Effect of pipe characteristics in umbrella arch method on controlling tunneling-induced settlements in soft grounds

Ali Morovtdr, Mssoud Plssi, Rez S. Ashtini

a Department of Civil Engineering, The University of Texas at El Paso, El Paso, TX, 79968, USA

b College of Engineering, Faculty of Civil Engineering, University of Tehran, Tehran,14155-6619, Iran

Keywords:Tunnel reinforcement Umbrella arch method (UAM)Urban tunneling Forepoling pipes Finite element analysis Numerical simulation

ABSTRACT Recent developments in tunneling have stimulated design practitioners to more effectively utilize the underground spaces. However, tunneling at shallow depth in soft grounds gives rise to concerns associated with tunnel instability.Umbrella arch method(UAM),as a pre-reinforcement approach of tunnels in complex geological conditions,is widely used to maintain the tunnel stability.Quantitative assessment of the impacts of the entire approach and forepoling pipe features on tunnel stability remains challenging due to the complex nature of the UAM application. This study aimed to assess the effect of pipe design parameters on reinforcing the tunnels excavated in soft grounds. This practical investigation considered the actual field conditions attributed to the tunneling procedure and UAM deployment.Then,the tunneling process was modeled and the tunnel excavation-induced settlements were calculated.The post-processed results confirmed that deploying the UAM substantially reduced the tunnel crown and ground surface settlements by 76% and 42%, respectively. Investigation of various design parameters of pipes underscored the significance of incorporating the optimum value for each individual parameter into design schemes to more effectively control the settlements.Additionally,contrasting the settlement reduction rates (SRRs)for pipe design variables showed that the tunnel stability is more sensitive to the changes in the values of diameter and length,compared to values of the installation angle and center-tocenter distance of the pipes.

1. Introduction

In recent years, due to the drastic changes in urban-rural developments,underground projects such as tunneling have provided one of the most effective solutions for transportation problems.However, the excavation procedure requires special attention at both design and construction stages to maintain stability during construction. In fact, in order to find optimal excavation method and design variables satisfying the tunnel stability, design practitioners should accurately assess the tunnel and ground settlements considering various design strategies to mitigate and control excavation-induced settlements in actual field conditions. Otherwise, success in construction of the tunneling project will be seriously jeopardized. Particularly, in the case of tunneling at shallow depths that the ground consists of soft soils or weak rocks, safe construction of tunnel without causing any damages is of utmost importance. Hence, one of the main challenges for engineers to construct tunnels in such critical regions is to limit the settlements to acceptable ranges.This is extremely important from not only the tunnel stability viewpoint but also the safety perspective.

Tunnel excavation using the new Austrian tunneling method(NATM), in combination with auxiliary supporting techniques, is widely used to overcome the significant difficulties encountered while tunneling in soft and weak grounds. Several reinforcement techniques such as umbrella arch method (UAM), jet grouting,mechanical pre-cutting, and sub-horizontal fiberglass reinforcement have been deployed to limit the tunnel excavation-induced settlements. Specifically, UAM has been used to a great extent,due to its potential pre-reinforcement capabilities (Schumacher and Kim, 2016; Song et al., 2013). Several field cases of tunnels excavated using the UAM were reported by Haruyama et al.(2001),Sekimoto et al.(2001),Ocak(2008),Aksoy and Onargan(2010),Gao et al. (2015), Elyasi et al. (2016), Salmi et al. (2017), Taromi and Eftekhari (2018), Klotoé and Bourgeois (2019), and Morovatdar et al. (2020a).In this approach,prior to tunnel excavation,a series of forepoling pipes is installed along the tunnel circumference in the crown.Subsequently,by injecting the grout through the pipes,the stiffened soil (between the pipes) coupled with the forepoling pipes creates an umbrella-shaped arch above the tunnel. This arrangement considerably enhances the stiffness properties of the impacted soil and improves the tunnel excavation stability.Tunneling procedure using pre-reinforcement UAM is well explained in the literature by Carrieri et al.(2005),Kim et al.(2009),Aksoy and Onargan (2010), and Klotoé and Bourgeois (2019).

2. Background

Several analytical and experimental studies have been conducted to investigate the performance of the UAM in the tunnel construction procedure. Ranjbarnia et al. (2018) developed an analytical approach to evaluate the behavior of the UAM in deep tunnels. In the proposed approach, the displacement of the supported span of the tunnel was calculated using the convergenceconfinement method. The results showed that the pipe diameter is a significant factor controlling the excavation-induced settlements in deep tunnels. Ocak (2008) studied the second stage excavation of Istanbul Metro, which was constructed using NATM in combination with UAM and the results showed that using the UAM can effectively control the surface deformations,especially in clay-bearing formations.Yoo and Shin(2003)conducted laboratory studies on the deformation behavior of tunnel face supported by longitudinal pipes. Their results showed that the face-reinforcing technique could efficiently control the ground settlements during tunneling. Shin et al. (2008), deploying a large-scale model,investigated the UAM reinforcing mechanism in granular soils.They found that the pipe reinforcement of heading can significantly decrease the induced settlements, and improve the tunnel face stability.Heidari and Tonon(2015)considered the hardening effect of jet grouting umbrella elements in controlling of tunnel convergence.Hisatake and Ohno(2008)conducted centrifugal model tests to evaluate the effect of using UAM on tunnel displacement reduction.They found that deploying the pipe roof supports could decrease the ground displacements by 75%.

Several researchers have also studied numerically the overall impacts of the UAM on tunnel stability.Elyasi et al.(2016),using a finite difference program, numerically simulated the tunneling procedure,as well as the UAM deployment in a case study that was under severe geological conditions. The numerical results, accompanied by in situ monitoring and instrumentation efforts, in general, indicated the effectiveness of using UAM in controlling the tunnel displacements. Aksoy and Onargan (2010) assessed the influence of implementing UAM and tunnel face bolts on ground surface settlements induced during tunnel construction of the second phase of Izmir Metro, which was located in the densely populated district. The numerical results indicated that the UAM and face bolt applications could considerably reduce the risk of buildings’ failure by decreasing the ground settlements by 69%.Ocak and Selcuk(2017)deployed two-dimensional(2D)numerical models to investigate the performance of the UAM in tunneling.It was revealed that although implementation of the UAM is timeconsuming, it is a practical pre-supporting method that can significantly control the tunneling-induced displacements.

