14. 14.Distribution Distribution of of vertical vertical stresses stresses behind behind the the soil soil mass mass at at different different nail nail lengths. lengths. Appl. Sci. 2021, 11, x FOR PEER REVIEW 17 of 30 Appl. Sci. 2021, 11, 4842 16 of 28

3.2. Inclinations of Nails 3.2. Inclinations of Nails 3.2.1.3.2.1. Lateral Movement of of the the Soil Soil Nailing Nailing Slope Slope Figure 1515 representsrepresents thethe effectseffects ofof thethe nail nail inclinations inclinations on on the the horizontal horizontal movement movement of theof the slope slope face face with with and and without without footing footing pressure. pressure. TheThe laterallateral displacements ratio ratio (D/H) (D/H) atat thethe mid height of the slope is taken for for different different nail nail inclination inclinations.s. It It is is evident evident from from the the figuresfigures thatthat the increase in the inclination inclination of of the the nails nails result resultss in in a a decrease decrease in in the the horizontal horizontal movementmovement ofof thethe slope slope face. face The. The percentage percentage decrease decrease in lateralin lateral movement movement with with the increasethe in- increase surcharge in surcharge loading loading and nail and inclination nail inclination ranges range froms 7.1% from to 7.1% 25.0%. to 25.0%.

FigureFigure 15. InfluenceInfluence of nail inclination inclination on on the the horizontal horizontal movement movement at at mid mid height height of of slope slope..

3.2.2.3.2.2. Footing Settlement The footing settlements settlements at at different different nail nail inclination inclinationss are arepresented presented in Figure in Figure 16 at 16dif- at differentferent footing footing pressures. pressures. From From the thefigure, figure, it is itobserved is observed that thatthe footing the footing settlement settlement de- decreasescreases as asthe the nail nail inclination inclination increases increases,, and and the percentage the percentage increases increases with withincreases increases in the in thefooting footing pressure. pressure. The Thepercentage percentage decrease, decrease, with withthe nail the i nailnclination inclination of 00 ofto 00100, to in 100, the in thefooting footing settlement settlement in terms in terms of the of slope the slope height height at lower at lower footing footing pressures pressures is around is around 20%, Appl. Sci. 2021, 11, x FOR PEER REVIEW20%,while while at higher at higher footing footing pressures pressures,, it is around it is around 40%. The 40%. reason The reason may be may due be to due the tofact18 the ofthat fact30

thatthe inclined the inclined tensile tensile force force may maybe resolved be resolved in two in components two components,, resisting resisting the horizontal the horizontal set- settlementtlement and and vertical vertical settlement, settlement, but but horizontal horizontal nails nails resist resist horizontal horizontal settlement settlement only. only.

FigureFigure 16.16. InfluenceInfluence of nail inclination on on the the settlement settlement of of the the footing footing..

3.2.3. Nail Maximum Tensile Force Figure 17 shows the influence of the nail inclination on the maximum tensile force in the nails at different levels of soil slope. It is seen from the figure that with the increase in the nail’s inclination, the maximum tensile force in the nails is increased. In other words, reduction in the nail inclination results in a decrease in the maximum tensile force. A de- crease in the nail maximum tensile force increases with the increase in the footing pressure and nail inclination. A maximum of 35% reduction in the maximum tensile force is ob- served with a 10° nail angle decrease.

Appl. Sci. 2021, 11, x FOR PEER REVIEW 18 of 30

Appl. Sci. 2021, 11, 4842 Figure 16. Influence of nail inclination on the settlement of the footing. 17 of 28

3.2.3. Nail Maximum Tensile Force Figure3.2.3. Nail17 shows Maximum the influence Tensile of Forcethe nail inclination on the maximum tensile force in the nails at different levels of soil slope. It is seen from the figure that with the increase in the nail’s inclination,Figure 17 showsthe maximum the influence tensile force of the in nail the inclinationnails is increased. on the In maximum other word tensiles, force in reductionthe nailsin the at nail different inclination levels results of soil in a slope. decrease It isin seenthe maximum from the tensile figure force. that withA de- the increase creasein in thethe nail nail’s maximum inclination, tensile the force maximum increases with tensile the forceincrease in in the the nails footing is increased.pressure In other and nailwords, inclination. reduction A maximum in the nail of inclination 35% reduction results in the in amaxi decreasemum intensile the maximumforce is ob- tensile force. servedA with decrease a 10° nail in the angle nail decrease. maximum tensile force increases with the increase in the footing pressure and nail inclination. A maximum of 35% reduction in the maximum tensile force ◦ is observed with a 10 nail angle decrease.

