Numerical investigation of gravity-grouted soil-nail pullout capacity in sand

Myoung-Soo Won; Shamsher Sadiq; Sung-Uk Seo; Jun-Yong Park

doi:10.1515/geo-2022-0543

Article Open Access

Numerical investigation of gravity-grouted soil-nail pullout capacity in sand

Myoung-Soo Won , Shamsher Sadiq , Sung-Uk Seo and Jun-Yong Park

Published/Copyright: November 8, 2023

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From the journal Open Geosciences Volume 15 Issue 1

Abstract

Soil nailing reinforces soil slopes and retaining walls by installing reinforcing elements into the soil, which rely on bonding strength with surrounding soil to transfer axial forces. This study focuses on the pullout capacity evaluation of grouted soil-nailing, which is conventionally determined through costly and time-intensive site-specific field pullout tests or simplified design methods, Federal Highway Administration (FHWA), and Effective Stress Method (ESM). However, these methods neglect important soil nail configuration parameters governing the pullout capacity. To address this limitation, we present a parametric study on a validated Finite-Element model using PLAXIS 3D to comprehensively investigate the pullout characteristics of grouted soil nailing. The study considers various factors such as sand relative densities, lengths, diameters, and inclination angles of the soil nails. The results reveal that the pullout capacity is significantly influenced by the sand relative density, diameter, and the length of the nailing, while the angle of inclination has only a marginal effect. The comparison with FHWA and ESM methods shows significant scatter, attributed to their lack of consideration for these governing parameters in determining pullout capacity. These findings provide valuable insights into the design and optimization of grouted soil nailing pullout capacity for geotechnical applications.

Keywords: grouted soil nailing; pullout force; numerical simulations; relative density; diameter; length; angle of inclination

1 Introduction

Ground improvement techniques for slopes and earth-retaining structures are employed to enhance stability. A diverse range of methods are utilized, including geosynthetics reinforcement [1,2] and soil nailing systems [3,4]. Soil nailing systems encompass various types, from grouted and non-grouted to helical nailing systems [5–8], offering adaptable solutions for stability enhancement.

Grouted soil nailing technique gained significant usage in stabilizing slopes [3,9,10] and excavation support systems [11,12] by enhancing the resistance to pullout at the interface between the grouted nailing surface and the surrounding soil mass [13]. They are also employed in repairing roadway landslides adjacent to watercourses, river margins, bluffs, and other ecologically fragile riparian zones [14]. Additionally, soil nails have been utilized in large-scale levee construction projects along lengthy channels [15].

Typically, the grouted soil nailing construction technique involves drilling and grouting. Initially, a hole is drilled into the existing soil, after which a steel bar with or without corrugated tube, known as a nail, is inserted into the hole and fully grouted. This process results in a soil nail consisting of three layers: a steel bar enclosed within a grout column and a corrugated pipe enclosed with outer grout column, which is further enclosed by the surrounding soil. The grout and the surrounding soil form a bond, known as nail bond strength. This bond strength at the nail-soil interface plays a crucial role in restraining the deformation of the soil mass secured by the nails and thereby ensuring its stability. In engineering practice, project-specific pullout field tests are conducted to measure the pullout capacity of soil-nailing. However, in the absence of the field tests, two methods Federal Highway Administration (FHWA) [11] and Effective Stress Method (ESM) [16–19] are widely used in engineering practice to estimate the pullout capacity.

Additionally, several model lab tests [10,20–22] and numerical simulations [23–26]-based studies on the soil nails have been conducted to understand the pullout characteristics. Nevertheless, although prior investigations primarily concentrated on analyzing the pullout resistance of pressure-grouted soil nails, limited attention has been given to examining the pullout effects of gravity-grouted soil nailing. This includes studying the influence of different diameters, lengths, angle of inclination, and sand-relative densities on the pullout resistance.

As mentioned earlier, the widely used methods FHWA and ESM, as well as previous studies, have not explored the impact of gravity-grouted soil nails, considering the combined influence of various factors such as nail diameters, lengths, angle of inclination, and sand relative densities on pullout resistance. Therefore, to bridge this research gap, we conducted a parametric study aiming to understand the governing parameters of pullout force in gravity-grouted soil nailing. The study involves a pullout field test at a selected site to validate the numerical model, followed by a parametric evaluation using the finite element (FE) software PLAXIS 3D [27]. The effects of sand relative density (RD), nail length, diameter, and inclination on the pullout force of gravity-grouted soil nailing are quantified and discussed. Furthermore, the analysis results are compared with the widely used FWHA and ESM methods in engineering practice. Overall, these findings offer valuable insights into the pullout capacity of grouted soil nailing.