A number of studies have been carried out on the design parameters of the elements in the UAM supporting system.Volkmann and Schubert (2010), through calibration of the three-dimensional(3D) numerical model (FLAC3D) with in situ monitoring of tunnel settlements, investigated the influence of the UAM design parameters on the deployed pre-support system. Based on the backcalculations of the in situ measurements, the authors assessed the structural properties for the components of UAM and the changes in load redistribution. Wang (2012) conducted a systematic parameter study to evaluate the effects of some of UAM design parameters on the mechanical behavior of pipe roof reinforcement.The study showed that each individual reinforcement parameter has a critical value in which the tunnel reinforcing effect would be the maximum.Oke et al.(2014)used 2D and 3D models to evaluate the influential design parameters attributed to the use of UAM technique. They later developed a second-order equation for distributed load through a semi-analytical solution in which, it is assumed,the beam lays on the elastic foundation(Oke et al.,2016).Song et al. (2013) developed a finite element software package to evaluate various conditions and variables of the UAM. The developed model was instrumental in estimating the quantity of forepoling steel pipes needed for the UAM at an early stage of the tunnel design protocol.

Recently, Zarei et al. (2019) investigated the role of using the UAM in the tunnel stability by the 3D numerical simulations.They deployed a finite difference program,FLAC3D,for further numerical modeling purposes. It was found that the UAM could effectively transfer the earth pressure to the primary support systems,leading to improvement in the tunnel stability. They also assessed the influence of pipe design parameters on the efficiency of the deployed UAM. The results indicated that decreasing the installation angle and transverse spacing of pipes and increasing the diameter of pipes led to a reduction in the tunneling-induced displacements.Qian et al. (2019), using the Winkler-spring model, developed an analytical approach to simulate the behaviors of the UAM pipes.They found a relatively good agreement between the results obtained from the proposed model and the numerical modeling using FLAC3D. In another study, Abdollahi et al. (2019), through the deployment of the finite difference technique, as well as 3D numerical simulations, investigated the suitable reinforcement strategies associated with a case study with mechanized tunneling.The numerical modeling of various reinforcement alternatives in the evaluated case study showed that the UAM was an effective approach in order to maintain the tunnel stability. Klotoé and Bourgeois (2019), conducting 3D finite element simulations, evaluated the influence of the UAM on the settlements induced by shallow tunneling. Through a parametric analysis, they found that the influence of using the UAM on the settlements remained modest for the range of parameters considered in the analysis.

Previous studies have provided insights into the working mechanism and behavior of the tunnel reinforced by the umbrella arch technique. However, deploying nonuniform and inconsistent analysis approaches in some studies for evaluation of the effect of using UAM in tunneling led to widespread and even contradicting results that sometimes defy common sense. In terms of previous numerical studies, one of the primary sources of inaccuracy could be attributed to the fact that some of these studies relied on several simplified assumptions made in the analysis. For instance, in a number of numerical analyses,the elements in the primary support system of the tunnel, i.e. steel frame, shotcrete, and wire mesh,were simulated by an equivalent section representing the entire composite support system. Likewise, several studies have documented that the UAM elements, i.e. steel pipes, cement grout,and soilcrete, were simulated as one single element with equivalent material properties based on the weighted averages (Barla and Bzowka, 2013). The root of the problem attributed to these approaches is that determination of the internal forces generated in the pipes would be extremely challenging. Consequently, making these simplifications, instead of modeling the aforementioned elements individually, simulates the circumstance that is significantly different from the actual field conditions,and hence,this can seriously jeopardize the accuracy of the analysis results.

Another anomaly in some other previous studies pertains to the incorporation of the typical values, instead of the laboratoryderived geotechnical properties for the existing soil and formed soilcrete zones into the analysis. Additionally, appropriate assignment of the interactions between the UAM elements and the surrounding soil sometimes was overlooked in the numerical simulations to expedite the computation time.However,it is noted that the UAM performance is highly sensitive to the accurate incorporation of the material properties into the analysis,as well as the proper definition of the existing interactions between UAM elements and the surrounding soil.Hence,these properties should be properly characterized and considered in numerical simulations.

Another noticeable remark from previous researches is link to the type of analysis technique deployed in the numerical modeling of the tunnels reinforced by the UAM. Essentially, the majority of the previous studies used the finite difference method, a wellknown and robust method, in order to investigate the beneficial impacts of the UAM on tunnel stability. FLAC3D program is one of the prime examples that are based on finite difference algorithms.It should be noted that, besides finite difference, finite element method is another methodologically sound and robust approach that has been deployed in a limited number of studies for evaluation of the overall impacts of UAM on tunneling procedure.Therefore, a comprehensive evaluation of the UAM deployment,using the finite element method,still needs to be investigated and quantified to improve the existing knowledge associated with this tunnel reinforcement technique. The aforementioned issues were the motivations of the authors to investigate the UAM applications in tunneling.

3. Research objective

The primary objective of this research study was to accurately assess the beneficial impacts of the UAM on the stability of the tunnels in soft grounds. In this study, through a comprehensive evaluation, initially, the information on the tunneling procedure,UAM deployment, and the various aspects of staged construction was gathered from Ghazvin-Rasht tunnel project,in consideration of actual field conditions. This information coupled with laboratory-derived geotechnical properties of the existing soil was in turn incorporated into a series of finite element simulation models using the ABAQUS program. An all-encompassing procedure was then devised to simulate all the UAM and primary support elements separately, in consideration of the appropriate interactions. Subsequently, the tunneling-induced settlements were calculated for further comparative analysis in this context.Furthermore, because the majority of the previous studies have concentrated on general practices of the UAM, and a limited number of studies focused on the influential design parameters of UAM pipes, the second stage of this study was to quantitatively assess the main impacts of pipe characteristics on the tunnel stability.For this,we also investigated the optimum values of different design parameters of the UAM pipes, i.e. diameter, total length,overlap length,installation distance,and installation angle,to help design engineers excavate tunnels in a stable, safe, and costeffective manner.

