Evaluation of the Performance of Soil-Nailed Walls in Weathered Sandstones Utilizing Instrumental Data

Abstract

Used for soil and weathered rocks, soil nails are rigid reinforcements positioned at certain angles on the ground to provide slope stability. A rigid reinforcement element placed in a well filled with cement grout mix after completing drilling will generate adherence stress between the grout-mixed nail bar and soil. Due to this stress, load is transferred to the soil along the soil–grout interaction surface. In the case discussed herein, the slope at the parcel border needed to be made steeper in order to accommodate the construction of a facility in the Taşkısığı region of Sakarya province. Soil-nailed walls, which are inexpensive and suitable for weathered rocks, were needed as a support system because the slope was too steep to support itself. Support system performance was measured using two inclinometers and two soil nail pull-out tests conducted on different sections observed during and after construction. Contrary to the design-phase prediction, it was determined that the stresses started to dampen in the region closer to the slope-facing zone. Field measurement data and numerical analysis revealed that higher parameters than necessary were selected. In this context, sensitivity and parameter analyses were carried out using the Hoek–Brown constitutive model. The GSI value was re-evaluated and found to be compatible with the observation results obtained from the field performance. Since the retaining wall performance observed was higher than expected, geometric parametric analysis of the structural elements was performed; high safety coefficients were found across variations. The effects of the inclination of the slope, nail length, nail spacing, and nail slope design parameters on the safety coefficient and horizontal displacement were examined. The optimal design suggested nail lengths of 4.00 m, a spacing of 1.60 m, and slopes of 20°. It was discovered that the effect of the inclination degree of the slope on the safety coefficient was lower than expected. The results revealed that a more economical design with a similar safety factor can be obtained by shortening the lengths of the nails.

1. Introduction

Soil nails are rigid reinforcement elements placed on specific slopes to provide temporary or permanent stability in soils or weathered rock environments [1]. These reinforcement elements are placed within the borehole after the drilling is completed. Following the installation of a soil nail, a cement grout mixture is injected to ensure good resistance to adherence stress (bond strength) via load transfer between the cement-grouted soil nail and the soil/weathered rock.

In situ observations and field practices emphasize the importance of evaluating the support system’s performance after soil nail installation and grouting.

Retaining wall monitoring is a widely used method of ensuring long-term stability. Inclinometer measurements are particularly useful for assessing retaining wall deformations, and many researchers have applied this method to soil-nailed support systems [2,3]. Furthermore, in situ soil nail pull-out tests also provide reliable data on nail performance and soil nail adhesion stress during the construction of soil-nailed walls [4,5,6,7,8,9,10,11,12,13]. It is well known that some environmental effects may change the behavior of a soil nail. The roots of plants basically have a positive effect on soil strength. Vegetation reduces runoff water on the surface of the soil. However, if the vegetation layer on the soil’s surface is damaged, then the soil will be exposed to meteorological conditions and weathering effects, which can easily decrease shear strength and cause slope erosion [14,15]. The engineering geological properties of weathered residual soil also change with time [16]. Nail force is affected by time and excavation [17]. This leads to an increase in nail force. As the shear strength of the soil decreases, there is an increase in the displacement and interaction between the soil and nails. During the excavation phases, nail forces tend to increase. Groundwater also has an adverse effect on fully grouted rock bolts during the pull-out test: the pull-out strength is lower than under dry conditions [18]. Fluctuations in groundwater levels and weathering effects, especially on the roots of soil nails, decrease the shear strength between soil nails and the soil in the long term. Therefore, groundwater penetration should be prevented or limited in soil-nailed sections. Also, slopes should be protected against weathering agents (e.g., water infiltration). Despite the ISRM’s requirements, the height-to-width ratio is lowered by the water-sensitive nature of shale rock [19]. Furthermore, water infiltration increases the deformation of weathered rocks [20].

In this study, we examined a 200.0 m long soil-nailed retaining wall with a height varying between 8.00 m and 10.0 m constructed in the Taşkısığı region of Sakarya province (Türkiye) within the Çakraz Formation (Figure 1).

Inclinometers were placed behind the retaining wall to monitor horizontal deformation, and soil nail pull-out tests were conducted to determine adhesion stress values. The second phase involved numerical analysis using the Mohr–Coulomb constitutive model, incorporating site-specific engineering geological properties and geotechnical data used in the design. The study continued with a comparison of the deformation data obtained from in situ measurements and numerical analyses. In order to investigate discrepancies in deformation, the engineering geological and geotechnical parameters of the slope were used in sensitivity and parameter analysis. All these parameters were then re-analyzed using the Hoek–Brown constitutive model (Figure 2).

2. Materials and Methods

Field observations, in situ experiments, and laboratory tests were conducted to determine the geotechnical parameters necessary for designing the soil nail support system in the sandstones of the Çakraz Formation. Various images of the study area at different stages are shown in Figure 3.

Three boreholes were drilled at different depths to obtain geological, engineering geological, and geotechnical data. The boreholes (BH-23: 35.0 m, BH-24: 30.0 m, and BH-19: 20.0 m) were located near the soil-nailed support structure (Figure 4). The weathered rock mass was classified according to the six-grade weathering system suggested by the ISRM [21] (

Table 1. Weathering grades and typical properties of rocks [21].

