1 Introduction

Arid saline sabkha soils are composed of fine-grained sediments that have been deposited in a shallow marine environment and are subject to high evaporation rates [1, 2]. Evaporite-saline minerals such as gypsum and anhydrite accumulate because of high evaporation rates, contributing to the soil's heightened salt content [3, 4]. They are characterized by high compressibility and low shear strength, posing challenges for construction [2, 5, 6]. These soils display cohesive properties in their upper layers during dry seasons but lose strength upon contact with water, declaring them unsuitable for construction applications [7, 8]. Depending on the sedimentary deposition, the resulting sabkha structure can vary from loose to medium compact and the thickness could vary from a few meters to great depths exceeding 10 m [9]. Extreme variations in layer thickness and the highly variable compressibility of its distinct components contribute to the excessive differential settlement issues. Al-Amoudi in 1995, stated that the collapse characteristics of Sabkha soils are affected by the presence of salts [10]. These aspects illustrate the difficulties involved with using Sabkha soils as a foundation layer for construction projects, emphasizing the importance of careful investigation study and proper improvement techniques to handle their low bearing capacity. In addition, the weakness of Sabkha soil also requires excavation support for completing deep excavation activities, making the selection of an appropriate excavation support system a significant concern in construction project. Traditional approaches such as sheet piles and soldier beams prove costly and time-consuming to install. As a result, it is becoming increasingly vital to examine innovative excavation support systems, particularly given the growth of urban and industrial activity in Sabkha-containing areas.

Deep soil mixing (DSM) walls have recently arisen as an innovative method of excavation support. Its application in sabkha soil has yet to be investigated. DSM was initially developed as a ground improvement technique with a long history of improving soil strength and stability [11, 12]. This technique involves mixing cement, lime, or other additives with the existing soil to create a homogeneous mixture with improved mechanical properties and minimize permeability [13]. The construction of DSM requires the use of an auger to blend in-situ soil with injected cement grout by using a set of mechanical cutting blades to generate soil–cement columns. The use of DSM was extended to varied geotechnical applications, such as improving slope stability, providing embankment support, creating cut-off barriers, strengthening against seismic forces, and remediating environmental issues [14,15,16]. Due to its cost-effectiveness and need for fewer manpower and materials than alternative approaches, DSM has attracted the focus of many researchers for excavation support [14].

The use of DSM in excavation support design has been increasingly prominent, particularly in urban areas. It offers distinct advantages, including reduced construction noise and vibration compared to conventional excavation support methods [13, 17]. The construction process of DSM for excavation support entails the utilization of an auger, which blends in-situ soil with injected cement grout with mechanical cutting blades. This results in the formation of circular soil–cement columns that overlap, forming a continuous soil–cement wall. To enhance the ability of DSM walls to withstand lateral pressures, it is a common practice to insert steel pipes or H-beams within them to augment bending and shear strength [18]. Anchors become a viable option for improving wall stability when faced with significant lateral soil pressure and concerns about potential DSM wall lateral displacement. Numerous studies have reported successful applications of DSM walls for excavation support. For example, McMahon (2001) employed deep soil mixing for the excavation of a highway tunnel underpass in Pennsylvania, USA, with excavation depths ranging from 0 to approximately 6.7 m [14]. Ruffing (2012) presented a comprehensive case study that included site history, design methodology, and DSM wall installation procedures. The results of this study demonstrated that DSM walls, having a width of 2.4 m and an excavation depth of 4.9 m, exhibited exceptional stability and resistance to lateral displacement. They displayed no significant settlement or cracking during the construction process [19]. These findings emphasize the reliability and effectiveness of DSM walls as a solution for excavation support.