4. Theoretical principles of umbrella arch method (UAM)

4.1. Tunnel reinforcement mechanism

In tunnel excavations,the tunnel faces using UAM is reinforced with forepoling steel pipes.This reinforcement mechanism is called as “steel-pipe-reinforced UAM” (Song et al.,2013). Essentially, this method has two reinforcement mechanisms: (1) structural reinforcement effect of the steel pipes, and (2) ground improvement effect of the cement grouting.The steel pipes installed ahead of the tunnel face transfer the earth pressure to the primary support, i.e. on the supported span, and ground ahead of the tunnel face, i.e. on the unsupported span (Song et al., 2013), as shown in Fig. 1. Hence, the steel pipes enhance the stability of the unsupported excavation section before installation of the primary supporting system of the tunnel.

In order to clarify the effect of UAM on the tunnel reinforcement,vertical stress distributions at tunnel crown in both cases (tunnel excavation using UAM and without using UAM) are compared, as shown in Fig. 2. In the case where the UAM is not employed(Fig. 2a), due to the rapid decline of vertical stress to zero in excavation face (Point A), concentrated stress is induced ahead of the excavation face and zero stress continues along the unsupported section (Muraki, 1997). Further vertical stress increase is expected by installing tunnel supports in specified distances beyond the excavation face.In the case of deploying UAM(Fig.2b),the umbrella arch structure covers the unsupported tunnel section and carries the ground pressure. The Mohr-Coulomb failure envelope is also shown in Fig.2 to better evaluate the stress state of the soil element.The initial stress condition for a soil element far from the excavation face is demonstrated as a dashed-line Mohr circle.During the tunnel excavation procedure, as the tunnel face approaches the soil element, an increase in the Mohr circle radius is witnessed due to the increase in the major principal stress.Hence,in the case without using UAM, in a close distance from the soil element, Mohr circle is tangent to the Mohr-Coulomb failure envelope,and consequently,the soil failure occurs.In contrast,when the UAM is deployed, the major principal stress is not increased considerably; hence, the Mohr circle is not tangent to the Mohr-Coulomb failure envelope, leading to failure prevention. Consequently, implementing the UAM could enhance the stability of tunnel excavation face by controlling the increases in major principal stresses in soil elements during excavation (Muraki,1997).

4.2. Design conditions and variables

Proper evaluation of design conditions and variables is of importance for accurate assessment of the efficiency of UAM in mitigating excavation-induced settlements.Tunnel dimensions,soil properties, and tunnel primary support characteristics are selected as per the design conditions associated with the tunnel excavation process. Essentially, these parameters rely on several contributing factors that are determined by tunnel type,existing soil profile in the tunnel construction site, and strength properties of steel and concrete (as the steel supports and shotcrete). Hence, tunnel design engineers often find limited alternatives to propose various design schemes,specifically in weak ground conditions.On the other hand,design variables attributed to the UAM steel pipes need to be defined in consideration of the site-specific conditions in the field.However,the impacts of these variables on tunnel reinforcement require further evaluation to obtain optimized and cost-effective design plans.The major pipe-related variables affecting the design of UAM are categorized into geometric characteristics(i.e.length,thickness,and diameter), and installation-related variables (i.e. longitudinal and transversal installation intervals, installation angle, and transversal reinforcement range).Fig.3 shows the design conditions and variables when the pre-support UAM technique is deployed to the tunnel.This information is also tabulated in Table 1.

5. Research methodology

Fig.1. Reinforcement mechanism of the umbrella arch method (Song et al., 2013).

Fig.2. Stress condition in tunnel excavation face,when(a)Umbrella arch method is not employed,and(b)Umbrella arch method is employed(Muraki,1997).σ1:minor principal(horizontal) stress, and σ2: major principal (vertical) stress.

Fig. 3. Schematic illustration of design parameters associated with the umbrella arch method (Song et al., 2013).

Table 1Design conditions and variables for steel pipes in the umbrella arch method (Song et al., 2013).

Using a series of 3D finite element models, the efficiency of deploying the UAM on improving the tunnel stability,in which the tunnel was excavated in soft soils with weak geotechnical properties, was investigated in this study. We gathered detailed information on deployed UAM,tunnel construction procedure,as well as tunnel design conditions (tunnel dimensions, soil properties, and tunnel primary support characteristics) from the Ghazvin-Rasht tunnel project as a case study. The field-derived information was a direct input to the finite element analysis to more accurately simulate the actual conditions. Subsequently, tunnel excavation procedure with conventional NATM was simulated in ABAQUS finite element software, considering two different conditions, i.e.using the pre-support UAM technique, and without using it. All UAM elements consisting of forepoling pipes, injected cement grout,and soilcrete were separately simulated in the finite element program to improve the analysis reliability. Then, the tunnel excavation-induced settlements such as tunnel crown and ground surface settlements were calculated for further comparative analysis.

Additionally,geometric and installation-related design features of forepoling pipes (as the key components in the UAM) such as diameter, length, overlap length, transverse distance, and installation angle of the pipes were investigated. This was achieved by post-processing the results obtained from numerical simulations of the umbrella arch-supported tunnel in consideration of various design schemes for forepoling pipes. Through another sensitivity analysis, a new design measure, named settlement reduction rate(SRR), was proposed for each individual pipe parameter to further understand the sensitivity of the tunnel settlements to different parameters of the pipes evaluated in this study. The following sections provide detailed information on the case study used,tunnel excavation procedure, UAM technique implemented, numerical simulations,and rationale for extensive investigation of the pipe design parameters.

5.1. Case study

Ghazvin-Rasht tunnel in Northern District of Iran was considered as a case study. This arch-shaped tunnel with a height and width of 8 m is categorized into railway tunnels. Geometriccharacteristics of the Ghazvin-Rasht railway tunnel are tabulated in Table 2.