Weathering Term	Degree of Weathering	Typical Features (kN/m3)
Residual Soil	W6	All rock material is converted into soil. The mass structure and material fabric are destroyed. There is a large change in volume, but the soil has not been significantly transposed
Completely Weathered	W5	All rock material is decomposed and/or disintegrated into soil. The original mass structure is still largely intact
Highly Weathered	W4	More than half of the rock material is decomposed or has disintegrated into soil. Fresh or discolored rock is present either as a continuous framework or as core stone
Moderately Weathered	W3	Less than half of the rock material is decomposed or has disintegrated into soil. Fresh or discolored rock is present either as a discontinuous framework or as core stones
Slightly Weathered	W2	Discoloration indicates weathering of rock material and discontinuity surfaces. All rock material may be discolored by weathering
Fresh Rock	W1	No visible signs of rock material weathering. There is perhaps slight discoloration on the major discontinuity surface

).

In order to determine the mechanical properties of the studied weathered rock based on the profile given above, a standard penetration test (SPT) was conducted on the top of the landform, particularly in residual and completely weathered sections. Additionally, pressure meter tests were also carried out in all the existing boreholes to obtain the deformation parameters of the rock and soil masses. Unconfined compressive strength tests and triaxial compression tests were conducted to determine the mechanical properties of the soil layers. Additionally, the uniaxial compressive strength of the rock was determined using uniaxial compression tests, and point load tests were performed when UCS samples were unavailable. Physical properties (e.g., unit weights and porosities) were also evaluated for both rock and soil sequences in accordance with the ISRM [22] and ASTM [23] guidelines.

Numerical models were generated via the finite element method using the obtained geotechnical parameters. Horizontal displacement values and safety coefficients were identified through finite element analysis using the Mohr–Coulomb constitutive model. The performance of the soil-nailed wall system was assessed based on numerical analysis results, inclinometer measurements, and soil nail pull-out tests in which strain gauge sensors were employed. Nail behavior and the load transfer mechanism from nail to soil were evaluated using strain gauge sensors placed on the nails subjected to pull-out tests. During soil nail pull-out tests, only the displacement at the tip of the soil nail can be measured under tensile load. To evaluate the shear strength along the interaction surface between the grout mixture and the nail bar, the axial elongation (tension) along the entire length of the nail was measured. By analyzing the axial elongation data, the shear strength at the interface between the grout-embedded nail bar and the surrounding soil could be determined. The measurement of axial elongation (tension) can be facilitated by using vibration-based strain gauge sensors [12,13,24,25,26,27].

Due to discrepancies in wall performance data, the design was reassessed using back-analysis. During the back-analyses, the Hoek–Brown constitutive model, commonly applied in finite element analyses of rock masses, was utilized [28]. Sensitivity analysis was conducted to align the model’s predictions with the observed performance measurements.

In this research, the finite element method, a method of mathematically solving defined continuous problems, was utilized. The Plaxis 2D Connect Edition V22 program was used, incorporating coating surface plate elements, ground nail geogrid elements, and a mesh network with 15-node elements. Medium intensity and plane stress were selected. In two-dimensional slope modeling, the model boundaries were positioned at a distance of at least two to three times the excavation depth, as recommended by Brinkgreve [29], to minimize the boundary effects.

Engineering Geological Parameters of the Studied Weathered Rock Profile

This study was carried out on weathered sandstones from the Çakraz Formation. This Miocene-aged formation is a reddish-brown color. The sedimentary unit generally consists of round-grained and poorly graded arkosic sandstones and sandstone–claystone alternations in the upper levels. The layers of the unit are primarily inclined 30–40° SW. According to the ISRM weathering classifications [21,22], the unit falls between moderately and completely weathered grades (Figure 5).

The cores and samples obtained from the boreholes (BH19, BH23, and BH24) revealed highly weathered sandstone layers extending approximately 10 m below the surface. Below this level, moderately weathered sandstones can be observed (Figure 6). The uppermost section of the profile (approximately 4 m below the surface) consists of thin residual soil, which was excavated. Field studies including a standard penetration test (SPT) on this soil section yielded high SPT-N values due to the presence of completely weathered rock (

Table 2. Measured SPT-N values in the boreholes.

Borehole	Depth (m)	SPT-N Values
BH-19	1.50–1.95	9
BH-19	3.00–3.45	R
BH-23	1.50–1.95	R
BH-24	1.50–1.95	R
BH-24	3.00–3.45	33

).

The physical and mechanical properties of the representative samples obtained from varying depths were ascertained through physical and mechanical tests to determine unit weight, point load index, and uniaxial compressive strength variation by depth (Figure 7). Furthermore, a pressure meter test provided the modulus-of-elasticity values by depth, which ranged from 30 to 150 MPa for completely weathered sandstone and 180 to 280 MPa for moderately weathered sandstone.

The unit weight of the completely weathered sandstone units ranged between 21.0 and 24.0 kN/m³, while for the moderately weathered units, it ranged from 24.0 to 28.0 kN/m³.

The point load index values based on the data obtained from the point load tests showed irregular trends due to the inhomogeneous rock mass structure, but a general increase with depth was observed. In the completely weathered units, the point load values remained below 2.00 MPa, while they ranged from 1.00 to 3.00 MPa in the moderately weathered units.

The uniaxial compression test results indicated values below 10 MPa for weathering grades W4–W5, while they ranged from 18 to 25 MP for W3.

Triaxial compression tests showed that the effective internal friction angle was 40° for grades W4–W5 and 42–57° for W3. The effective cohesion values were 4.00 MPa for degrees W4–W5 and 1.50–2.00 MPa for W3 (Figure 8).