Analysis and design of DSM for excavation support, they are still highly empirical with several assumptions due to unclear understandings of the behaviour of the DSM walls in different soil types. Currently, standardized guidelines for the design of DSM walls are not available. Despite some differences in performance, geotechnical engineers typically consider DSM walls for excavation supports similar to pile secant walls or soldier pile walls [20, 21]. One of the most notable distinctions is the presence of steel beams within the DSM columns. The steel beams embedded into the DSM are significantly stiffer than the surrounding soil–cement mixture, allowing the soil–cement mixture to be arched. The soil cement mixture must be designed to withstand and transfer the lateral stresses imposed by the retained soil and the potential surcharge load to the adjacent steel beam [14]. The steel beams are designed to withstand bending and shear stresses, and the DSM wall must be sufficiently deep to ensure adequate stability. According to Briaud et al., when doing preliminary design for DSM walls, an embedment depth equal to 1.3 times the height of excavations is a widely accepted method [22]. While DSM walls have proven effective as excavation support in various soil types, their application in sabkha soils remains unexplored. Jung et al. have reported that DSM has the potential to enhance the bearing capacity of sabkha soils [23]. The success of this technique in improving sabkha soil properties has raised the possibility of using it for excavation support. Projects situated in soft soils such as sabkha, with a high groundwater table, often provide favourable conditions for the application of DSM walls. The lack of a designated design approach for DSM walls in the context of Sabkha soils demands dependence on numerical methods to measure their performance entirely. Sabkha soils present special difficulties that render conventional design methods for DSM walls ineffective. Numerical methods provide a flexible platform for simulating DSM wall behaviour in Sabkha environments.

The existing literature highlights the requirement for further investigation and innovation in Sabkha soil excavation support system design. This research explores the feasibility of employing DSM as an excavation support system in Sabkha soils. The primary objective is to evaluate DSM wall performance in Sabkha soils using numerical analysis, considering factors like excavation depth. The paper commences with an examination of the mechanical properties of the sabkha-cement mixture. The findings from this study illustrate that appropriately designed DSM walls, when combined with anchoring methods, substantially improve excavation stability in Sabkha soils. This work lays the foundation for future research in this essential field.

2 Sabkha cement mix

The evaluation of the cement-soil mixture on-site is a crucial aspect of the design of DSM walls since it has a substantial effect on the design and the overall failure of the DSM walls. Ordinary Portland Cement (OPC) serves as the primary DSM binder. In cases of high sulfate contamination, as found in sabkha soils, Resistant Cement (SRC) replaces OPC [24]. Soil cement behaves similar to weak concrete, greater the strength of typical soils [14]. Unconfined compressive strength (UCS) is the widely accepted parameter for evaluating soil cement mixtures, serving as both a design and quality control measure [25]. In the review of the literature on the properties of the sabkha cement mixer, only a small amount of research was done in the field. Jung et al., studied stabilization of sabkha soils using DSM to increase the bearing capacity under foundation. Representative samples were selected and tested in the laboratory. The average value of unconfined strength obtained for design is \({\mathrm{f}}_{\mathrm{ck}}=2\mathrm{ MPa}\) [23]. On the other hand, numerous laboratory studies on the stabilization of sabkha soils using cement have been conducted. Al-Amoudi performed an investigation into the stabilization of Sabkha soils using cement. In the laboratory, 10% cement was added to the Sabkha, and the UCS reached 5 MPa [26]. Mohamedzein studied Sabkha soil stabilization in a laboratory, and he found the UCS of the Sabkha increased to 4.5 MPa when 10% cement was applied [27]. The significant difference between UCS values in the field and laboratory for Sabkha-cement mixes in prior studies indicates a preference for employing highly conservative UCS values in modelling DSM walls. This study utilizes the average UCS value obtained by Jung et al. in 2020.

3 Numerical model

The numerical model was used to analyse the effects of various parameters on the performance of DSM walls in Sabkha soils. Plaxis 3D Software, a finite element model (FEM) tool, facilitated model development. Parameters under investigation encompassed wall geometry, soil properties, and excavation depth. The study tested a self-supporting excavation wall system's capability to withstand excavation without horizontal bracing. The selected soil profile represented typical conditions in the coastal area of Arabian Gulf Region where sabkha strata form: a top layer of sand, followed by sabkha. A dense to very dense sand layer extended up to 20 m under the Sabkha soil’s lower surface. The groundwater table was estimated at 2.4 m depth. Three different sabkha thicknesses were investigated: 3 m, 5 m, and 7 m. Due to its low tensile strength and being usually excavated without struts, a DSM wall typically has a thick cross section [15]. Determinants of DSM wall thickness include soil properties, wall height, and design loads. These walls can range in thickness from 0.3 to 1.2 m [16]. For this study, DSM was assumed to have a 1m diameter, with columns arranged in a 0.2 m overlapping honeycomb pattern. Initially, DSM wall depth estimation is D = 1.3 H, where H signifies excavation depth from the ground surface [28]. During the DSM's soft phase, wide H-beams spaced at 1.6 m are installed to withstand shear and bending forces. Figure 1 illustrates the typical arrangement and construction sequence of DSM walls for excavation support, as employed in this research.