Table 2Geometric properties of Ghazvin-Rasht railway tunnel.

In the early stages of design, field observations and measurements associated with the lithology of the site indicated that the tunnel was mainly located within the regions with conglomerate layers, sandstone layers, and calcareous beds. Fig. 4 illustrates the stratigraphic map attributed to the existing ground around the tunnel.Based on the provided map,it was revealed that by moving from point 1 towards the exit portal of the tunnel,i.e.points 5 and 6, sedimentary layers consisting of conglomerate and sandstone layers are becoming more pronounced.

Ultimately,considering the longitudinal profile of the tunnel,as well as laboratory investigation of the drilled boreholes in the vicinity of the project site,the geotechnical soil profile of the existing ground surrounding the tunnel was classified into three different zones,as indicated in Table 3.The information provided in the table showed that the existing soil around the tunnel was relatively weak; essentially, the most portion of the tunnel was surrounded by sand and clay soils with weak mechanical properties.

Fig. 4. Geological structure map of existing soil around the tunnel site.

Table 3Geotechnical soil profile around the evaluated section of the tunnel.

Due to the fact that clayey soils with very weak mechanical characteristics were not able to ensure the tunnel stability during tunnel excavation,zone 2 of the studied tunnel(middle part of the tunnel) was excavated using the NATM in combination with the UAM technique to improve the tunnel stability.The stability of the tunnel was crucial not only because of the engineering-related issues but also from the safety point of view, since the tunnel was exactly located beneath the constructed roadway with a large volume of truck traffic operations. The whole tunnel construction procedure, as well as the post-processed laboratory investigation results,was further incorporated into a 3D finite element system,as explained below.

5.2. Numerical simulation

5.2.1. Model dimensions and boundary conditions

Fig. 5. Simulated soil block in ABAQUS.

Proper characterization of the geometry of the model is of utmost importance to mitigate the systematic errors associated with boundary effect problems (Ashtiani et al., 2019; Morovatdar et al., 2019). We carried out a sensitivity analysis to determine the adequate model dimensions for simulation purposes. For this,the model dimensions were incrementally increased from 20 m to 80 m; the variations of the calculated tunnel crown vertical displacement were monitored accordingly. It was found that the sensitivity of the tunnel crown vertical displacement was negligible when the simulated model dimensions exceed 50 m, 50 m and 70 m for height, width, and length of the model, correspondingly.Therefore,a 3D soil block with dimensions of 50 m×50 m×70 m was modeled in ABAQUS using continuum rigid elements,as shown in Fig. 5.

Fig. 6 shows different types of boundary conditions defined in the simulation of the tunnel.Encastre boundary condition was used only at the bottom of the model,restraining the displacement and rotation in all directions (Morovatdar et al., 2020b, c). Moreover,two other boundary conditions were defined in the finite element models to restrict the displacement in the orthogonal direction to the surfaces highlighted with red,as shown in Fig. 6.

5.2.2. Mechanical behaviors and material properties

In order to properly evaluate the geotechnical properties of the tunnel surrounding soils, the Mohr-Coulomb model was assigned to the soil and soilcrete elements(Satvati et al.,2019;Beizaei et al.,2020; Dehghani et al., 2020; Rahimi et al., 2020). Mechanical behaviors of shotcrete,steel frames and pipes were defined as classic elastoplastic and elastic,respectively.Defined mechanical behavior models are summarized in Table 4.

Additionally,a number of boreholes were drilled in the studied site to obtain the desirable geotechnical characteristics. The postprocessed results from the laboratory experiments on the samples extracted from the boreholes, in terms of the geotechnical properties of the soil, are indicated in Table 5. Moreover, to characterize these properties associated with the jet grouted soilcrete in the vicinity of the tunnel, a few core samples were taken from the formed umbrella at the tunnel crown region.Table 5 also indicates the analysis results attributed to the soilcrete zone. Table 6 shows the material properties associated with the primary supporting system as well as the forepoling pipes.It should also be noted that the forepoling pipes deployed at this tunneling project were made of steel with a yield stress of 392 MPa.5.2.3. Meshing and load allocation

Fig. 6. Assigned boundary conditions in (a) XZ plane, the bottom surface (UX = 0， UY = 0， UZ = 0), (b) YZ plane (UX = 0), and (c) XY plane (UZ = 0).

Table 4Mechanical behaviors of different elements.

Table 5Geotechnical properties attributed to the soil and soilcrete.

Table 6Mechanical properties of the supporting system components.

Fig. 7. Soil block meshing.

Considering the fact that the most critical response points during tunnel excavation are located at the tunnel crown region,we defined a finer mesh in this area to obtain more accurate results.However,to expedite the computation time and reduce the output files size, a coarser mesh in the areas far from the tunnel axis is used,as shown in Fig.7.The meshing of the soil block surrounding the tunnel was assigned using the C3D8 elements (eight-node linear brick). Furthermore, gravity load was applied to the whole simulated soil block to monitor the settlements induced by the weight of soil elements during tunnel excavation procedure(Alimohammadi et al., 2019; Beyzaei and Hosseininia, 2019).Additionally, due to the complexity of the simulated model consisting of various element types,different contact interactions,and a huge number of elements, we deployed the explicit analysis method to optimize the iteration process adopted for convergence(Zamanian et al., 2020a, b).

5.2.4. Tunnel primary supporting system

As stated earlier, the tunnel was excavated using the NATM. In this approach, the primary supporting system consisted of steel frames and shotcrete. The supporting system in the implemented NATM process was comprised of shotcrete of 20 cm in diameter and IPE18 as the steel frames. These components with the assigned dimensions were simulated,as shown in Fig.8.The following steps describe the tunnel excavation sequences:

(1) Excavating 1 m of the tunnel, and

(2) Installing associated primary support system.