The rock mass properties were obtained using the Hoek–Brown constitutive model, as shown in Section 3.3.1 and Section 3.3.2.

3. Results and Discussion

3.1. Numerical Model: The Mohr–Coulomb Constitutive Model

The Mohr–Coulomb constitutive model allows one to calculate a fixed average stiffness or a stiffness that increases linearly with depth for each soil layer, enabling rapid estimation of deformation [30]. It is widely used for assessing rock slopes’ stability, with the factor of safety determined using fundamental shear strength parameters, such as cohesion (c) and the internal friction angle (ϕ). The simplicity of these parameters makes the results easy to comprehend [31].

A soil nail support system was designed using the Mohr–Coulomb model based on an idealized soil profile. The material parameters for the structural elements of the slope model were determined after establishing boundary conditions (

Table 3. Soil nail and shotcrete parameters used in the project-based design.

	Parameter	Symbol	Unit	Value
	Normal Stiffness	EA	kN/m	2.32 × 105
	Drilling Hole Diameter	Dh	m	0.127
	Rebar Diameter	dr	m	0.028
Soil Nail	Rebar Elasticity Modulus	Er	kN/m2	2.11 × 108
	Grout Elasticity Modulus	Eg	kN/m2	3.8 × 106
	Horizontal Spacing	Sh	m	1.60
	Rebar Length	Lx	m	4.00–6.00
	Normal Stiffness	EA	kN/m	2.5 × 106
Shotcrete	Flexural Stiffness	EI	kN/m2/m	8333
	Thickness	d	m	0.2
	Poisson’s Ratio	ʋ	-	0.2

). In Section 1–1, soil nail lengths at all levels were set to 6.00 m, while the slope inclination was 65°, and the nail spacing was 1.60 m. In Section 2–2, the length of the soil nails for the upper three stages was 6.00 m, while that in the last two stages was 4.00 m. The slope inclination was 85°, with a nail spacing of 1.40 m. All nails in both sections had a 15° inclination. The borehole diameter was 127 mm, and the nail reinforcement consisted of 28 mm diameter ribbed construction iron. The shotcrete surface, created using Q188/188-class steel mesh, was 200 mm thick.

The soil profile was classified as completely weathered sandstone from a depth of 0.00 to 7.50 m and moderately weathered sandstone below 7.50 m (

Table 4. The Mohr–Coulomb soil model structure parameters used in the project-based design.

Parameter	Symbol	Unit	W3 Sandstone	W4 Sandstone
Modulus of Elasticity	E	MPa	417	40
Unit Weight	γ	kN/m3	26	21
Cohesion	c	kPa	87	5
Internal Friction Angle	Φ	°	32	26
Poisson’s Ratio	ʋ	-	0.25	0.25

).

Mohr–Coulomb model analysis conducted along Section 1–1′ revealed the maximum horizontal displacement in the coating to be 2.78 cm, with a maximum horizontal displacement of 2.22 cm at the position of the inclinometer behind the wall (Figure 9).

Similarly, for Section 2–2′, the maximum horizontal displacement in the coating was 1.62 cm, while it was 1.53 cm at the position of the inclinometer behind the wall (Figure 10).

3.2. Performance of the Soil Nail System

Instrumental observations, including visual inspections and measurements, were made to assess the performance of the soil nail system. Monitoring deformations during the application phase is crucial for evaluating the safety of a ground support system. Additionally, soil nail pull-out tests were performed at each excavation stage to determine the final bond strength in situ. The data collected during this phase allowed for potential project revisions to optimize the design.

In order to determine the performance of the soil nail support system, two inclinometers were placed behind the wall, and two soil nail pull-out tests were conducted: one at an elevation of +146.00 near Section 1–1′ and another at an elevation of +138.50 near Section 2–2′. The locations where the inclinometer measurements (IM1 and IM2) and pull-out tests (PT1 and PT2) were conducted are shown in Figure 11. Upon completion of the soil nail slope support system, the site conditions and measurement locations were documented (Figure 12).

3.2.1. Inclinometer

Inclinometers are commonly used to monitor horizontal deformations in soil nail systems [31]. These instruments enable precise long-term monitoring of borehole positions. The setup of an inclinometer consists of an electrical cable with graduated depth markings, a handheld computer for data display, a plastic casing tube with four longitudinal grooves, and a probe with guide wheels to maintain rotational stability.

Measurements are taken at predefined depth intervals, typically 0.50 m, with the slope angle (ψ) recorded at each increment.

The total displacement (∑ L sin ψ) at the top of the hole is calculated as described by Dunnicliff [32] (Figure 12). To ensure accuracy, readings are verified by rotating the probe 180° and allowing time for an oscillatory equilibrium to be reached.

Lower slope angles measured via an inclinometer indicate greater wall performance [29].

The horizontal displacement values measured at IM1 (Section 1–1′) and IM2 (Section 2–2′) inclinometers are shown in Figure 13. The maximum displacement at IM1 was 2.30 mm, while that at IM2 was 3.90 mm. These values are significantly lower than those predicted by the Mohr–Coulomb model, demonstrating that the actual soil nail system provides a higher level of safety than initially estimated. This result indicates that the current design of soil-nailed walls provides a higher level of safety than the minimum required for the project, as the actual horizontal displacement values are lower than those predicted by the Mohr–Coulomb model during the design phase. Consequently, implementation costs may be reduced without compromising stability. The initial design and field displacement measurements for Section 1–1 and Section 2–2 are summarized in

Table 5. Comparison of preliminary-design horizontal displacement versus field measurements.

ux	Section 1–1′	Section 2–2′
Preliminary Design	2.22	1.53
Field Measurement	0.23	0.39

.