Fig. 1
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Execution sequence diagram for DSM Walls

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The study employs the Mohr–Coulomb constitutive model to simulate soil layer behaviour. This model assumes soil behaves as a linear elastic material, defined by the Mohr–Coulomb failure criterion. It incorporates shear strength, cohesion, and friction angle to determine soil layer behaviour. Model parameters are sourced from published data [2, 18, 19], as detailed in Table 1, which presents soil layer properties. Figure 2 depicts the schematic utilized in this study for DSM wall FEM model. The simulation adopts the undrained model for sabkha soils due to the quick installation and excavation timetable for DSM walls.

Table 1 Soil layer properties
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Fig. 2
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Schematic used to simulate DSM walls in sabkha soil

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The unconfined compressive (UCS) strength of the Sabkha mix with cement was taken from (Jung et al., 2020) study [23]. As a result of this research, it was concluded that the UCS value of the Sabkha mix with cement is 2 MPa [23]. The elastic models of soil mix with cement assessed from Briaud et al. research [22], as a result of full-scale DSM project at Texas A&M University. The model assumes that the soil–cement mixture behaves as a homogeneous material. It was suggested the equation below to estimated elastic models of DSM walls:

$${\mathrm{E}}_{\mathrm{soil}-\mathrm{cement}}=12900{\mathrm{q}}_{\mathrm{u}}^{0.41},$$

where \({\mathrm{E}}_{\mathrm{soil}-\mathrm{cement}}\) is the elastic modulus of soil–cement mixture (kPa).\({q}_{u}:\) Unconfined compressive strength of Sabkha mix with cement.

The DSM walls properties are shown in Table 2. The interface between the DSM walls and the surrounding soils is modelled as a frictionless contact, meaning that there is no resistance to sliding or shearing between the two materials. The embedded beam elements in Plaxis software are used to model the H- beams because they can accurately capture the bending and shear behaviour expected on the H- beams.

Table 2 Parameter properties of DSM walls for a linear elastic model
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A row of anchors is added to DSM walls to reduce deformation and promote effective load transmission from the H-beams to the anchor system, as is normal engineering practice. This integration plays a crucial role in maintaining the stability of DSM walls. Figure 3 illustrates the arrangement of anchors used in this study within the soil profiles for different Sabkha thicknesses: (a) for a Sabkha thickness of 3 m, (b) for a Sabkha thickness of 5 m, and (c) for a Sabkha thickness of 7 m. This information is vital for comprehending anchor behaviour under various Sabkha thickness scenarios, contributing to an overall understanding of the excavation support system. The material properties for the anchor and the embedded beams (grout body) employed in this study are detailed in Table 3.

Fig. 3
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Alignment of anchors within the soil profiles: a Sabkha thickness: 3 m b Sabkha thickness 5 m, and c Sabkha thickness 7 m

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Table 3 Material properties of anchor and embedded beams (grout body)
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The soil volume was discretized into a finite element mesh consisting of ten-node tetrahedral volume elements. The mesh is generated with a very fine global coarseness. Additional refinement was made around the wall. This allows for more accurate simulations and better resolution of complex geometries. At the bottom of the FEM, the displacements were set to zero in the three directions of x, y, and z. This is done to ensure that the model is fixed at the bottom and does not move. This is important because it allows for accurate results to be obtained from the FEM. By fixing the bottom of the model, it prevents any potential errors that could arise from a moving base. Additionally, this also helps to ensure that the boundary conditions are properly applied and that all the forces and moments are accurately calculated. The excavation process was simulated by following the actual construction process. This was done by activating or deactivating packages that included associated elements. The construction sequence was then simulated in several phases. The simulation allowed for a detailed analysis of how different construction methods would affect the overall performance of DSM walls.