2 Field pullout test

2.1 Site condition

The site is in a flat area located in Pyogyo-ri, Majang-myeon Icheon-si, South Korea. Its landscape is predominantly characterized by low elevation, a result of extensive weathering of granite, except for the highlands in the western region. The area features a basin-like formation with substantial alluvium, particularly around the Bokhacheon stream, which flows through the central part of the city from south to north before merging into the South Han River, one of Korea’s longest rivers. The Bokhacheon stream is surrounded by a substantial layer of alluvium, varying in thickness from 5 to 20 m, and the lowland areas are characterized by sandy soils originating from the underlying granite. These geological features play a pivotal role in forming favorable catchment conditions in the region. Regarding the geology of the study area, it primarily comprises biotite granite, with lesser occurrences of two-mica granite and porphyritic granite, along with dikes. The granites found in the area are part of the Daebo Granite group, which belongs to the Jurassic period and is commonly distributed in the central region of the Korean peninsula. These granites are distinctive for their S-type magma origin, resulting from partial melting of continental crusts. Biotite granite’s main constituents are quartz, feldspars, biotite, and trace muscovite, with calcite occurring as fracture-coating minerals. Two-mica granite occurs as a zonal stock, distributed in certain areas containing numerous pegmatite dikes, and the composition of the granite comprises coarse grains of quartz, feldspars, and micas, with the presence of minerals such as muscovite and biotite. Porphyritic granite is found as a stock in gradual contact with the biotite granite, originating from cogenetic magma of the biotite granite. The primary minerals composing the porphyritic granite are feldspars, quartz, and biotite, with the latter notably displaying a coarser grain size.

The soil conditions at the field pullout test site are determined through geotechnical testing by boring to a depth of 15 m. The subsurface profile reveals that up to a depth of 4.8 m, there is silty sand with an average Standard Penetration Test (SPT) [28] value of 7.4. From 4.8 to 8.8 meters, there is clayey sand with an SPT value of 35, while from 8.8 to 15 m, there is a weathered rock with a refusal SPT value. The SPT values are adjusted for the energy and overburden corrections [29,30]. The shear strength and stiffness parameters of the upper silty sand layers are determined based on the corrected SPT-N values using empirical correlation [31,32]

(1) E = 300 ( N 1 , 60 + 6 ) .

On the other hand, for the clayey sand, the shear strength and stiffness parameters are directly measured through borehole shear tests [33], as summarized in Table 1.

Table 1

Pullout test site soil properties

Depth	Soil description	SPT, N	Soil shear strength		Stiffness parameters
Depth		SPT, N	φ	c	E	v
m		Blows/30 cm	Degrees	kPa	kPa	–
1	Silty sand (SM)	3	29.5^a	0	3,200^c	0.3
2		4
3		6
4		8
4.8		16
5.8	Clayey sand (SC)	29	32.7^b	30.7^b	12,100^c	0.3
6.8		34
7.8		35
8.8		42
10	WR	50	N/A
15	WR	50	N/A
End of borehole

^a(N ₁)₆₀-φ Empirical correlation [31].

^bBorehole shear test [33].

^b(N ₁)₆₀-E Empirical correlation [32].

2.2 Description of grouted nail and field pullout test

The soil nailing system configuration installed for the field pullout test is shown in Figure 1. The nailing system comprises of 28.6 mm diameter deformed ribbed steel bar referred to as a nail, corrugated tube having 21 mm thickness with 84.5 and 65 mm outer and inner diameters, respectively, and grouting. The following procedure for grouted soil nailing construction and pullout test is adopted:

Drilling: The grouted soil nailing system begins by drilling a hole with a diameter of 120 mm and a depth of 7 m (Figure 1(b)).
Inserting the nail: After drilling the holes, the next step is to insert the nailing system that comprises of assembly of 29 mm diameter reinforced ribbed steel bar with corrugated tubes having grouting pipes into the hole (Figure 1(c)).
Grouting: Once the nail with the corrugated tube is in place, the next step is to inject grout into the hole to fill any voids and provide additional support. The grout, cement-based mixture is injected by the force of gravity, it flows downward through the grout delivery pipes inside and outside the corrugated tube (Figure 1(d)).