3.2.2. Soil Nail Pull-Out Tests Employing Strain Gauge Sensors

The soil nail pull-out test is another method used to evaluate system performance.

This test determines the interaction between the soil and nail via measuring bond strength. Figure 14 shows a picture of the soil nail pull-out test being applied.

The ultimate bond strength is influenced by shear stresses along the soil–grout interface, which depend on tensile force application, injection properties, and geological conditions. The mobilized unit length is defined using the tensile value Q [3].

$$\mathrm{Q}=\mathsf{\pi }\mathrm{q}{\mathrm{D}}_{\mathrm{D}\mathrm{H}},$$

(1)

where q is shear strength mobilized at the grout–soil interaction surface, and D_DH is effective drilling hole diameter.

The relationship between tensile force and the shear stress at the interface is expressed as follows:

$$\mathrm{d}\mathrm{T}=\mathsf{\pi }{\mathrm{D}}_{\mathrm{D}\mathrm{H}}\mathrm{q}\mathrm{d}\mathrm{x}=\mathrm{Q}\mathrm{d}\mathrm{x}$$

(2)

At any reinforcement distance (x), the tensile force (T) equates to the following:

$$\mathrm{T}\left(\mathrm{x}\right)={\int }_0^{\mathrm{x}}\mathsf{\pi }{\mathrm{D}}_{\mathrm{D}\mathrm{H}}\mathrm{q}\mathrm{d}\mathrm{x}={\int }_0^{\mathrm{x}}\mathrm{Q}\mathrm{d}\mathrm{x}$$

(3)

At the point where the length of the soil nail reinforcement root (Lp) is subjected to tension ends, the nail force is as follows:

$$\mathrm{T}\left({\mathrm{L}}_{\mathrm{P}}\right)={\mathrm{T}}_0=\mathrm{Q}{\mathrm{L}}_{\mathrm{P}}$$

(4)

The nail pull-out capacity (T_max) is expressed as follows:

$${\mathrm{R}}_{\mathrm{p}}={\mathrm{T}}_{\mathrm{m}\mathrm{a}\mathrm{x}}={\mathrm{Q}}_{\mathrm{u}}{\mathrm{L}}_{\mathrm{p}}=\mathsf{\pi }{{\mathrm{q}}_{\mathrm{u}\mathrm{l}\mathrm{t}}\mathrm{D}}_{\mathrm{D}\mathrm{H}}{\mathrm{L}}_{\mathrm{p}}$$

(5)

where Q_u is the tensile capacity per unit length (pull-out resistance per length), and q_ult is the ultimate bond strength.

Within the scope of the in situ test, two soil nail pull-out tests were conducted. The first of the pull-out tests (PT1) was carried out on a completely weathered sandstone unit, and the second (PT2) was conducted on a moderately weathered sandstone unit. In PT1, 28 mm ribbed reinforcement was used, and a 40 mm diameter ribbed reinforcement was used to increase the cross-sectional area. Both tests had a free length of L = 2.00 m and a root length of L = 4.00 m, with a drill diameter of 127 mm.

In the experiments, strain gauge sensors and comparator clocks were used to measure the amounts of displacement and extension. The strain gauges were placed at certain points on the ribbed rebars in the experimental setup (Figure 15).

Each strain gauge sensor was secured to soil nail reinforcement using a stabilizer guide and welded to ribbed reinforcement from both ears, allowing for free movement within the sensor (Figure 16).

The loading program recommended by the FHWA [33] was used to determine which soil nail pull-out test procedure to use (

Table 6. Loading stages and stage time periods.

Load Stage * DL	0.125 DL	0.25 DL	0.50 DL	0.75 DL	1.00 DL	1.25 DL	1.50 DL	1.75 DL	2.00 DL
Time Period (min)	1	10	10	10	10	10	10	10	10

). The design loads (DLs) in the pull-out tests were determined using bond strengths obtained from the literature. In experiments PT1 and PT2, the DL values were determined to be 120 kN and 320 kN, respectively.

GeoSense [34] was used to explain the values measured via the strain gauges used within the scope of this study and convert the raw data. Micro-stress change (Δµε) could be calculated using frequency unit (Hz) and linear digit (B) values obtained from a handheld computer (a data logger) using Equation (6).

$$\mathrm{B}={\displaystyle \frac{{\mathrm{H}\mathrm{z}}^2}{1000}}$$

(6)

The stress change in the sensor is given in Equation (7):

$$\mathsf{\Delta }\mathrm{\mu }\mathsf{\epsilon }={\mathrm{B}}_{\mathrm{f}}-{\mathrm{B}}_{\mathrm{i}}\mathrm{\ast }{\mathrm{C}}_{\mathrm{f}}\mathrm{\ast }{\mathrm{G}}_{\mathrm{f}}$$

(7)

where Δµε is the change in the micro-tensile value, B_f is the final B value (the data logger output), B_i is the initial B value (the data logger output), C_f is the calibration factor (obtained from the calibration device), and G_f is the grout factor.

The formula for the grout factor calculation is shown in Equation (8).

$${\mathrm{G}}_{\mathrm{f}}={\displaystyle \frac{{\mathrm{A}}_{\mathrm{g}}}{{\mathrm{E}}_{\mathrm{a}\mathrm{v}\mathrm{e}}}}$$

(8)

where A_g is the grout cross section, and E_ave is the average modulus of elasticity.