4 Results and discussion

The finite element analysis was thus carried out by properly taking in consideration the properties of soils, properties of DSM walls, boundary conditions, and analysis procedures to obtain the responses of the soil layers and DSM walls, which could not be directly obtained from the field. The following section focuses on the main factors that influence the performance of DSM walls when used as excavation support in Sabkha soils.

4.1 Horizontal displacements

Horizontal displacement serves as a critical criterion for evaluating the design of excavation support. It quantifies the lateral movement that DSM walls experience due to lateral earth pressure, water pressure, and imposed loads near the excavation site. The acceptable level of horizontal displacement in an excavation varies, contingent upon factors such as soil type, excavation depth, and other parameters. Therefore, engineering codes do not provide specific values for allowable horizontal displacement, requiring a comparison of study-derived values with well-documented published data on excavation support in soft soils.

In Figs. 4, 5, 6, horizontal displacement in the DSM wall's center between H-beams is analyzed for sabkha layers of 3 m, 5 m, and 7 m, and excavation depths of 3 m, 5 m, and 7 m. The analysis considers three scenarios: DSM walls with an H-beam and anchor, DSM walls with an H-beam but no anchoring, and DSM walls without an H-beam. In this study, two rows of anchors were used, positioned at depths of 0.5 m and 2.5 m, respectively, and connected to the H-beams. Horizontal displacement is highest near the top of the DSM wall, decreasing with depth. In addition, DSM walls with H-beams and anchors exhibit minimal displacement, while those without H-beams display more significant displacement This underscores the effectiveness of DSM walls, steel beams, and anchoring in reducing horizontal displacement. H-beams, with their advantageous mechanical properties like elastic modulus and moment of inertia, contribute significantly to this reduction. Meanwhile, anchoring reduces horizontal displacement by providing additional support to the H-beams, preventing them from sliding or lateral deformation because of lateral stress. These findings emphasize the need of adapting geotechnical DSM wall designs to keep horizontal displacement within acceptable limits. The observed increase in lateral earth pressure with excavation depth is a crucial finding. As excavation depth increases, the lateral earth pressure acting on the DSM wall also increases. This heightened lateral earth pressure directly correlates with increased horizontal displacements within the DSM wall. The rationale behind this phenomenon lies in excavation processes. As excavation progresses, the front of the DSM wall is exposed to a decrease in lateral soil pressure. This decrease diminishes the horizontal restraint on the front of the DSM wall, allowing it to deflect outward, moving away from the surrounding soil layers. This observation highlights the interplay between excavation depth and lateral earth pressure, and how it influences the stability of DSM walls.

Fig. 4
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Variation of horizontal displacement with DSM wall Depth for a 3 m thick Sabkha

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Fig. 5
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Variation of horizontal displacement with DSM wall Depth for a 5 m thick Sabkha

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Fig. 6
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Variation of horizontal displacement with DSM wall Depth for a 7 m thick Sabkha

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To deepen our discussion, it's essential to consider these findings in relation to previous research. Wang's extensive dataset of 300 case histories on wall displacements and ground settlements from deep excavations in soft Shanghai soils provides a benchmark for assessing our results. Our recorded range of horizontal displacement, spanning from 0.09 to 0.62% of the excavation wall height (H), notably falls within the lower range of wall displacements reported by Wang, whose maximum value was 0.91% of H. This suggests that the application of DSM walls in sabkha soils display favorable performance in terms of horizontal displacement when compared to excavations in soft Shanghai soils [29]. In contrast, Xiao's study on 92 braced excavations in China reported a maximum lateral displacement of 0.5% of H, which is slightly lower than our observed range. This variation may reduce from differences in soft soil conditions and excavation methodologies between our sabkha soil study and the braced excavations in China [30]. However, using struts in the design of braced excavations reduces horizontal displacement more; in the following study, struts were not used due to the large span of the excavation.