Figure 1

(a) Illustration of the grouted nailing system, (b) drilling hole, (c) inserting the nail, (d) grouting, (e) final grouted soil nail with rebar left un-grouted for pullout test, (f) reference beams with load cell and LVDTs, and (g) application of pullout loading.

Pullout testing is performed as per ASTM D-3689 [34] method to evaluate the pullout capacity of the grouted soil nail. The procedure for pullout testing involves the following steps:

Placement of reference beams: Reference beams are installed in the ground adjacent to the grouted soil nail (Figure 1(f)).
Attachment of the load cell and mounting the LVDTs: The rebar is left ungrouted at the nail head so that the load cell is attached to the nail. The load cell is used to measure the force required to pull the nail out of the soil. The LVDTs to the reference beams are attached ensuring proper alignment with reference beams to accurately measure the displacement of the grouted soil nail as it was pulled out.
Application of the load: A hydraulic jack is used to apply a load to the nail. The load is applied slowly to allow for the measurement of the force required to pull the nail out of the soil (Figure 1(g)).

During the pullout test, the load cell measured the force exerted to extract the nail from the soil while simultaneously capturing the associated displacement, and this data is recorded to assess the performance of the grouted soil nail.

3 Numerical simulation

The load–displacement behavior of the field pullout test of corrugated tube soil nailing is simulated using three-dimensional (3D) FE software PLAXIS 3D [27]. The single soil nailing pullout at the surface can be better simulated by 3D modeling rather than two-dimensional (2D) modeling. The objectives of the simulations are to validate the numerical model, understand the pullout load transfer mechanism along the nailing system, and investigate the governing factors of pullout force.

Boundary conditions can impact the simulation results [35]; therefore, the lateral and bottom boundaries are defined at 25D and 15D respectively. The computational domain as shown in Figure 2(a) has been defined such that the numerical boundaries have no effect on the obtained results. Soil and nails are simulated using the 10-noded tetrahedral and embedded beam element respectively. Mohr–Coulomb failure criterion [36,37] and the linear elastic [38] constitutive models are used for the soil and nailing, respectively. The pullout load is applied as a point load at the nail head. The mesh size and distribution have been shown to be sensitive when simulating soil–structure interface responses [39,40,41]. Nonetheless, in the present study, we employ the mesh-independent embedded beam element [42] featuring a formulation that remains unaffected by mesh size, signifying that the mesh size does not exert control over the interaction between soil and the nail. The computational domain and the medium-dense mesh with 22,249 elements and 32,115 nodes are shown in Figure 2(b). According to the embedded beam concept depicted in Figure 3(a), the embedded beam/nail consists of line elements. Specifically, an elastic region with dimensions equivalent to the diameter of the nail is assumed. The embedded beam has been developed with a beam element capable of intersecting a 10-node tetrahedral element at any location and orientation and an embedded interface element to simulate the nailing elastic behavior and the grouting interface skin resistance respectively [43]. The presence of the beam element necessitates the inclusion of three additional virtual nodes within the 10-node tetrahedral element (Figure 3(b)). The nail and soil interaction has three components of stiffneses as shown in Figure 3(c). The normal and shear stiffnesses are used to capture the axial and lateral load transfer between the beam and the soil, respectively. These springs are typically defined based on the soil properties and the behavior of the embedded beam. The skin resistance represents the frictional resistance along the surface of the nailing as it interacts with the surrounding soil. Therefore, a depth-dependent function is selected to simulate the skin resistance of the soil nailing. Skin resistance (T _i) is defined as

(2) T i = 2 π R eq τ i ,

where τ _i is the interface shear strength. In the context of depth-dependent skin resistance, the interface shear strength is automatically calculated based on the soil constitutive model, considering the direct soil shear strength and stiffness inputs.

Figure 2

(a) Computational domain and (b) finite element mesh used in analysis.

Figure 3

(a) Elastic cylindrical zone around the embedded beam, (b) virtual nodes of the embedded beam and soil tetrahedral element, and (c) soil interaction with nailing showing interface normal and shear stiffnesses [43].

Field pullout test site conditions as summarized in Table 1 are used for the validation of the numerical model to evaluate the soil nailing interaction simulation capability of FE and embedded beam. The lateral and bottom boundaries of the domain are fixed normally and fully, respectively. During the analyses, the numerical pullout capacity of the nail is simulated using both the plastic analysis method and the staged construction calculation method.