Hence, the tunnel excavation process was followed in a fullsection excavation method with 1 m steps. After each excavation step,steel sets were modeled by wire elements with 1 m intervals.Then the tunnel excavation face, tunnel wall, and tunnel invert were covered by shotcrete shell elements. It should also be noted that at each excavation step,the gravity load is applied to the whole excavated tunnel,including the supported and unsupported spans of the tunnel. Hence, it deems necessary to properly consider the unsupported span, which is defined as the distance between the tunnel face and the closest installed support.

In this study, by defining a series of analysis steps in the finite element program, the unsupported span, formed after each excavation step, was intended in the numerical modeling to consider the excavation sequences better and to more realistically simulate the actual in situ conditions in the studied tunnel project. Essentially, the weak mechanical characteristics of the existing soil and relatively large tunnel diameter, coupled with operational restrictions on support installation, were the major reasons that the unsupported span of the tunnel was determined to be no more than 1 m. This explains the rationale behind selecting the 1 m intervals for both tunnel excavation process and steel frame installation, in consideration of the sufficient space required for installation of the subsequent set of tunnel support systems.

Fig. 8. Primary supporting system components: (a) 3D model, and (b) Dimensions of the steel frames.

Accordingly,the maximum allowable length for the unsupported span of tunnels needs to be properly determined and incorporated into the design schemes, considering the project-specific characteristics of the studied tunnel.Particularly,this is a key step in design procedures of the tunnels excavated in shallow ground with weak geotechnical properties. Based on our experience in relevant projects,it is not practically feasible to maintain the stability of a large span of such tunnels, without immediate installation of the appropriately-spaced steel frames after each excavation step.

5.2.5. Deploying the umbrella arch method

The UAM elements consisting of pipes, injected cement grout and soilcrete were simulated in the finite element program, as shown in Fig.9.Forepoling pipes (wire elements)were embedded at the tunnel crown. Additionally, injected cement grout and improved soil around the pipes(soilcrete)were separately modeled in the ABAQUS software to accurately simulate the UAM implementation. Regarding the incorporation of the radius of injected cement grout and the thickness of the formed soilcrete into the numerical simulations,it should be noted that these parameters are greatly interconnected with the injection pressure magnitude.Additionally, in design practices, the transversal distance between pipes is another major factor in determination of the radius of injected grout and soilcrete’s thickness.Therefore,in this study,the soilcrete zone was continually simulated in consideration of the values of pipes’ transverse distance in different design scenarios.However, it is noted that the applied injection pressure, under actual field conditions, directly changed with the variations in the transversal distance of the pipes to ensure the continuity of the formed cement grout and soilcrete zones.

Considering the pipes’total length(Lp)and overlap length(Lov)with the next set of pipes, the whole procedure of umbrella arch installation was consistently repeated after Lp-Lovof drilling.Fig.10 illustrates the simulated tunnel using the UAM after the 5th set of pipe installation.

5.2.6. Interactions between simulated elements

Appropriate assignment of the interactions between different elements is one of the key steps in numerical simulations(Mansourkhaki et al., 2020a, b). This concern is even more important in modeling tunnels that have numerous contributing elements with distinct material properties. Hence, in this study,careful attention is devoted to properly assigning the interactions between UAM elements in order to improve the reliability of the analysis results. To do this, using the tie constraint, the primary support system consisting of shotcrete and steel frame elements was connected to the simulated soil around the tunnel. Moreover,forepoling pipes were defined as embedded elements in the surrounding soil.Soilcrete elements were also modeled by partitioning of the improved soil around the pipes with better geotechnical properties compared to the whole simulated soil elements.

5.2.7. Design variables of assembled forepoling pipes

Tunnel engineers, at the initial stages of the project, generally designed the features of the forepoling pipes in consideration of the site-specific project characteristics of the Ghazvin-Rasht railway tunnel. This information is tabulated in Table 7. However, in order to more accurately assess the impact of forepoling pipes on tunnel stability, various parameters such as length, diameter, installation distance and installation angle of the pipes were investigated in this study. Fig. 11 illustrates the various design parameters of forepoling pipes evaluated for further comparison purposes.

Table 8 indicates several cases through parametric study to capture the effect of forepoling pipe parameters on controlling the induced settlements. It should be also noted that to evaluate the effect of each pipe parameter, the other parameters were considered as the initial values defined in the design plan of Ghazvin-Rasht tunnel.

Table 7Characteristics of the forepoling pipes employed in the Ghazvin-Rasht railway tunnel.

Fig.10. Schematic view of the simulated UAM-reinforced tunnel, after the 5th set of pipe installation.

Fig.11. Illustration of the design variables of forepoling pipes.

6. Numerical results and discussion

Fig.12a and b plots the vertical displacements for the cases of tunnel excavation with and without using the UAM, respectively.Based on the provided plots, it is revealed that the UAM has effectively controlled the excavation-induced settlements, especially in critical locations, i.e. tunnel crown and ground surface regions. Another observation was that the area close to tunnel invert experienced upward movements.This is primarily attributed to the fact that the tunnel invert sustains an intense pressure from the underneath soil caused by stress relaxation mechanism of the tunnel, explaining the rationale behind applying the shotcrete to the tunnel inverts in the weak soil conditions.

6.1. Influence of deploying umbrella arch method on controlling the settlements (quantitative assessment)

Fig.13 shows the post-processed results for tunnel crown and ground surface settlements after 42 m tunnel excavation, for the cases with and without UAM deployment. The descending nature of the settlement patterns in both cases in Fig.13 truly justifies that the maximum settlements tend to occur at the tunnel entrance portal, while the values are decreasing along the tunnel axis. For this reason, tunneling-induced settlements at the tunnel portal,representing the most critical situation, were contrasted throughout this study. As evidenced in the plots, deploying the UAM resulted in a decrease in the tunnel crown vertical displacement (at the tunnel portal) from 166 mm to 40 mm. Likewise, the maximum ground surface settlement was reduced from 62 mm to 36 mm as a result of adopting this method,which in turn translated into greater stability of the tunnel. In other words, in the case evaluated in this study, using the UAM technique in combination with the NATM can significantly control the tunnel crown displacement and the induced ground settlement by approximately 76% and 42%, respectively.

