Pilot Tunnel Research Articles

Creep Versus Consolidation in Tunnelling through Squeezing Ground—Part B: Transferability of Experience

This paper investigates potential differences between creep and consolidation in mechanised tunnelling through squeezing ground, placing focus on the practical question of using experiences gained from existing tunnels about the required thrust force as a reference for tunnels of different diameter or adjacent tunnels. The investigations focus on two aspects. First, the effect of the tunnel diameter on the risk of shield jamming is examined. The paper demonstrates that larger-diameter tunnels are more favourable in poor-quality ground, while the opposite holds in better-quality ground, as well as in the case of pronouncedly time-dependent ground behaviour due to consolidation or creep. Second, the effect of a tunnel on the required thrust force in a neighbouring tunnel built later is examined. The paper shows that this interaction effect is particularly important in water-bearing ground of low permeability, where the drainage action of the first tunnel induces pore pressure relief and ground consolidation in an extensive area, leading to a remarkable reduction of the thrust force in the second tunnel. Conversely, in the case of creep the interaction is negligible even under extremely squeezing conditions, due to the fundamentally different nature of the purely mechanical rheological processes from coupled hydromechanical processes. The presented investigations into the transferability of experiences are valuable for tunnelling practice, in cases of twin tunnels as well as in situations where a smaller-diameter tunnel is constructed prior to the main tunnel (e.g. a pilot tunnel for exploration, advance drainage or ground improvement), or also the opposite (e.g. upgrade of a road tunnel by later construction of a safety tunnel with a smaller diameter).

Damage and reliability analysis of double-arch tunnel without a middle pilot tunnel under blast load

In this study, a new type of multi-arch tunnel construction method is proposed. This effort is undertaken due to the many disadvantages of the traditional multi-arch tunnel construction method. Furthermore, this method omits the construction of a middle pilot tunnel, and it has the advantages of safety, high efficiency, and being economical. When using the method of continuous arch tunneling without a middle pilot tunnel, the blasting of the first tunnel and the following tunnel has a greater impact on the surrounding rock damage, as well as on the supporting structure of the same cross-section. Therefore, this study uses LS-DYNA finite element software to construct a three-dimensional numerical model. In addition, the perimeter rock damage law and mechanical response characteristics of the supporting structure in the same cross-section of the first tunnel, as well as the following tunnel after blasting without a middle pilot tunnel, are analyzed. At the same time, the results of the study are based on optimizing the blasting program, and these are then applied to the field. Through the results, it is found that, after blasting a continuous arch tunnel without a medial pilot tunnel, the surrounding rock damage in the arch cross-region of the double-arch tunnel (where the arch top and the arch shoulder are more significant) and the effective stress of the supporting structure exceed the strength design value. In addition, the maximum adequate pressure is distributed in the medial diaphragm wall. With the optimized blasting scheme, the range of the peripheral rock damage is reduced by a maximum of 67%, and the effective stress in the supporting structure is reduced by 25.9–64.8%. The research results are of great significance in terms of improving construction safety, economic efficiency, and project quality, as well as in promoting the research and development of new work methods for double-arch tunnels.

Excavation response and reinforcement practice of large underground caverns within high-stress hard rock masses: The case of Shuangjiangkou hydropower Station, China

The construction of large-scale underground caverns poses numerous challenges due to their massive scale and high complexity. Among them, stability has always been a major concern during the construction process of large underground caverns within high-stress hard rock masses. It is not only influenced by the geological background of the project but also by the engineering activities during construction. This study takes the construction of the Shuangjiangkou (SJK) hydropower station as a case study and combines field investigations to summarize engineering issues and solutions under high geostress in three aspects. Firstly, it focuses on estimating and modifying the in-situ stress field of the underground caverns in the deep-cut valley area using limited geostress testing data and the observed failure phenomena in the pilot tunnel. Secondly, it discusses the typical failure phenomena of caverns under high geostress, including global stress-induced failures and local vein-controlled failures, as well as the corresponding failure mechanisms and treatment measures. Finally, it addresses the special failure phenomena occurring in the protective layer of the rock-anchored beam and optimizes the excavation scheme based on the observed failure patterns. The research results and solutions provided in this study, based on the case of the SJK hydropower station, are expected to serve as a reference for subsequent construction of large underground caverns within high-stress hard rock masses.

Performance of the Flexible and Rigid Lining under Earthquake Impact and Weakness of the New Austrian Tunneling Method (NATM) Principles, a Specific Case Study of the Bolu Tunnel

The Bolu tunnel is located between the Istanbul-Ankara Highway and its construction took approximately 13 years. Since the beginning of the tunnel excavation, serious deformations and stability problems have been encountered. The basis of the problems encountered during the tunnel excavation is the fact that the geological units through which the tunnel passes are very weak and fault lines cut the tunnel location. The fault lines pass through secondary faults in the seismically active North Anatolian Fault. At these fault crossings, deformations occurred continuously so that revisions had to be made in the support systems. The 12 November 1999 Düzce earthquake occurred on the Düzce fault and a surface rupture 40 km long was caused. The rupture terminated 1.5 km west of the tunnel; it did not reach the tunnel. Throughout the earthquake, instances of collapse occurred at the areas excavated on the fault line at the entrance of Elmalık and where the deformations exceeded 1.0 m; this section of the tunnel had to be abandoned. After these problems, a new improved design for tunnel excavation was developed. These new support systems, which are Bernold lining and bench pilot tunnel systems, contain allowance for rigid lining that is the opposite of the new Austrian tunneling method (NATM) principles. Within the scope of this study, the causes of the collapse in the tunnel are investigated and the effect of the Düzce earthquake on the tunnel is discussed. Also, the applicability of the NATM in tunnels excavated on weak zones is also discussed.