The formula for average elasticity modulus calculation is shown in Equation (9).

$${\mathrm{E}}_{\mathrm{a}\mathrm{v}\mathrm{e}}={\displaystyle \frac{{\mathrm{A}}_{\mathrm{r}}}{{\mathrm{A}}_{\mathrm{g}}}}\mathrm{\ast }{\mathrm{E}}_{\mathrm{r}}+(1-{\displaystyle \frac{{\mathrm{A}}_{\mathrm{r}}}{{\mathrm{A}}_{\mathrm{g}}}}\mathrm{\ast }{\mathrm{E}}_{\mathrm{g}})$$

(9)

Micro-strain values can be positive or negative. A positive value suggests tensile behavior, whereas a negative value indicates compression behavior. The soil nail tensile test data obtained from the portable computer were converted into micro-tension and kN using the formula provided.

3.2.3. Examination of the Data Obtained from the Soil Nail Pull-Out Test

Yielding occurred in the soil nail reinforcement in both tensile tests under axial loads. The ultimate bond stress could not be measured because the friction between the soil and the injection was not fully reproduced. However, assuming a conservative approach is employed, soil–grout stripping of the reinforcement at yield load is acceptable. In this case, the q_ult values obtained from tensile tests can be accepted as minimum q_ult values. Since the q_ult value obtained in test PT-1 was the minimum acceptable, the reinforcement cross-sectional area was increased, and a higher q_ult value was sought in test PT-2. While the soil nail reinforcement broke under 31.0 tons of axial load at completely weathered levels, the soil nail reinforcement broke under 71.0 tons of axial load in the moderately weathered sandstone unit (Figure 17).

In the literature, the bond strength (q_ult) value for a sandstone unit is 200 kPa, and the q_ult value for a completely weathered sandstone unit is 75 kPa [35]. According to the data obtained from tensile tests, in the completely weathered unit, the q_ult was determined to be >190 kPa, while it was found to be >440 kPa in the moderately weathered unit. There was a significant discrepancy between the estimated bond strengths based on the design and the actual values, which were >190 kPa for fully weathered sandstone and >440 kPa for moderately weathered sandstone.

Table 7. Parameters used in calculating micro-strain values.

Parameter	Value	Unit
Strain Gauge Factor	3.962	Micro-strain/digit
Rebar Cross-Sectional Area (Ar = 28 mm)	6.16 × 10−4	m2
Rebar Cross-Sectional Area (Ar = 40 mm)	50.24 × 10−4	m2
Grout Cross-Sectional Area (Ag)	1.13 × 10−2	m2
Rebar Elasticity Modulus (Er)	2.11 × 108	kN/m2
Grout Elasticity Modulus (Eg)	10 × 106	kN/m2
Avera Elasticity Modulus (Eave)	21 × 106	kN/m2
Grout Factor (Gf)	5.4 × 10−10	kN/m2

shows the results obtained by using Equations (8) and (9) to transform the raw data from the strain gauge sensors into micro-strain values.

The changes in micro-tension were calculated using Equation (7) by comparing linear digit (B) values, strain gauge factor, and injection factor values from tensile experiments. The obtained micro-stress values were converted to kN (µε = 10⁻⁶ kN). The load distribution created by tensile tests PT1 and PT2 on the strain-measuring sensors at different load levels is given in Figure 18.

The mechanical behavior of the nails was examined using strain gauge sensors during the pull-out tests in order to determine the distribution of loads acting on them. In both experiments, the nail loads were high on the side close to the coating. The axial load acting on the nails decreases as it moves away from the coating. Experiment PT1 shows a significant decrease in the axial loads acting on the nail after the second meter, even at a maximum load level of 240 kN. Experiment PT2 showed a sudden decrease in nail loads at a maximum load level of 640 kN after two and a half meters.

3.3. Design Review with Back-Analysis

Instrumental observations revealing smaller horizontal displacements indicated that the geotechnical parameters used in the design phase were conservatively chosen. As a result, numerical analyses predicted higher displacements than those measured in the field. To improve the accuracy of the model and ensure consistency with field data, the geotechnical parameters were reassessed. Initially, due to limitations in representing the non-linear behavior of rock masses, the Hoek–Brown (HB) constitutive model was adopted. The HB model is more preferred and validated for application to rock masses [29], so we continued this study using the HB model. A parametric analysis was conducted to determine the most influential parameters. Since the effective parameter has a direct relationship with geomechanical classification, classification values were re-evaluated. Based on the results obtained, geometric parameter analyses were carried out to optimize the design for improved efficiency and cost effectiveness.

3.3.1. The Hoek–Brown Constitution Model

The MC constitutive model assumes a linear elastic–perfectly plastic stress–strain relationship exists, but this assumption does not fully account for the wide range of stress levels in exposed rock masses. The Mohr–Coulomb (MC) strength criteria have been widely utilized in many classical analytical expressions and numerical modeling studies [36] because they can be physically computed simply and easily comprehended, although they are not appropriate for defining the failure envelope of rock masses. The analysis of rock slopes is complicated by the existence of heterogeneous and discontinuous rock masses with bedding planes, joints, faults, and fractures [37].

The HB constitutive model, on the other hand, provides a superior non-linear stress–strain relationship for rock masses [38]. Therefore, the new design was developed using the HB constitutive model. The HB constitutive model requires six key parameters to define the stress–strain relationship of the rock. These parameters are the elasticity modulus of the rock mass (E), the uniaxial compressive strength of the intact rock (σ_ci), Poisson’s ratio (ʋ), the disturbance factor (D), the geological strength index (GSI), and the empirical model parameter of the intact rock (m_i).