Appl. Sci. 2021, 11, x FOR PEER REVIEW 19 of 30

FigureFigure 17. Influence 17. Influence of nail inclination of nail inclination on the maximum on the maximum tensile force tensile of the force footing of.the footing.

3.2.4. Slope Face Horizontal Stress Figure 18 shows the influence of the nail inclination on the slope face horizontal stress at mid height of the slope. It is clear from the figure that as the inclination of the nails increases, the horizontal stresses at the slope face decreases. The surcharge loadings up to 20 kN/m2 with the inclined nail slope has no effect on the slope face horizontal stress. With further increase in surcharge loadings, the slope face horizontal stress decreases with an increase in the nail inclination. Appl. Sci. 2021, 11, 4842 18 of 28

3.2.4. Slope Face Horizontal Stress Figure 18 shows the influence of the nail inclination on the slope face horizontal stress Appl. Sci. 2021, 11, x FOR PEER REVIEW 20 of 30 at mid height of the slope. It is clear from the figure that as the inclination of the nails increases, the horizontal stresses at the slope face decreases. The surcharge loadings up Appl. Sci. 2021, 11, x FOR PEER REVIEW 20 of 30 to 20 kN/m2 with the inclined nail slope has no effect on the slope face horizontal stress. With further increase in surcharge loadings, the slope face horizontal stress decreases with an increase in the nail inclination.

Figure 18. Influence of nail inclination on the slope face horizontal stresses at mid height of slope.

Figure3.2.5.Figure Vertical18. 18.InfluenceInfluence Stress of ofundernail nail inclination inclination Soil Mass on on the slopeslope face face horizontal horizontal stresses stresses at mid at mid height height of slope. of slope. 3.2.5.Figure Vertical 19, which Stress underpresents Soil the Mass observed vertical stresses under the soil mass with dif- 3.2.5. Vertical Stress under Soil Mass ferent nailFigure angles, 19, which clearly presents shows the that observed the nail vertical inclination stresses has under a small the soil effect mass on with vertical stressesdifferent under nail the angles, soilFigure mass clearly 19, and which shows that thatpresents there the is nail athe slight inclination observed increase hasvertical in a smallthe stresses vertical effect onunder stresses vertical the under soil mass with dif- the stressessoil mass under atferent a thehigher soil nail massangle angles, and of inclination that clearly there s ishows of a slight the that nails. increase the With nail in tthehe inclination verticalincrease stresses to has the a undermaximum small effect on vertical constheidered soil mass surchargestresses at a higher underloading, angle the ofthe soil inclination increase mass and ofin the thethat nails. vertical there With is stress a the slight increase is justincrease to 10%. the in maximum the vertical stresses under considered surchargethe soil mass loading, at a higher the increase angle in of the inclination vertical stress of the is justnails. 10%. With the increase to the maximum considered surcharge loading, the increase in the vertical stress is just 10%.

Figure 19. Influence of nail inclination on the slope face vertical stresses at mid height of slope. Figure 19. Influence of nail inclination on the slope face vertical stresses at mid height of slope.

3.2.6.Figure Horizontal 19. Influence and of Verticalnail inclination Stress onbehind the slope Soil face Mass vertical stresses at mid height of slope. Figures 20 and 21 show the influence of nail inclination on the horizontal and vertical 3.2.6. Horizontal and Vertical Stress behind Soil Mass stresses behind the soil mass at the middle of the soil slope. The figures depict that the vertical stress behindFigures the soil 20 andmass 21 decreases show the with influence the increase of nail inclination in the nail onangle. the horizontalWith the and vertical increase in surchargestresses loading,behind the the soildecrease mass inat thethe verticalmiddle stressof the due soil to slope. a larger The nail figures angle depict that the further increases.vertical The stresshorizontal behind stress the behindsoil mass the decreases soil mass with at a lowerthe increase footing in pressure the nail isangle. With the constant underinc differentrease in nailsurcharge inclination loading,s but the at decreasea higher footingin the vertical pressure, stress the due horizontal to a larger nail angle stress considerablyfurther decreases increases. with The the horizontal increase stressin the behind nail inclination. the soil mass at a lower footing pressure is constant under different nail inclinations but at a higher footing pressure, the horizontal stress considerably decreases with the increase in the nail inclination. Appl. Sci. 2021, 11, 4842 19 of 28