Figures 7, 8, 9 present FEM results for horizontal displacement at H-beams, offering insights into anchor effectiveness in mitigating lateral movement. DSM walls with H-beams and anchors, showing little horizontal displacement and emphasizing anchor efficiency. Conversely, DSM walls with H-beams but without anchoring, displays higher horizontal displacement, highlighting the importance of anchors in reducing lateral movement. In addition, DSM walls without H-beams, reveals substantial lateral displacement, underscoring the role of H-beams and anchors in decreasing horizontal displacement.

Fig. 7
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Horizontal displacement of the H-beam (Sabkha thickness is 3 m)

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Fig. 8
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Horizontal displacement of the H-beam (Sabkha thickness is 5 m)

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Fig. 9
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Horizontal displacement of the H-beam (Sabkha thickness is 7 m)

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4.2 Variation of bending moment

Determining the maximum bending moment in H-beams is essential to prevent localized failures from exceeding the section's moment capacity. To investigate bending moment variation, two scenarios were analysed: DSM walls without anchors and DSM walls with anchors for lateral support. Figures 10, 11, 12 provide a detailed overview of how bending moments in H-beams change with varying excavation depth. Bending moments start at zero, reach their extremes, and then fluctuate as excavation depth and lateral earth pressure vary. The placement of anchors in DSM walls aims to reduce deformation by providing lateral support for H-beams. Consequently, greater moments are generated in H-beams. It is noteworthy that the bending moment values do not possess a uniform pattern. They are influenced by numerous factors, including the thickness of soil layers, excavation depth, and anchor placement. This variability underscores the importance of conducting numerical studies to accurately assess the performance of DSM walls, H-beams, and anchors in these specific conditions.

Fig. 10
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Variation of the H-Beam Bending Moment (Sabkha thickness is 3 m)

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Fig. 11
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Variation of the H-Beam Bending Moment (Sabkha thickness is 5 m)

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Fig. 12
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Variation of the H-Beam Bending Moment (Sabkha thickness is 7 m)

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Table 4 shows the axial force generated in anchors at different excavation depths and Sabkha thicknesses. As the excavation depth increases, the axial force exerted by the anchors tends to increase as well. This indicates that deeper excavations impose more lateral earth pressures on H- Beam, resulting in increased load transfer to the anchors. When anchors are employed in DSM walls, they serve as load-bearing elements that resist lateral forces. This transfer of load results in an increase in the axial force within the anchors, which directly affects the bending moment experienced by the H-beams. This relationship highlights the importance of properly designing and considering the load transfer mechanism between the anchors and the H- beams, and the need for accurately determining the maximum bending moment to ensure that it does not exceed the capacity of the beam section.

Table 4 Axial force generated in anchors
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5 Conclusion

This study has explored the feasibility of implementing Deep Soil Mixing (DSM) as an excavation support system in Sabkha soils, which are known for their challenging characteristics in terms of high compressibility and collapse tendencies. The investigation employed finite element analysis using PLAXIS 3D to simulate the DSM process in Sabkha soils.

The results indicate that DSM can indeed serve as an effective excavation support system in Sabkha soil, provided certain factors are taken into consideration, such as the depth of excavation. The results of a study conducted on sabkha thicknesses of 3 m, 5 m, and 7 m, along with the corresponding depths of excavation. Horizontal displacement, a critical parameter in evaluating excavation support, was found to be within acceptable limits when DSM walls were combined with H-beams and anchors. This combination effectively reduced lateral displacement, demonstrating its efficacy in enhancing excavation support stability. Moreover, the study highlighted the influence of factors such as Sabkha thickness and excavation depth on horizontal displacement and bending moments in H-beams. These findings highlight the importance of careful design, considering the properties of DSM, steel beams, anchors, soil characteristics, and other relevant factors. A well-planned geotechnical design that addresses these aspects can mitigate lateral displacement issues in DSM walls.

As future work, it is recommended that researchers investigate into the conceptual challenges related to DSM wall design in Sabkha soils. Additionally, cost-effectiveness comparisons with other excavation support alternatives should be explored to assess the economic viability of DSM in Sabkha soil applications. Such research endeavours will contribute valuable insights into the potential of DSM walls as an efficient excavation support system in the context of Sabkha soils.