The Hoek–Brown failure criterion is expressed in Equation (9) as the non-linear relationship between large principal stress and small principal stress values. (Tensile stresses are positive values, and compressive stresses are negative values.)

$$\mathsf{\Delta }\mathrm{\mu }\mathsf{\epsilon }={\mathrm{B}}_{\mathrm{f}}-{\mathrm{B}}_{\mathrm{i}}\mathrm{\ast }{\mathrm{C}}_{\mathrm{f}}\mathrm{\ast }{\mathrm{G}}_{\mathrm{f}}$$

(10)

The value of m_b is defined as the rock coefficient (Equation (11)) depending on the rock discontinuity content.

$${\mathrm{m}}_{\mathrm{b}}={\mathrm{m}}_{\mathrm{i}}{\mathrm{e}}^{{\displaystyle \frac{\mathrm{G}\mathrm{S}\mathrm{I}-100}{28-14\mathrm{D}}}}$$

(11)

Auxiliary parameters with s and a values are defined in Equations (12) and (13).

$$\mathrm{s}={\mathrm{e}}^{{\displaystyle \frac{\mathrm{G}\mathrm{S}\mathrm{I}-100}{9-3\mathrm{D}}}}$$

(12)

$$\mathrm{a}={\displaystyle \frac{1}{2}}+{\displaystyle \frac{1}{6}}[{\mathrm{e}}^{{\displaystyle \frac{-\mathrm{G}\mathrm{S}\mathrm{I}}{15}}}-{\mathrm{e}}^{{\displaystyle \frac{-20}{3}}}]$$

(13)

Parameters s and a are used to define a material’s behavior. The inclusion of these factors provides a more realistic representation of rock mass behavior than the MC model.

3.3.2. Sensitivity and Parameter Analysis

A sensitivity analysis was conducted to evaluate the effects of variations in geotechnical parameters on displacement, shear stress, and the factor of safety. This analysis was conducted according to the approach suggested by Sert and Önalp [39], who proposed that for n geotechnical parameters, all 2n + 1 models should be analyzed. A range of ±25% from the reference values was considered for different lithologies to assess their influence on stability (

Table 8. Parameters used in calculating micro-strain values (for d = 28 mm reinforcement).

	Parameter	Symbol	Unit	(%-25) Min.	Ref.Val	Max. (%+25)
Highly Weathered to Completely Weathered Sandstone W4-W5	Weight per unit of volume	γ	kN/m3	16	21	26
	Elasticity modulus	E	MPa	22.5	30	37.5
	Poisson’s ratio	ν	-	0.15	0.2	0.25
	Uniaxial compressive strength	σci	MPa	12	16	20
	Material constant for intact rock	mi	-	13	17	21
	Geological strength index	GSI	-	20	25	30
	Disturbance factor	D	-	0.5	0.7	0.8
	Weight per unit of volume	γ	kN/m3	20	26	30
	Elasticity modulus	E	MPa	225	300	375
Moderately	Poisson’s ratio	ν	-	0.15	0.2	0.25
Weathered Sandstone	Uniaxial compressive strength	σci	MPa	16	20	25
W3	Material constant for intact rock	mi	-	13	17	21
	Geological strength index	GSI	-	30	40	50
	Disturbance factor	D	-	0.5	0.7	0.8

).

In order to examine the effect of changing a parameter value as a percentage, the analysis was conducted while keeping all other parameters constant. The safety coefficient and its effect on displacement were examined. For sensitivity analysis, 2 × (2 × 7 + 1) = 30 models were created using the HB body model in both moderately and completely weathered sandstone units, and their effects are shown as an average percentage (Figure 19).

The results indicated that the displacement values in the completely weathered rock masses were primarily controlled by unit weight and Poisson’s ratio, while GSI had a more significant effect in the moderately weathered units. As the weathering level of the rock mass decreases, the effect of the GSI value increases noticeably. It was determined that the effect of the GSI value on displacement was greater in the moderately weathered units than in the completely weathered units.

It has been determined that shear stress is controlled by unit weight in completely weathered rocks. As the degree of moderate weathering decreases, the effect of the GSI value increases noticeably. Notably, defining a low GSI value in a moderately weathered rock mass reduces shear stresses considerably.

When the parameters affecting the safety coefficient are examined, the GSI and the disturbance factor have a high impact, regardless of the weathering degree. The disturbance factor was recommended by Brinkgreve [29] to be 0.7 for weak rock slopes subjected to mechanical excavation. Thus, no modifications were made to the disturbance factor, D, in the updated design.

Brinkgreve [40] defined the m_i value of claystone as 4 ± 2 and the m_i value of sandstone as 17 ± 3. In this study, based on the design, the Çakraz Formation was determined to be intercalated with completely weathered sandstone–claystone. Therefore, selecting 17 as the value of m_i, which is accepted for completely weathered sandstones, cannot allow a full description of the sandstone–claystone weathering zone. Therefore, in the new design created at the completely weathered sandstone level, an m_i value of 13 was adopted to better represent the geological conditions.