3.2.6. Horizontal and Vertical Stress behind Soil Mass Figures 20 and 21 show the influence of nail inclination on the horizontal and vertical stresses behind the soil mass at the middle of the soil slope. The figures depict that the vertical stress behind the soil mass decreases with the increase in the nail angle. With the increase in surcharge loading, the decrease in the vertical stress due to a larger nail angle further increases. The horizontal stress behind the soil mass at a lower footing pressure is Appl. Sci. 2021, 11, x FOR PEER REVIEW 21 of 30 constant under different nail inclinations but at a higher footing pressure, the horizontal stress considerably decreases with the increase in the nail inclination.

Figure 20. InfluenceInfluence of nail inclination on horizontal stresses behindbehind thethe nailednailed soilsoil massmass atat midmid heightheight ofof slope.slope.

Figure 21. InfluencInfluencee of nail inclination on vertical stresses behindbehind thethe nailednailed soilsoil massmass atat midmid heightheight ofof slope.slope.

3.3. Spacing of Nails 3.3.1. Lateral Movement of the Nailed Soil Slope Figure 22 shows the relation between the nails’nails’ spacing and the horizontal movement of the slope at the middle of the slope. The figure figure clearly shows that a decrease in the nailnail spacing results in a decrease in the horizontal movement of the slope face. The percentage decrease in the lateral movement of the slope face decreases with the increase in the foot- ing pressure. This may be due to the increase in the overall stiffness of the nailed soil mass with smaller spacing between the nails. Appl. Sci. 2021, 11, 4842 20 of 28

Appl. Sci. 2021, 11, x FOR PEER REVIEWspacing results in a decrease in the horizontal movement of the slope face. The percentage22 of 30

Appl. Sci. 2021, 11, x FOR PEER REVIEW decrease in the lateral movement of the slope face decreases with the increase22 of in 30 the footing pressure. This may be due to the increase in the overall stiffness of the nailed soil mass with smaller spacing between the nails.

Figure 22. Influence of nail spacing on the horizontal movement at mid height of slope. FigureFigure 22. Influence 22. Influence of nail of nailspacing spacing on the on thehorizontal horizontal movement movement at atmid mid height height of of slope slope.. 3.3.2. Footing Settlement 3.3.2. Footing Settlement 3.3.2. Footing SettlementThe footing settlements for different nails-spacing at various footing pressures are The footinggiven settlementsThe in footing Figure for settlements23. different From the fornails figure, different-spacing it can nails-spacing at be various seen that footing at various the footingpressures footing settlement pressuresare decreases are given in Figuregivenwith 23. inFromthe Figure decrease the 23 figure,. From in nail it the canspacing. figure, be seen it The can that bedecrease seen the thatfooting in thefooting footingsettlement settlements settlement decreases, i decreasesn terms of with the per- the decrease in nail spacing. The decrease in footing settlements, in terms of the percentage with the decreasecentage in nail ratio spacing. of the The slope decrease height in, is footing increased settlements with the, i nincrease terms of in the footing per- pressure and ratio of the slope height, is increased with the increase in footing pressure and decrease in centage ratio ofdecrease the slope in heightnail spacing., is increased The decrease with the in increase footing insettlements footing pressure with decreases and in the nail nail spacing. The decrease in footing settlements with decreases in the nail spacing varies decrease in nail spacing. The decrease in footing settlements with decreases in the nail fromspacing 31.8% varies to 60.0% from at 31.8% various to footing60.0% at pressures. various footing pressures. spacing varies from 31.8% to 60.0% at various footing pressures.

Figure 23. Influence of nail spacing on the settlement of the footing. Figure 23. Influence of nail spacing on the settlement of the footing. Figure 23. Influence of nail spacing on the settlement of the footing. 3.3.3. Nail Maximum Tensile Force 3.3.3. Nail MaximumThe Tensile effect Force of nail spacing on the maximum tensile force in the nails at different levels The effect isof presented nail spacing in Figureon the maximum24 with various tensile footing force in pressur the nailses. Theat different figure depict levelss that increases is presented in inFigure the nail 24 withspacing various increases footing the pressur maximumes. The tensile figure force depict in thes that nails. increases The same effect of the in the nail spacing increases the maximum tensile force in the nails. The same effect of the Appl. Sci. 2021, 11, 4842 21 of 28