4 Validation of numerical model

The embedded beam, being a zero-thickness element, must be modeled with volume-like behavior to accurately capture its characteristics. The nail-grout system is represented by an embedded beam assumption, assuming an elastic region with an equivalent diameter. Consequently, when the nail is pulled out and displaced within the soil, it is anticipated that the soil within the elastic region will experience the same displacement as the embedded beam. This expectation was effectively demonstrated through simulation, as depicted by the total displacement contours surrounding the system (Figure 4).

Figure 4

Displacement contours along and around the elastic nail equivalent diameter.

The pullout load–displacement curve measured at the nail head is compared with the curve extracted from numerical analyses in Figure 5. It can be seen that the overall characteristics of the experimental curves are effectively captured over the elastic as well as yielding range. As shown in Figure 5, the pullout load–displacement curve does not exhibit a clear ultimate point, therefore the pullout capacity is calculated by extending the linear elastic portion of the curve and the yield portion of the curve until both intersects. Remarkably, the pullout load capacity numerically calculated exhibits a mere 3.8% error when compared to the field pullout test results. In contrast, the widely used methods FHWA and ESM exhibit significant discrepancies, as they tend to over-predict and under-predict the measured values by 39 and 63%, respectively. This suggests that the simulation can effectively capture the soil-nailing interaction using the embedded beam element. This level of accurate prediction indicates a good agreement between the simulated behavior and the actual response of the soil-nailing system.

Figure 5

Comparison of field and numerical pullout load–displacement curves at the nail head.

The distribution and extent of the plastic deformation/slip surfaces by the plastic point and relative shear stress contours are shown in Figure 6. These provide important information on the load transfer mechanism and the nail–soil interaction. The shape of the failure surface is a curved wedge-like starting from the base and expands outward as the pullout increases near the surface (Figure 6(a)). Nail–soil interaction influenced the relative shear stress contours; at the surface, the nail head have experienced higher shear stresses due to the applied pullout and the resistance offered by the soil. As depth increases, the soil provides more confinement and lateral support to the nail, resulting in a decrease in shear stresses (Figure 6(b)).

Figure 6

Distribution of (a) plastic points and (b) relative shear stress contours.

The distribution of axial forces is shown in Figure 7; it can be seen that at the nail head, where the pullout is applied, the axial force is maximum and gradually decreases toward the base. This is because the pullout is directly transferred to the nail head resulting in a higher force concentration near the soil nailing head. As the load is transferred through skin friction along the nail system through the grout soil interface, the axial force gradually decreases with depth. The reduction in axial forces occurs due to the dissipation of load through the interaction between the nailing surface and the surrounding sand.

Figure 7

Axial force distribution along soil nailing length.

5 Parametric study

In this study, a suite of analyses have been performed to simulate the effects of the RD of sand, nailing length, diameter, and angle of inclination on the soil nailing pullout capacity. The variable parameters used in the study are summarized in Table 2. Three different states of sand characterized by varying granulometric characteristics are simulated. Loose sands are associated with poor grading, typically indicated by C _u values exceeding 6 and C _c values greater than 1. Medium sands fall within a moderate grading range, with C _u values ranging from 4 to 6 and C _c values between 1 and 2. Dense sands exhibit well-graded characteristics, featuring C _u values below 4 and C _c values less than 1. According to Brinkgreve et al. [44], empirical formulas for sand are referred to calculate the properties of the based on the RD, and the properties are summarized in Table 3. The integrated nailing system in this study comprises of 28.6 mm diameter deformed ribbed steel bar referred to as a nail, corrugated tube having 21 mm thickness with 84.5 and 65 mm outer and inner diameters, respectively, and variable grouting based on the drilling hole diameter. The lengths and diameters of the nailing system are summarized in Table 2. The various properties and respective parameters of the nailing system used in the study are summarized in Table 4. The equivalent modulus of elasticity of the integrated soil nailing system is defined as

(3) E eq = E n A n A + E t A t A + E g A g A .