Additionally, the pre-support umbrella arch technique was found to be more efficient in mitigating the tunnel crown vertical displacements compared to measures of induced ground surface displacements. However, controlling the settlements at ground level in urban tunneling, in which the tunnels are mostly located under adjacent buildings in densely populated areas, is of utmost importance. Hence, based on the post-processed results of this study, a 42% reduction of ground surface settlements due to UAM deployment can greatly contribute to the improvement of the safety and stability during the tunnel construction procedure.

6.2. Bearing capacity of the tunnel primary supporting system

As stated in Introduction,the main reason behind the reduction of the settlements when the UAM system is deployed is its influence on transferring the earth’s pressure to the primary support system. Fig.14 shows a comparison of the maximum axial forces applied to the primary supporting system of the tunnel for the cases with and without UAM deployment. As illustrated in the figure, the deployment of the UAM system has resulted in an increase of approximately 66%in the maximum axial forces induced in the primary support systems.

Despite the beneficial impacts of this behavior of the UAM system on transferring the loads to the primary support system,it deems necessary to investigate the robustness and stability of the primary supporting systems against the increased applied loads.Hence,we initially extracted the associated loads and moments at different cross-sections of the tunnel. Subsequently, the bearing capacity diagrams were developed to properly assess the robustness of the primary support system against the induced loads, in consideration of the specific properties of the supporting systems used in this study. Figs. 15 and 16 show the analyzed results attributed to the bending moment vs.axial force and shear force vs.axial force, respectively, at the entrance part of the tunnel and for different design schemes of forepoling pipes. As shown in the figure, all the case scenarios evaluated in this study are located within the permissible region. Similar results were also found for different sections of the tunnel. Consequently, the results of the stability analysis indicated that the deployed primary support system was sufficient to sustain the loads induced by tunnel excavation.

Fig.12. Contours of vertical displacement (m), in the cases (a) without UAM application, and (b) with UAM application.

Fig.13. Comparative results between tunnel excavation-induced settlements for the cases with and without deploying the umbrella arch method.

6.3. Validation of the numerical modeling results

In order to verify the finite element analysis results and the accuracy of the simulated excavation procedure of the tunnel reinforced with UAM,we initially extracted the information on the in situ measurements from the available historical records of the project.Subsequently,tunnel crown vertical displacements from in situ measurement records were compared with the corresponding values calculated by the numerical simulation models. This was accomplished in the case of the tunnel reinforced by the UAM system. As evidenced in Fig. 17, the values of tunnel vertical displacements based on the finite element analysis were in good agreement with those achieved from the in situ measurement records. The comparison results also show some variations between the two methods,which can be attributed to the anomalies arising from in situ measurements;however,the differences fit in a limited range.

Subsequent to the stability analysis of the support systems,and the validation of the numerical modeling results, the influence of different design parameters of the forepoling pipes was comprehensively evaluated; the associated results and discussions are provided in the following section.

Fig. 14. Maximum axial forces applied to the primary support system for the cases with and without deploying UAM.

Fig. 17. Tunnel crown vertical displacement values obtained from in situ measurements and numerical simulations.

Fig.15. Axial force vs. bending moment of the primary support system of the tunnel.

Fig.16. Axial force vs. shear force of the primary support system of the tunnel.

Fig.18. Tunnel crown vertical displacements along the tunnel axis and the maximum settlements at tunnel portal for various values of the pipe design parameters: (a) Diameter(Dp), (b) Length (Lp), (c) Installation angle (θL), and (d) Installation distance (ST). Red rectangles in right-side panels indicate the optimum value of pipe design parameter.

6.4. Influence of design variables of forepoling pipes on the efficiency of the UAM

Fig.18 presents the results of the parametric study of the various design parameters of the forepoling pipes. Crown settlements along the tunnel axis(panels on the left side of the figure),as well as the maximum settlements at tunnel portal (panels on the right side of the figure),are calculated and illustrated in the plots as the major critical measures for excavation-induced displacements.Fig. 18a-d provides relative comparisons of these settlements associated with various design parameters of the pipes: (1) geometric parameters such as diameter (Dp) and length (Lp); and (2)installation-related parameters such as installation angle (θL) and installation distance(ST).It should be noted that a non-remarkable change in settlements at tunnel portal was seen after 42 m excavation length; hence, the comparative results are provided for the first 42 m excavated tunnel segment in the subsequent section, to apply similar conditions in various cases.

Based on the analysis results provided in Fig.18a, a consistent trend of decreasing tunnel crown vertical displacements with increasing pipe diameter from 6 cm to 12 cm is evident, which in turn translates into higher tunnel stability. This observation was expected as the increase in the moment of inertia with enlargement of the pipe diameter, leading to a higher bending capacity of the whole umbrella arch system under earth pressure. However, the settlements tend to level off at 12 cm, indicating that any further increase in the pipe diameter would not contribute to a significant reduction of the tunnel crown vertical displacements.Hence,such limiting value (12 cm) represents the optimum value of the pipe diameter, giving the best performance in controlling the tunnel crown vertical displacements for the case evaluated in this study.

Fig. 18b shows the variations of tunnel settlements corresponding to different pipe lengths. As illustrated in the figure,similar settlement trends were observed for pipe length. Essentially, increasing pipe length from 8 m to 12 m resulted in a significant decrease in tunnel crown vertical displacements, while employing pipe length that exceeds 12 m could not make a remarkable reduction in the settlements. This is attributed to the fact that a certain part of the forepoling pipes designed to resemble cantilever beams,far beyond the failure zone,would offer no extra benefits in terms of the structural capacity of the umbrella arch system.Considering the equivalent tunnel diameter(Dtunnel=8 m),the results indicate that the optimum value of the pipe length is approximately 1.5Dtunnel(12 m).