3.3.3. Nail Maximum Tensile Force Appl. Sci. 2021, 11, x FOR PEER REVIEW 23 of 30 The effect of nail spacing on the maximum tensile force in the nails at different levels is presented in Figure 24 with various footing pressures. The figure depicts that increases in the nail spacing increases the maximum tensile force in the nails. The same effect of the spacingspacing of of the the nailsnails is visible at at different different footing footing pressure pressures.s. The lower The lower nails have nails lesser have lesser tensile force as compared to the upper nails, while the middle nails have the maximum tensile force as compared to the upper nails, while the middle nails have the maximum tensile force. This may be because the maximum horizontal displacements are at mid tensileheight force. of the slope. This may be because the maximum horizontal displacements are at mid height of the slope.

Figure 24. Influence of nail spacing on the maximum tensile force of the footing. Appl. Sci. 2021, 11, x FOR PEER REVIEW 24 of 30

Appl. Sci. 2021, 11, x FOR PEER REVIEW 24 of 30

Appl. Sci. 2021, 11, 4842 Figure 24. Influence of nail spacing on the maximum tensile force of the footing. 22 of 28

3.3.4. Slope Face Horizontal Stress Figure 24. Influence of nail spacing on the maximum tensile force of the footing. The influence of nail spacing on the horizontal stress at the slope face at the middle 3.3.4. Slope Face Horizontal Stress point3.3.4. of Slopethe slope Face isHorizontal depicted Stress in Figure 25 at various footing pressures. From the figure, it The influence of nail spacing on the horizontal stress at the slope face at the middle is evidentThe that influence with the of nailincrease spacing in onthe the spacing horizontal between stress the at thenails, slope the face face at horizontal the middle stress point of the slope is depicted in Figure 25 at various footing pressures. From the figure, point of the slope is depicted in Figure 25 at various footing pressures. From the figure, it increases.it is evident The horizontal that with the stress increase increases in the spacingwith the between increase the in nails, footing the facepressure horizontal and nail is evident that with the increase in the spacing between the nails, the face horizontal stress spacing.stress The increases. increase The horizontalin the slope stress face increases horizontal with stresses the increase range in footing from 9.1% pressure to 18.5% and at increases. The horizontal stress increases with the increase in footing pressure and nail variousnail spacing.footing Thepressure increases. in the slope face horizontal stresses range from 9.1% to 18.5% at spacing.various footingThe increase pressures. in the slope face horizontal stresses range from 9.1% to 18.5% at various footing pressures.

FigureFigureFigure 25. Influence 25. 25. InfluenceInfluence of nailof of nail nail inclination inclination inclination on on on the the the slope slope slope face face horizontalhorizontal horizontal stresses stresses stresses at at atmid mid mid height height height of of slope slope.of slope. .

3.3.5. Vertical Stress under Soil Mass 3.3.5.3.3.5. Vertical Vertical Stress Stress under under Soil Soil Mass Mass FigureFigure 26 26 showsshows the the effect effect of of nail nail spacing spacing on on the the ver verticaltical stress stress under under the the nailed nailed soil soil Figure 26 shows the effect of nail spacing on the vertical stress under the nailed soil massmass at at mid mid-point,-point, i.e., point E.E. FromFrom thisthis figure,figure, it it is is seen seen that that the the effect effect of of nail nail spacing spacing on massonvertical atvertical mid stresses- stressespoint, under i.e., under point the the soil soilE. massFrom mass is isthis small. small. figure, The The increaseincreaseit is seen inin that nailnail spacingspacingthe effect leads of to nail slight slight spacing on differencesverticaldifferences stresses in in vertical vertical under stress stress the under undersoil mass the the soil soilis small. at at different different The increase values of in surcharge nail spacing loading. leads to slight differences in vertical stress under the soil at different values of surcharge loading.

Figure 26. Influence of nail inclination on the slope face vertical stresses at mid height of slope.