Table 2

Parametric Study Matrix

Parameters	Range	Simulation cases
Soil	Loose, medium, and dense sand	03
Nailing length (m)	4, 8, and 12	03
Nailing diameter (mm)	105, 152, and 203	03
Nailing inclination angle (°)	0, 10, 20, 30, and 45	05
Total cases		135

Table 3

Sand properties considered in study

Description			Loose	Medium dense	Dense
Granulometric characteristics	Sorting/grading		Poorly	Moderately	Well
	C _u	—	>6	4–6	<4
	C _c	—	>1	1–2	<1
RD	(%)	25	50	75
Effective parameters	γ	(kN/m³)	16	17	18
	E	(kN/m³)	15,000	30,000	45,000
	φ’	(^o)	31.1	34.3	37.4
	ψ‘	(^o)	1.1	4.3	7.4
	v	—	0.25	0.25	0.25

Table 4

Nailing properties considered in study

Size, diameter (mm)	Material model	Parameters
Size, diameter (mm)	Material model	γ (kN/m³)	E ¹ (kN/m³)	Type	Axial skin resistance
105	LE	23	1.63 × 10⁷	Circular	Layer dependent
152			8.43 × 10⁶
203			5.37 × 10⁶

¹The nailing system (nail + corrugated tube + grout) deforms consistently during pullout test, therefore is simulated as an elastic body with an equivalent Young’s modulus.

E eq = E n ( A n A ) + E t ( A t A ) + E g ( A g A ) .

Also, the simulated nailing inclination angle (θ) configuration from the vertical plane in the computational model is shown in Figure 13(a).

6 Analysis and discussion of parametric study results

6.1 Effect of RD

In the analyses, the influence of RD on the pullout capacity is investigated. The analyses encompassed three distinct relative densities, namely loose (RD = 25%), medium (RD = 50%), and dense (RD = 75%). The results are expressed in terms of the pullout load–displacement curves extracted at the nail head (Figure 8). The pullout load–displacement curve at the nail head provides insight into the behavior of the nail soil system and its response to the applied pullout loading. When a nail is pulled out from loose sand, the sand particles tend to move and spread apart, increasing the void ratio. This process is known as dilatancy. As the void ratio increases, the effective stress within the sand decreases, resulting in a reduction of its shear strength. As a consequence, the pullout force decreases in loose sand. [45]. In contrast, when a nail is pulled out from dense sand, the sand particles are tightly packed together with a lower void ratio. As the pullout displacement increases, the sand particles experience less movement and retain their compact arrangement due to the limited dilation. This leads to an increase in the effective stress and shear strength of the dense sand, making it more resistant to the pullout force compared to loose sand [45]. Various studies [46,47] reported similar impact of dilatancy effect on the pullout behavior as observed in the current study.

Figure 8

Effect of soil RD on pullout load displacement behavior for 200 mm diameter nailing system and L = 4 m.

To further understand the mobilization of the shear stress and pullout capacity for different relative densities, the relative shear stress ratio contours (Figure 9) are extracted at the yield point loading step of the pullout load–displacement curve as shown in Figure 8 (points A, B, and C). Relative shear stress is an important parameter that indicates the level of shear resistance that the soil offers to the nailing during pullout and is defined as the ratio of the mobilized shear stress acting to the maximum shear stress that the soil can resist without failure. It can be seen from the contours that the relative shear stress ratio generally increases with increasing sand RD. When the sand is relatively loose, the nailing experiences less resistance to pullout, resulting in a lower relative shear stress ratio. On the other hand, when the sand is relatively dense, the nailing experiences more resistance to pullout, resulting in a higher relative shear stress ratio.

Figure 9

Effect of soil RD on relative shear stress contours for L = 4 m and D = 203 mm nailing system: (a) loose, (b) medium dense, and (c) dense sand.

A relative shear stress ratio of 1 indicates that the maximum shear stress that the soil can resist without failure has been reached, and any further increase in the pullout force will cause failure. The location of the failure surface is complex as it depends on the level of the nailing pullout displacement. From the maximum value, it can be seen that failure surface is effected by the RD of the sand, generally observed that the failure surface tends to be deeper in loose sand compared to medium and dense sand. This is because loose sand typically has a lower shear strength and less interlocking between the soil particles, which allows the soil to deform and fail more easily under the applied pullout force. As a result, the failure surface tends to be wider and deeper in loose sand, which can result in lower pullout force. On the other hand, as density increases, shear strength increases and more interlocking between the soil particles, which allows the soil to resist the applied pullout force more effectively. As a result, the failure surface tends to be narrower and shallower in medium and dense sand.

The effect of the RD on the pullout capacity for all the cases is presented in Figure 10. It can be seen that with the increase in sand RD, the pullout force increases across all cases. When comparing loose to dense sand, which had a three-fold difference in RD, the average increase in pullout capacity for all diameters is 1.31 times for the 4 m long nailing, 1.42 times for the 8 m long nailing, and 1.5 times for 12 m long nailing. The rate of increase is influenced by the length and nail diameter.