Installation-related variables of forepoling pipes such as installation angle and installation distance were also evaluated, and the corresponding results are shown in Fig. 18c and d, respectively.Generally,these plots reflect an opposite trend in the variations of the tunnel crown vertical displacements with the changes in the installation angle and installation distance of the pipes.Comparing the results for different installation angles of the pipes showed that decreasing this parameter from 12°to 6°resulted in a substantial reduction in the tunnel settlements, as shown in Fig. 18c. Essentially, by increasing the installation angle of the pipes, the umbrella-shaped arches formed above the tunnel crown keep a considerable distance apart from the other counterparts.Hence,in this case,the umbrella arch system could not efficiently transfer the overburden stresses across the various sets of installed pipes. It should also be noted that any further decrease in the critical value of pipes’ installation angle (6°) leads to an increase in the settlements.

Fig.18d also shows that as the installation distance of the pipes decreases from 60 cm to 30 cm, the tunnel crown vertical displacements witness a noticeable drop. This is in line with our expectations since the reinforcing effects of the UAM would be more significant when the steel pipes are installed with a closer transverse distance from the other pipes. However, similar to the other design variables, this parameter has an optimum value (30 cm),after which the descending trend of the tunnel settlements was halted. In other words, installing the forepoling pipes at a closer distance than 30 cm is not likely to secure the improvement of tunnel stability.Additionally,since the local arching between pipes has a significant effect on determination of the transversal distance of the pipes,in design practices,the distance needs to be calculated in consideration of the minimum value of the local arching to properly utilize the load-bearing capacity of the ground, and to optimize the design schemes.It should also be noted that injection pressure, soil properties and structural capacity of the pipes are other contributing factors in determination of the installation distance of the pipes.

As shown in Fig.19a-d, similar analysis results were obtained associated with the influence of the pipe design parameters on controlling the ground surface settlements. However, the analysis of the ground surface displacements resulted in comparatively lower values for settlements compared to those values calculated associated with the tunnel crown vertical displacements. As evidenced in the figure,the overall patterns of the variations of ground surface settlements indicated similar trends for optimized design parameters of the pipes to those suggested by the analysis carried out for the tunnel crown vertical displacements.

6.5. Settlement reduction rate (SRR) for pipe parameters

Considering the costs,constraints and complexities of deploying the UAM in the field conditions,it is necessary to keep on refining the design schemes to develop an optimized and cost-effective plan, proposing the best stability performance of the reinforced tunnel. In line with this need, we conducted another sensitivity analysis to assess the influence of different pipe parameters on controlling the excavation-induced settlements. To achieve this,analyzing the obtained results from finite element simulations,we calculated the maximum settlement reductions caused per one unit change (either decrease or increase) in the investigated design parameters of the forepoling pipes. Then, SRR, as a new design measure tailored towards the pipes’ parameters, was defined,indicating how intensely the incurred tunnel settlements rely on different characteristics of the pipes.

Fig. 20 illustrates the results of the performed sensitivity analysis for key design parameters of the forepoling pipes.As shown in Fig.20,the efficiency of the UAM technique in terms of controlling the tunnel settlements is found to be more sensitive to the diameter of the pipes compared to the other design variables.In fact,with a 1 cm increase in the diameter of the pipes, tunnel crown vertical displacements decrease by 6.9% approximately.

Comparing the general trends of SRRs showed that the geometric design characteristics of the pipes, such as diameter with 6.91%per centimeter and length with 4.83%per meter,are the key factors that are substantially more contributing to the settlement reductions, in comparison with installation-related parameters.This is primarily attributed to the fact that the bending strength capacity of the pipes is highly affected by their geometric properties rather than the installation-related characteristics. Another observation was that the installation angle of the pipes with 3.4% per degree SRR acted in a more controlling manner compared to pipe installation distance with the corresponding rate of 0.9% per centimeter. Hence, full care and attention should be paid in situ,where the pipes are inserting the tunnel crown to ensure that the installation angle of the pipes complies with the design schemes,resulting in improvement of the tunnel stability. Based on our experience in relevant projects, installing the pipes in their predefined desired angle in soft and weak grounds could be challenging.

6.6. Effect of pipes’ overlapping length

By approaching the end parts of the forepoling pipes during the tunnel excavation process, their beneficial impacts on the tunnel stability are minimized,and the UAM system is not well capable of transferring the overburden-related loads to the primary support system and ground ahead of the tunnel face anymore.Therefore,it is imperative to insert the subsequent set of forepoling pipes into the tunnel crown to provide a desirable overlapping region to maintain tunnel stability. In design practices, the overlapping length of the forepoling pipes is one of the critical design parameters that substantially impact the stability of the tunnels supported by the UAM system.This parameter greatly depends on the effective length of the forepoling pipes and their supporting effects on the tunnel, which are noticeably interconnected with the characteristics of the tunnel geometry and the ground conditions.

Fig.19. Ground surface settlements along the tunnel axis and the maximum settlements for various values of the pipe design parameters: (a) Diameter (Dp), (b) Length (Lp), (c)Installation angle (θL), and (d) Installation distance (ST). Red rectangles in right-side panels indicate the optimum value of pipe design parameter.

We conducted a separate series of sensitivity analyses in this study in order to investigate the influence of pipes’ overlapping length in the tunneling-induced settlements.To achieve this,a new parameter named overlapping length ratio was defined, which represents the ratio of overlapping length to the total length of forepoling pipes. The case studies of forepoling pipes with 15 m length, and different overlapping length ratios, i.e. 20%, 25%, 30%and 40%, were investigated in this section.

Fig.21 shows the results attributed to the maximum settlements calculated at tunnel crown and ground surface levels, corresponding to different overlapping length ratios for forepoling pipes.As illustrated in the figure, an overall decreasing trend of the settlements with increasing overlapping length ratio from 20%to 40%is apparent.This is expected since increase in the effective length of the contributing pipes results in a higher reinforcement capacity of the whole UAM system. However, in consideration of the high construction costs, as well as the difficulties pertaining to implementation of the pipes with higher overlapping length,it is of great interest to design practitioners to determine the optimum value of this design parameter. Based on the results provided in Fig. 21, it is also found that the minimum appropriate ratio of overlapping length should be approximately 25%, meaning that employing consecutive pipe sets with overlapping length ratio below 25%leads to a noticeable increase in the tunneling-induced settlements.