Appl. Sci. 2021, 11, x FOR PEER REVIEW 25 of 30 Appl. Sci. 2021, 11, x FOR PEER REVIEW 25 of 30

Appl. Sci. 11 2021, , 4842Figure 26. Influence of nail inclination on the slope face vertical stresses at mid height of slope. 23 of 28 Figure 26. Influence of nail inclination on the slope face vertical stresses at mid height of slope. 3.3.6. Horizontal and Vertical Stress behind Soil Mass 3.3.6. Horizontal and Vertical Stress behind Soil Mass 3.3.6.The Horizontal effect of andnail Verticalspacing Stresson the behind horizontal Soil Massand vertical stresses behind the soil mass The effect of nail spacing on the horizontal and vertical stresses behind the soil mass at various surcharge loading values at the middle point are given in Figures 27 and 28. It at variousThe effect surcharge of nail loading spacing values on the at horizontal the middle and point vertical are stressesgiven in behindFigures the 27 soiland mass 28. It is clear from the figures that the vertical stress behind the soil mass increases with an atis variousclear from surcharge the figures loading that valuesthe vertical at the stress middle behind point the are soil given mass in Figures increases 27 withand 28an. increase in the nail spacing. With the increase in surcharge loading and nail spacing, there Itincrease is clear in from the nail the figuresspacing. that With the the vertical increase stress in surcharge behind the loading soil mass and increasesnail spacing, with there an is a further increase in the vertical stress behind the soil mass. The horizontal stress behind increaseis a further in the increase nail spacing. in the vertical With the stress increase behind in the surcharge soil mass. loading The horizontal and nail spacing, stress behind there the soil mass at a higher footing pressure is constant at different nail spacings, but at a isthe a furthersoil mass increase at a higher in the verticalfooting stresspressure behind is constant the soil mass.at different The horizontal nail spacing stresss, but behind at a lowerthe soil footing mass pressure, at a higher there footing is a considerabl pressure ise constant increase atin horizontal different nail stresses spacings, at higher but atnail a lower footing pressure, there is a considerable increase in horizontal stresses at higher nail spacinglower footings. pressure, there is a considerable increase in horizontal stresses at higher spacings. nail spacings.

Figure 27. Influence of nail inclination on horizontal stresses behind the nailed soil mass at mid height of slope. FigureFigure 27.27. InfluenceInfluence ofof nailnail inclinationinclination onon horizontalhorizontal stressesstresses behindbehind thethe nailed nailed soil soil mass mass at at mid mid height height of of slope. slope.

FigFigureure 28. InfluenceInfluence of nail inclination on vertical stresses behind thethe nailednailed soilsoil massmass atat midmid heightheight ofof slope.slope. Figure 28. Influence of nail inclination on vertical stresses behind the nailed soil mass at mid height of slope. 4. Numerical Modeling: Validation

The finite element numerical model of earth slopes is analyzed to judge the accuracy and validity of the experimental slope model results. The two-dimensional model of the nailed-soil slope is developed, using the finite element method-based software Appl. Sci. 2021, 11, x FOR PEER REVIEW 26 of 30

4. Numerical Modeling: Validation Appl. Sci. 2021, 11, 4842 24 of 28 The finite element numerical model of earth slopes is analyzed to judge the accuracy and validity of the experimental slope model results. The two-dimensional model of the nailed-soil slope is developed, using the finite element method-based PLAXIS software becausebecause of of the the plane plane strain strain condition condition of soil of soilslope. slope. Four Four types types of elements of elements are used are to used model to themodel sand, the steel, sand, and steel Perspex, and Perspex glass material. glass material. A nonlinear A nonlinear elastic (hyperbolic) elastic (hyperbolic) model is model used tois simulateused to simulate the sand the material. sand material. The soil The parameters soil parameter used ins used the material in the material model aremodel given are ingiven Table in3 . Table The discretized 3. The discretized model of model the soil of slope the soil with slope boundary with conditions boundary conditions is shown in is Figureshown 29 in. Figure 29.

TableTable 3. 3.Soil Soil parameters parameters of of sand sand used used in in material material model. model. Elastic Unload- Mohr–Coulomb Model Plastic Straining Plastic Straining Elastic Unload- Stress Density Mohr–Coulomb Model PlasticDue toStraining Deviator PlasticDue to Primary Straining ing/Reloading DependentStress 3 (kN/mDensity) ref ref ing/Reloadingref DueLoading to Deviator (E50) Comp.Due to (E oedPrimary) (Eur) DepStiffnessendent (m) 3 ϕ C (kPa) ψ υ ref υ (kN/m ) (kPa) (kPa) (kPa)(Eur) ur φ C (kPa) ψ υ Loading (E50) ref (kPa) Comp. (Eoed) ref (kPa) υur Stiffness (m) 16.41 34 0.2 4 0.31 1959 1959 5877(kPa) 0.2 0.5 16.41 34 0.2 4 0.31 1959 1959 5877 0.2 0.5

FigureFigure 29.29. DiscretizedDiscretized modelmodel ofof slope.slope.