In this analysis, we examined the influence of parameter modification on displacement, stress, and factor-of-safety values. It was found that unit weight and Poisson’s ratio exerted the most significant impact on the displacement value of a thoroughly weathered rock mass. It was also determined that the effect of the GSI value on displacement was greater in moderately weathered units than in completely weathered units. Additionally, it is clear that shear stress is controlled by unit weight in completely weathered rocks. Notably, defining a low GSI value for a moderately weathered rock mass reduces shear stresses considerably. The GSI and disturbance factor have a great impact on the factor of safety, regardless of the weathering degree. While the GSI value directly affects the factor of safety in both directions, it is effective only when the disturbance factor is reduced by 25%. These findings reveal that as the weathering degree decreases, the effect of the GSI on displacement and shear stress increases noticeably.

As a result, GSI values were reviewed since we found that they were effective for determining displacement and stability on weathered rock slopes.

3.3.3. Parameter Analysis of GSI Using RMR

The stability of rock slopes is influenced by various factors, including the strength of the rock, discontinuity type, discontinuity spacing, discontinuity continuity, discontinuity surface roughness, the degree of weathering, groundwater status, etc. RMR and GSI values can allow one to define the discontinuity parameters of rock slopes. The instrumental observation data revealed that the ground nail support system offers excellent performance based on this design. Thus, considering that the geotechnical parameters of the rock mass are defined, the Hoek–Brown constitutive model, which is the most commonly used numerical analysis model for rock masses [41], was used. According to the results of our parametric analysis, the GSI value is an important parameter for the HB constitutive model. Due to the exceptional performance seen in the soil-nailed support system, a new analysis was conducted using the HB constitutive model. The re-evaluated GSI values were then incorporated into the numerical analyses, ensuring better consistency with the field measurements.

Bienawski [42] introduced the RMR rock classification system. Uniaxial compressive strength, rock quality indicator (RQD), discontinuity intervals, discontinuity states, and groundwater are the parameters of this classification system. Hoek and Brown [28] introduced the geological strength index (GSI) classification system. Bienawski [42] defined the relationship between RMR and GSI values. Using the RMR classification, the RMR scores of the completely weathered and moderately weathered sandstone units and GSI values were determined using Equation (14) (

Table 9. Evaluation of RMR and GSI scores.

Parameter	Highly Weathered to Completely Weathered Sandstone	Moderately Weathered Sandstone
Average qu (MPa)	12	25
RMR Score	2	4
RQD (%)	0–25	25–50
RMR Score	3	8
Discontinuity Spacing (mm)	<60	200–600 mm
RMR Score	5	10
Discontinuity Status	Fault filling and 1–5 mm open joints	Slightly rough surfaces, separation of <1 mm, hard joint surfaces
RMR Score	10	15
Groundwater	Moist	Trickle
RMR Score	10	4
Total RMR Score	30	41
Total GSI Score (RMR-5)	25	36

).

$$\mathrm{G}\mathrm{S}\mathrm{I}=\mathrm{R}\mathrm{M}\mathrm{R}-5$$

(14)

3.4. Geometric Parameter Analysis

In order to investigate the effects of the slope geometry of the redesigned soil nail support system and the geometric properties of the elements used, one parameter was changed in the Hoek–Brown constitutive model, provided that all other parameters were kept constant. A total of 81 numerical analyses were performed. The factor-of-safety values of the model created using the moderately weathered parameters given in

Table 10. Parameter data pertaining to the Hoek–Brown constitutive model for weathered sandstone units.

Parameter	Symbol	Unit	Moderately Weathered Sandstone	Completely Weathered Sandstone
Unit weight	γ	kN/m3	26	21
Elasticity modulus	E	MPa	280	100
Poisson’s ratio	ν	-	0.25	0.25
Uniaxial compressive strength	|σci|	MPa	25	12
Material constant for intact rock	mi	-	17	13
Geological strength index	GSI	-	36	25
Disturbance factor	D	-	0.7	0.7

were examined using different geometric variations (

Table 11. Geometric model variations.

Inclination of Slope (°)	Soil Nail Spacing (m)	Inclination of Soil Nail (°)	Soil Nail Length (m)
65	1.20	10	4.00
75	1.40	15	6.00
85	1.50	20	8.00

). The results are shown in Figure 20.

Factor-of-safety values were compared in the geometric parameter analyses. When the effect of slope inclination on determining the safety number was examined, it was found that the highest safety numbers were obtained under all conditions on slopes with a slope of 65°. In this case, it can be said that reducing slope inclination significantly enhanced overall stability. According to the results, the most important structural element affecting slope stability was long soil nails. The positive effect of increasing soil nail length on stability is most clearly seen in the slope system with a 65°-inclined soil-nailed wall.

A parametric study has found that the soil nail inclination angle yields the highest performance for slopes with soil nail inclinations of between 10 and 20° [43]. In this context, studies were conducted with soil nail inclinations of 10–15–20° to determine the effect of the inclination angle of soil nails at different spacings on stability. The results of a study carried out on weathered granite rock suggested that soil nail spacing should not exceed 2.00 m. The use of soil nails at very frequent intervals increases the safety of a design [38].

As part of the geometric analysis, the influence of soil nail length on stability was systematically evaluated (Figure 20). The factor-of-safety (FoS) values for 4.00 m long soil nails ranged from 1.911 to 2.156, while those for 6.00 m long soil nails varied between 2.285 and 2.599. For 8.00 m long soil nails, the FoS values were observed to range from 2.559 to 3.024. Despite these variations, the 4.00 m long soil nails were considered potentially adequate in terms of the FoS. However, nail pull-out tests indicated that the applied loads were effectively dissipated at a depth of 4.00 m, suggesting that longer soil nails may be necessary to improve load distribution.