Figure 10

Effect of soil RD on pullout capacity: (a) 105 mm, (b) 152 mm, and (c) 203 mm diameters.

6.2 Effect of length

The effect of the nailing length on pullout force is shown in Figure 11. Increasing the nailing length results in a significant increase in pullout force, with a three-fold increase in length from 4 to 12 m leading to an average increase of nine times. This rate of increase in pullout force due to length is marginally dependent on the sand RD and nailing diameter. The increase in nailing length leads to greater skin resistance, which helps to increase the pullout capacity and improve its ability to resist pullout forces. This increase in pullout resistance is relatively consistent across different levels of RD, indicating that the effect of nailing length on pullout resistance is more significant than the effect of RD.

Figure 11

Effect of nailing length on ultimate pullout capacity: (a) 105 mm, (b) 152 mm, and (c) 203 mm diameters.

6.3 Effect of diameter

The effect of the nailing diameter on pullout force is shown in Figure 12. Increasing the nailing diameter results in increases in the pullout force linearly, with a two-fold increase in diameter from 105 to 203 mm leading to an average increase of 1.93 times. This rate of increase in pullout force due to diameter is marginally dependent on the sand RD and length of nailing. The increase of the nailing diameter provides a larger surface area for the sand to transfer pullout forces, which increases the skin friction of the nailing shaft. As a result, the large diameter nailing is able to resist pullout forces more effectively, which leads to an increase in pullout capacity.

Figure 12

Effect of nailing diameter on ultimate pullout capacity: (a) loose, (b) medium, and (c) dense sands.

6.4 Effect of inclination

Investigating the effect of inclination is crucial since nailing is installed at an angle. The effect of the inclination angle for 10, 20, 30, and 45° are investigated as shown in Figure 13. An increase in inclination angle from 0 to 30° results in an increase in nailing pullout capacity, which is only around 9.5%. However, at an inclination angle of 45°, there is a decrease in pullout force, which is less than 1% and not noticeable. The increase in pullout capacity of an inclined nail signifies the stress distribution around soil nailing due to increased nail skin friction, enhanced soil arching, and increased soil shear strength. However, when the inclination angle increases beyond 30°, a decrease in pullout capacity can be attributed to limited soil arching resulting in decreased soil shear strength. Furthermore, it is observed that the rate of pullout increase was more noticeable in dense sand as opposed to loose sand. Therefore, it is essential to carefully consider the inclination angle during the installation of nailing to achieve the desired pullout capacity.

Figure 13

(a) Inclination definition and (b) effect of nailing inclination on the ultimate pullout force for nailing having 4 m length and 203 mm diameter.

Although the literature lacks specific attention to the effect of inclination on the pullout force of grouted soil nailing. In Figure 14, the effect of inclination on the grouted soil nailing pullout force of the current study simulation is compared with the measured response of inclined plate anchors [48] and micro piles [49–51] model tests in the sand. The comparison reveals a reasonable agreement with the trends of the current study that an increase in inclination angle initially increases the pullout force up to 30°. Further experimental studies are warranted to validate the findings current study on the pullout of grouted soil nailing considering various angles of inclination.

Figure 14

Comparison of the inclination effect on pullout force with previous studies.

6.5 Location of active and passive failure zone

Locating the active and passive zones in the soil nailing pullout is a crucial aspect of designing the available length of the nail for optimal pullout resistance in the passive zone. In this study, we employed the concept of relative shear stress ratio to identify specific stress points at which the relative shear stress approaches a value of 1, as demonstrated in Figure 15. These relative shear stress values are extracted at the point of ultimate pullout force. The simulated results reveal a cylindrical shape and the slip surface angle in accordance with the principles of the Rankine earth pressure theory [52]; this finding aligns with previous studies conducted on piles pullout behavior in sandy soils [53,54]. The depth and width of the active zone measured from the center have been determined to be 0.2D and 0.25D, respectively, as drawn in Figure 15. It is important to note that the location of these active and passive zones remains independent of nail length, diameter, and sand relative densities.

Figure 15

Location of active and passive failure zones for L = 4 m and D = 203 mm nailing system: (a) loose, (b) medium dense, and (c) dense sand (legend range, 1–0.95).