Theoretically, the minimum overlapping length of the pipes could also be calculated by.

Fig. 20. Settlement reduction rate (SRR) per one unit change associated with various design parameters of the forepoling pipes.

where L represents the length of the failure zone ahead of the tunnel face.Using this equation,the minimum overlapping ratio for the case studied in this section was calculated to be 26%. Accordingly,the minimum acceptable overlapping length of the forepoling pipes, in consideration of the site-specific characteristics of different projects, and allowable settlements defined for each tunnel, should be determined and incorporated into the design protocols of the tunnels reinforced by the UAM system.

6.7. Investigation of the pipes’ internal forces

In addition to evaluation of the design variables of pipes and their impacts on controlling the tunneling induced settlements, design protocols of the UAM systems should also account for the internal forces applied to the forepoling pipes during excavation process.Hence, in this study, the associated internal forces, including the axial forces and bending moments, were extracted from the numerical modeling of the studied tunnel for three different crosssections. Evaluated sections were comprised of the entrance part of the tunnel(i.e.0-1 m distance from the portal),the middle section of installed pipes at the first stage (i.e. 6-7 m distance from the portal), and ultimately the end section of the installed pipes at the first stage(i.e.11-12 m distance from the portal).

Figs. 22 and 23 show the maximum axial force and maximum bending moment induced in the pipes for different cross-sections of the tunnel, respectively. Generally, the figures for axial force and bending moment were characterized by a similar trend.As displayed in these figures, the pipes installed at the first 1 m length of the tunnel tolerated the highest internal forces;while the corresponding values associated with the middle and end sections of the forepoling pipes were noticeably lower compared to the other counterparts.

Fig.22. Maximum axial forces induced in forepoling pipes at different sections of the tunnel.

Fig. 23. Maximum bending moment induced in forepoling pipes at different sections of the tunnel.

Subsequently, the bearing capacity of the forepoling pipes against applied forces also needs to be accurately assessed.Considering the most critical designed pipe with the lowest crosssectional area and 60 mm diameter, 5 mm thickness and the yield stress of around 392 MPa,the maximum force that can be endured by the pipe was calculated as 338 kN. Furthermore, based on the analysis results in Fig.22,the maximum axial force induced in the pipes was found to be 284 kN, indicating that the deployed forepoling pipes are capable of tolerating the loads applied during excavation process.

Fig. 21. Effect of pipes’ overlapping ratio on the maximum tunneling-induced settlements: (a) Tunnel crown vertical displacements, and (b) Ground surface settlements.

7. Conclusions

In this study, the efficiency of the UAM as a tunnel reinforcing approach in controlling the settlements induced by tunnel excavation in soft grounds was quantitatively investigated.Based on the information gathered from the Ghazvin-Rasht railway tunnel project, an all-encompassing approach was adopted to more realistically simulate the UAM deployment. Subsequently, using a series of 3D finite element models,tunnel crown and ground surface settlements due to excavation were accurately assessed. In a separate effort, various design parameters of forepoling pipes in terms of geometrical and installation-related design features were evaluated to obtain the optimized values for each individual parameter. Additionally, through a sensitivity analysis, an informative index named SRR was introduced, representing how induced tunnel settlements were sensitive to various characteristics of the pipes. The major findings of this research are summarized as follows:

(1) The numerical results confirmed that deploying the UAM in the tunnels in soft grounds can adequately decrease the tunnel crown and ground settlements by approximately 76%and 42%, respectively. Mitigating the settlements at the ground surface by 42% in tunnels located beneath the adjacent roadways and buildings in urbanized regions is significant.

(2) Analysis of the settlement variations indicated a clear descending trend with the increase in the values of the diameter and length of the pipes, up to a specific value.Additionally, to deliver a better performance, the values of the installation angle and installation distance of the pipes require to be decreased, up to a certain point.

(3) In any actual field conditions, the optimized values of the design parameters should be analyzed and incorporated in the design procedure to ensure tunnel stability. For the case used in this study, the best performance of the UAM was achieved when the pipes diameter,length,installation angle and installation distance were in the neighborhood of 12 cm,12 m, 6°and 30 cm, respectively.

(4) It was also found that the optimum value of the pipe length is approximately 1.5Dtunnel, where Dtunnelstands for the equivalent tunnel diameter.

(5) The overlapping length of the forepoling pipes was a significant design parameter of the tunnels supported by the UAM system.For the case evaluated in this study,25%was found to be the optimal ratio of pipes’ overlapping length.

(6) Juxtaposing the optimized values of the pipe design variables from numerical simulations with those extracted from the design plans of the Ghazvin-Rasht project has yielded identical results.This underscores the significance of incorporating the field-derived information into the numerical simulation models to improve the reliability of the analysis results.

(7) Overlooking different impact levels of the pipes’parameters on tunnel stability can jeopardize the safety and costefficiency of the UAM method. Introducing the SSR can bridge this gap, providing tunnel design practitioners a valuable insight into the efficiency of each design parameter.Tunnel stability was found to be more sensitive to values of the pipes’ diameter and length, compared to the other counterparts.Additionally,the installation angle of the pipes had a greater influence on tunnel reinforcement compared to the center-to-center distance of them, determined by the injection pressure of the grout.

(8) Determination of pipe diameter and pipe length is the primary concern in the design of the UAM. Using pipes with higher structural capacity in combination with higher injection pressure contributes more to the settlement reductions, instead of installing the pipes with a close transverse distance that imposes operation and installation restrictions on the UAM deployment.

(9) Employing the UAM requires considerable costs; however,the costs due to the tunnel collapse or imparting any damage to adjacent buildings when this approach has not been applied should also be considered. Consequently, utilizing the UAM as a practically sound and robust approach to improve tunnel stability, especially in the shallow ground with weak geotechnical properties, is becoming more common in the tunneling industry.

Declaration of competing interest

The authors wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.