ToTo verifyverify thethe accuracyaccuracy ofof thethelaboratory laboratory results,results, aa numericalnumerical modelmodel ofof thethenailed nailed soilsoil slopeslope ofof heightheight (H)(H) ofof 700700 mmmm isis developeddeveloped withwith thethe lengthlength ofof thethe horizontalhorizontal nailsnails asas HH andand thethe verticalvertical spacingspacing ofof thethe nailsnails asas 0.40.4 H.H. TheThe laterallateral oror horizontalhorizontal slopeslope displacementsdisplacements areare computedcomputed at the the top, top, middle middle and and bottom bottom nail nail locations locations,, i.e., i.e., at distances at distances of Z of = Z70, = 350, 70, 350,and and630 630mm mmfrom from the thetop topsurface. surface. These These distances distances are areexpressed expressed as 0.1 as 0.1H, H,0.5 0.5H, H,and and 0.9 0.9H. H.The The results results are aretaken taken at footing at footing pressure pressuress of 0.0, of 0.0, 10.0, 10.0, and and 30.0 30.0 kPa. kPa. The The plots plots of the of thecomputational computational and andexperimental experimental results results at different at different surcharge surcharge pressure pressures,s, i.e., a i.e.,t the at exca- the excavationvation stage stage and andloading loading stage, stage, are depicted are depicted in Figure in Figure 30. 30. ItIt isis clearclear fromfrom thethe figuresfigures of of horizontal horizontal slope slope displacements displacements (D/H, (D/H, %)%) thatthat thethe maxi-maxi- 2 mummum horizontalhorizontal slopeslope displacementdisplacement occursoccurs at at a a surcharge surcharge loading loading of of 30.0 30.0 kN/m kN/m2in in bothboth thethe laboratorylaboratory andand numericalnumerical models.models. TheThe maximummaximum horizontalhorizontal displacementdisplacement occursoccurs atat thethe lowerlower pointpoint ofof thethe slopeslope inin thethe numericalnumerical model,model, whereaswhereas itit occursoccurs at at thethe middlemiddle pointpoint inin thethe laboratorylaboratory modelmodel duringduring thethe excavationexcavation stage.stage. InIn thethe loadingloading stages,stages, thethe maximummaximum displacement is at the mid-point in both models. Moreover, the percentage of difference at displacement is at the mid-point in both models. Moreover, the percentage of difference2 maximumat maximum displacement displacement ranges range betweens between 14.68% 14.68% at at surcharge surcharge loading loading of of 30.0 30.0 kN/m kN/m2and and 29.01% at 10.0 kN/m2. It is inferred from the results that the trend of the behavior of the 29.01% at 10.0 kN/m2. It is inferred from the results that the trend of the behavior of the slope is almost the same in the experimental model and the numerical model. slope is almost the same in the experimental model and the numerical model. The settlement of the footing in the experimental model is also compared with numer- ical results of footing settlement at surcharge pressure of 0, 5, 10, 20, 30 kPa and Figure 31 shows the comparison of the footing settlement obtained in the experimental and finite element models. It can be seen from the figure that the maximum footing settlement occurs at a surcharge load exerting a foundation pressure of 30.0 kN/m2 in both models. The Appl. Sci. 2021, 11, 4842 25 of 28

Appl. Sci. 2021, 11, x FOR PEER REVIEW 27 of 30

percentage of difference in settlement between the laboratory and numerical model ranges from 13.37% to 40.59%.

Figure 30.Figure Horizo 30.nHorizontaltal slope displacement slope displacement..

The settlement of the footing in the experimental model is also compared with nu- merical results of footing settlement at surcharge pressure of 0, 5, 10, 20, 30 kPa and Figure 31 shows the comparison of the footing settlement obtained in the experimental and finite Appl. Sci. 2021, 11, x FOR PEER REVIEW 28 of 30

element models. It can be seen from the figure that the maximum footing settlement oc- curs at a surcharge load exerting a foundation pressure of 30.0 kN/m2 in both models. The

Appl. Sci. 2021, 11, 4842 percentage of difference in settlement between the laboratory and numerical model26 of 28 ranges from 13.37% to 40.59%.