7 Comparison with FHWA and ESM methods

The results of numerical simulation results are compared with estimates from widely used engineering methods such as FHWA and ESM (Figure 16). In the simplified method FHWA, the pullout force predictions tend to be overestimated by a factor of 1–2 at lower confining pressures, and the level of unpredictability increases as the confining pressure rises, with a range of 1.5–3.7 times. This indicates that the simplified method does not consider the influence of the confining pressure, resulting in significant scatter in the predictions. In the ESM method, the predictions consistently underestimate the values across all ranges, ranging from 1.4 to 2 times, with an average underestimation factor of 1.7 times. Both FHWA and ESM exhibit variations in the accuracy of their pullout force predictions, leading to scattered data points. This observation suggests that FHWA lacks consideration for both confining pressure and dilatancy, while ESM incorporates the confining pressure but fails to capture the dilatancy effect, resulting in a notable scatter in the predictions. Furthermore, neither of these methods takes into account the effect of the angle of inclination on the grouted nail pullout force predictions.

Figure 16

Comparison of the pullout capacity with the widely used FHWA and ESM methods.

8 Conclusion

In this study, the pullout capacity of grouted soil nailing is investigated using 3D FE simulation in PLAXIS. Initially, we evaluated the ability of numerical simulation to replicate the pullout behavior of a soil nailing by comparing the results with data from a field pullout test. The comparisons show that the measured pullout force–displacement curve fits favorably with numerical simulation over the elastic and yielding regions. The 3D FE model with embedded beam element successfully captures the essential features of soil nail pullout characteristics such as mobilized pullout shear stresses, pullout force, and displacements. A series of numerical analyses are performed to investigate the effect of sand RD, nailing length, diameter, and the angle of inclination on the nailing pullout capacity. The conclusions derived from this study are the following:

The RD of the sand has a noticeable impact on the characteristics of the pullout load–displacement curve of the nailing. In loose sand (RD = 25%), there is a noticeable peak and ultimate point, and as the density increases (RD = 50–75%) in the case of medium and dense sand, the dilatancy effect becomes more prominent. When comparing loose to dense sand, which had a three-fold difference in RD, the average increase in ultimate pullout capacity for all diameters and lengths was 1.40 times.
Nailing length has a significant effect on the ultimate pullout capacity, with an increase in length, greater skin resistance is mobilized along the nailing length. The length increase from 4 to 12 m results in an average ultimate pullout increase of nine times.
Increasing the nailing diameter provides a larger surface area for the load transfer and increases the pullout force linearly, with an increase in diameter from 105 to 203 mm, resulting in an average increase of 1.9 times.
When the nailing is inclined up to an angle of 30°, the pullout capacity increases due to the generation of the additional lateral resistance, however, the inclination beyond 45°, there is a reduction in the effective area of soil around the nailing resulting in a decrease of the pullout forces. An increase of 9.5% was observed for the 30° inclination. Future experimental studies are warranted to validate the findings regarding the effect of inclination on the grouted soil nailing pullout in the current study.
At the ultimate pullout point of the grouted soil nail, slip surface angle conforms to the Rankine earth pressure theory. The depth and width of the active and passive zones, measured from the center, remain consistent and unaffected by nail length, diameter, or sand relative densities, with values of 0.2D and 0.25D, respectively.
When comparing the estimation of pullout forces using commonly employed methods such as FHWA and ESM, it becomes evident that there are significant variations in the accuracy of their predictions. This discrepancy results in scattered data points, highlighting the need for the development of a new predictive model for grouted soil nail pullout force estimation considering the effect of dilatancy, length, and diameter of nailing as well as angle of inclination. Future research is warranted on addressing these inconsistencies to enhance the reliability and precision of pullout force predictions.
The primary focus of the study is to investigate the effect of nail length, diameter, and inclination angle, on pullout behavior. As a simplification, this study simulates dry sand conditions, excluding the consideration of water content. However, future studies are warranted to explore the influence of water content on the pullout behavior of grouted soil nails in sandy soils.

Acknowledgments

This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2021R1A6A1A03045185).

Conflict of interest: The authors state no conflict of interest.

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Received: 2023-05-26

Revised: 2023-09-05

Accepted: 2023-09-05

Published Online: 2023-11-08

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

https://doi.org/10.1515/geo-2022-0543

Keywords for this article

grouted soil nailing; pullout force; numerical simulations; relative density; diameter; length; angle of inclination

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