Beyond FoS considerations, factors such as the long-term stability of the slope, its performance over extended periods, and potential environmental impacts were also evaluated. Consequently, 6.00 m long soil nails were selected to provide an enhanced margin of safety. Notably, 8.00 m long soil nails were not adopted due to their higher cost implications. However, in Section 2–2′, 4.00 m long soil nails were utilized in the final two stages as a cost-saving measure while still ensuring structural integrity and compliance with safety requirements.

The horizontal displacement value and factor of safety obtained in the geometric parameter analysis of Section 1–1′, along with the horizontal displacement that was expected to be seen in the inclinometer section, are given in Figure 21.

Figure 22 shows the horizontal displacement value and safety coefficient obtained in the geometric parameter analysis of Section 2–2′, along with the horizontal displacement expected to be seen in the inclinometer section.

The numerical results of geometric parameter analysis for Sections 1–1′ and 2–2′ were compared with field inclinometer measurements. The results confirmed that the revised design provided enhanced stability, while identical maximum displacement results were achieved at the mm scale (see Figure 21, Figure 22 and Figure 23).

4. Discussion and Conclusions

During the design analysis phase, the u_x values were predicted to be 2.22 cm in the 1–1′ Section and 1.53 cm in the 2–2′ section. The ultimate bearing capacity (q_ult) value of sandstone, as suggested by Byrne [35], was accepted as 200 kPa for sandstones, while it was taken to be 75 kPa for weathered sandstone. The inclinometer measurements in Section 1–1′ recorded a field u_x value of 2.30 mm, whereas in Section 2–2′, the inclinometer measurements indicated a field u_x value of 3.90 mm. The q_ult value obtained from the PT1 pull-out test located near Section 1–1′ was determined to be 190 kPa, whereas the PT2 pull-out test yielded 440 kPa.

Given that the field measurements were significantly lower than the predicted values, the geotechnical parameters were re-evaluated. Sensitivity analyses were conducted on the Hoek–Brown (HB) constitutive model, commonly used for rock masses, revealing that the geological strength index (GSI) was the most influential parameter. The Rock Mass Rating (RMR) was reassessed based on field performance values to align the rating with the observed results. Using the revised RMR/GSI values, horizontal displacement variations with depth were analyzed for Sections 1–1′ and 2–2′ using the updated HB model parameters (Table 9, Figure 24 and Figure 25).

In order to accurately model rock behavior, stress-dependent parameters must be identified, as the failure envelope curvature increases when the GSI decreases and increases. Neglecting non-linear behavior can lead to an overestimation of the stability of nailed slopes [44]. The modified parameters produced analysis results consistent with those reported in previous studies [36,45].

According to the geometric parameter analysis incorporated in the design of the soil nail wall, the most influential parameters for stability, in descending order, are nail length [17], nail spacing, slope inclination, and nail inclination. Maximum horizontal displacements were observed at approximately 50–70% of the wall’s height (Figure 21). These results are also in good agreement with previous studies [36,45].

As shown in Figure 20, an optimal soil nail inclination of 20° and a nail spacing of 1.60 m were identified. Although selecting a slope inclination of 75° or 85° negatively impacts stability, the results remain within acceptable limits. Soil nail length emerged as the most critical factor for stability. For a 65° slope inclination, a 4.00 m nail length with a 20° soil nail angle yielded a factor-of-safety (FoS) value of 2.27. When the slope inclination was increased to 75°, the FoS for a 1.60 m spaced soil-nailed system was 2.22, while at an 85° inclination, the FoS was 2.16. The high FoS values obtained from the geometric analyses suggest that using 4.00 m nails instead of 6.00 m ones provides adequate stability while offering a more cost-effective solution, even for steeper slopes. This finding is consistent with results from soil-nail test studies [17,40]. Additionally, as lower forces are recorded away from the head of a soil nail, shortening the nail beyond a certain threshold may have only a minimal effect. Furthermore, nail length has a negligible effect on weathered rock [18]. Reducing the length of the soil nails from 8.00 m to 4.00 m yielded FoS values between 1.9 and 2.10, making it a cost-effective design choice. However, for permanent excavation, a length of 6.00 m is more suitable to ensure greater safety, long-term performance, and environmental stability.

Finally, geometric analysis of the structural elements confirmed that the support system can be optimized by using shorter nails, reducing overall costs.

Sensitivity analysis revealed that the GSI and parameters significantly impacted horizontal displacement and safety factor calculations. Consequently, the geomechanical properties defining the GSI were reassessed, and new values were determined. Further geometric parametric analyses were conducted using the HB constitutive model.

The HB model, as proposed by Hoek et al. [28], exhibits non-linear behavior under varying stress conditions. Analyses using the HB model demonstrated that accurately identifying in situ weathered rock parameters can lead to cost-effective and safe designs.

In this study, we evaluated the field performance of a soil-nailed slope design by comparing predicted horizontal displacements (u_x) with field measurements. The discrepancies between the design predictions and field data prompted a reassessment of geotechnical parameters, particularly the GSI and (m_i) values. Sensitivity analyses conducted using the Hoek–Brown model identified the GSI as a key factor influencing horizontal displacement and safety factor values. The revised RMR/GSI values improved prediction accuracy, aligning displacement estimates more closely with field observations.

Geometric analysis highlighted that soil nail length is the most critical factor affecting stability. Shorter nails (4.00 m) provided sufficient safety, even for steeper slopes, offering a more economical solution. These findings highlight the importance of incorporating field data and sensitivity analyses in order to optimize slope design and reduce implementation costs.