Figure 31. Footing settlement from laboratory and numerical model. Figure 31. Footing settlement from laboratory and numerical model. 5. Conclusions 5. Conclusions The earth nailing system is an earth slope stabilization technique accomplished by installingThe earth in situnailing closely system spaced is an nails earth in theslope ground. stabilization In the presenttechnique study, accomplished an experimental by installinginvestigation in situ ofclosely earth spaced nailing nails system in modelsthe ground. of non-cohesive In the present soil, study, having an differentexperimental nailing investigationparameters, of such earth as nailing nail spacing system and models orientations of non- andcohesive length soil of, nails,having was different carried na out.iling The parameters,distribution such of theas nail mobilized spacing tensile and orientations force in the and nail length and the of slope nails, face was horizontal carried out. pressure The distributionis nonlinear of withthe mobilized different nailingtensile force parameters. in the nail The and nail the tensile slope force face approacheshorizontal pressure zero at the is nonlinearends and increaseswith different toward nailing the middle parameters. third of The the nail.nail Thetensil maximume force approaches lateral displacement zero at theand ends slope and faceincrease horizontals toward pressures the middle ofthe third slope of the occur nail. in The the maximum middle third, lateral and displace- minimum mentlateral and displacementslope face horizontal and slope pressures face horizontal of the slope pressures, occur thein the lower middle third third of the, and slope min- with imumdifferent lateral surcharge displacement loading and and slope nailing face parameters. horizontalThe pressures minimum, the and lower maximum third of vertical the slopeand with horizontal different pressures surcharge behind loading the soiland massnailing occur parameters. in the upper The thirdminimum and lower and maxi- third of mumthe vertical slope, respectively, and horizontal with pressures different behind nailing the parameters. soil mass occur in the upper third and lower thirdThere of is the areduction slope, respectively in the lateral, with movement different of nailing the slope parameters. and footing settlements with anThere increase is a inreduction the length in andthe lateral inclination movement of the nailsof the and slope with and a decreasefooting settlements in the nailspacing. with an Theincrease mobilized in the tensilelengthforces and inclination in the nails of are the increased nails and due with to a the decrease increase in in the the nail nail spac- length ing.and The spacing, mobilized while tensile tensile forces forces in reducethe nails with are the inc increasereased due inthe to the inclination increase of in the the nails. nail length andThe spacing vertical, stresseswhile tensile under forces the soil reduce mass with are not the muchincrease affected in the by inclination changing of the the nail nails.parameters, i.e., length, inclination, and spacing. The horizontal stresses at the slope face decreaseThe vertical with thestresses increase under in the the nail soil inclination, mass are not while much they affect are increaseded by changing with the the increase nail parametersin nail length, i.e., andlength, spacing. inclination, and spacing. The horizontal stresses at the slope face decreaseThe with vertical the increase and horizontal in the nail stresses inclination behind, while the soil they mass are increase increased with with the the increase in- creasein the in spacingnail length of theand nails,spacing. while the vertical and horizontal stresses decrease with the increaseThe vertical in nail and inclination. horizontal The stress increasees behind in the the length soil mass of the increase nails causeswith the a decrease increase in in thethe verticalspacing andof the horizontal nails, while stresses the vertical behind theand soilhorizontal mass, up stress to thees decrease length of with the nailthe of increaseabout in the nail slope inclination. height, while The increase further increasesin the length in the of nailthe nails length causes increase a decrease the vertical in the and verticalhorizontal and horizontal stresses behind stresses the behind soil mass. the soil mass, up to the length of the nail of about the slope height, while further increases in the nail length increase the vertical and hori- Author Contributions: zontal stresses behind theConceptualization, soil mass. M.H.M. and M.A.; methodology, M.H.M. and M.A.; resources, J.M. and P.V.H.; writing—original draft preparation, M.H.M. and M.A.; writing—review and editing, J.M. and P.V.H.; project administration, P.V.H.; funding acquisition, M.A. All authors have read and agreed to the published version of the manuscript. Funding: Funding for this research was given under award numbers R.G.P2/73/41 by the Deanship of Scientific Research; King Khalid University, Ministry of Education, Kingdom of Saudi Arabia. Informed Consent Statement: Not applicable. Appl. Sci. 2021, 11, 4842 27 of 28

Acknowledgments: The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through the General Research Project under grant number (R.G.P2/73/41). The authors acknowledge the Dean of the Faculty of Engineering for his valuable support and help. Conflicts of Interest: The authors declare no conflict of interest.

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