Research and optimization of tunnel construction scheme for super-large span high-speed railway tunnel in poor tuff strata

Abstract The rapid traffic developments create demands for shallow four-line high-speed railway tunnels in weak soils, while construction technologies of such tunnels have yet to be reported. In this article, the construction schemes for a shallow four-line high-speed railway tunnel with a span of 26.3 m in weak tuff strata are investigated by numerical analysis and in-situ tests. First, 20 construction schemes of the shallow super-large span high-speed railway tunnel are proposed and simulated by the Finite Difference Method, including eight schemes for grade V rocks and 12 schemes for grades IV and III rocks. The mechanical response of grade V rock mass is simulated by the Bolt–Kelvin Mohr–Coulomb rheological model. The influence of construction method, rock grade, area, quantity, and excavation sequence of pilot tunnels on the rock deformation and the internal force of the primary support are comparatively explored. For further analysis, an 8 month field test was conducted to study the optimized effect of the construction scheme. Finally, a suggested construction method selection chart for super-large span tunnels in weak rocks (spans between 17 and 34 m) has been proposed. The research conclusion could provide a reference for building the super-large span tunnel in complex conditions.

Mechanical Behavior of Anchor Bolts for Shallow Super-Large-Span Tunnels in Weak Rock Mass.

Based on the Xiabeishan No.2 tunnel project of the Hang-Shao-Tai high-speed railway in China, the mechanical behavior of the anchor bolts for shallow super-large-span (SSLS) tunnels in weak rock mass is comprehensively investigated through laboratory tests, numerical simulation, and field tests. Firstly, an eight-month field test is conducted in the Xiabeishan No.2 tunnel, and it is discovered that the blasting vibration created by the construction of the middle pilot tunnel caused serious damage to the temporary support, seriously affecting the development of the bolt axial force and causing great construction risks. Then, the refined finite difference model of the SSLS tunnels is formulated, and a series of field and laboratory tests are conducted to acquire the calculation parameters. By comparing the monitored and simulated bolt axial force, the reliability of the numerical model is verified. Subsequently, the influence of the rock condition, construction scheme and bolt length on the mechanical behavior of anchor bolts is discussed. It is revealed that the rock grade significantly affects the bearing characteristics of anchor bolts. The construction scheme can greatly affect the magnitude and development mode of the bolt axial force, but the final distribution characteristics of the bolt axial force do not change regardless of the construction sequence. The axial force of the anchor bolts grows rapidly with the bolt length when the bolt length is within 18 m; meanwhile, when the bolt length exceeds 18 m, increasing the bolt length has a limited effect on the improvement in the bolt support performance. Finally, some optimization measures are proposed according to the monitoring data and simulation results.

Microseismic monitoring and experimental study on rockburst in water-rich area of tunnel

During the excavation of tunnels in the Hanjiang-to-Weihe River Diversion Project, many rockbursts occurred in water-rich (WR) areas. To study the mechanism of rockburst under such conditions, the features of microseismic events and rockbursts in WR tunnel sections excavated by both a tunnel boring machine (TBM) and “drilling and blasting” methods were statistically analysed and compared with those of adjacent water-poor (WP) areas. The results show that in both WR and WP areas, rockbursts are related to the classification of surrounding rock and are also affected by the excavation method. The rockbursts in most WP areas are more active than those in the nearby WR areas in sections excavated by TBM. However, the opposite is true under high in situ stress conditions. To explain the microseismic monitoring results, the mechanical behaviour of rock, including short- and long-term mechanical behaviour under different water and loading conditions, was also investigated, and the results show that under high stress conditions, water will accelerate the occurrence of rockburst. Therefore, the appropriate method to control rockburst is stress release, which can be achieved by advanced pilot tunnel excavation, hydraulic fracturing, and presplitting blasting, rather than high-pressure water spraying in the surrounding rock.

Rescue technology of the jamming accident for the double-shield TBM in complex geological conditions: A case study

More than 80 TBM jamming accidents had been recorded in the Water Diversion Project from the Hongyan River to the Shitou River in Shan’xi Province, China, resulting in substantial losses. This paper aims to investigate the rescue technology for the jamming accidents of the double-shield TBM in the project through a five-year geotechnical in-situ investigation. Firstly, the engineering background, the geological and hydrological conditions, the construction method, the possible jamming hazards, and the support system is introduced in detail. Then, the jamming accidents of the double-shield TBM are classified into the five kinds in total, namely, the shield jamming accident, the cutter head jamming accident, the jamming accident in the fault fracture zone, the jamming accident in the large-deformation section, and the jamming accident at water-rich and severely weathered broken rock section. And corresponding causes of accidents is analyzed at the same time. Afterward, the rescue technology adopted for the typical jamming accidents is explored, including the small pilot tunnel scheme, the advanced grouting scheme, the advanced large pipe shed scheme, the circular excavation scheme, and the auxiliary tunnel scheme. Finally, the prevent approaches for the jamming accident of the TBM are proposed, hoping to guide the same projects.

Pipe Curtain Deformation and Surface Subsidence Caused via Excavation of Transverse Pilot Tunnel under Pipe Curtain Support

Relying on the Shenyang Metro Line 4 Shifu Road station, the impact of the construction parameters of the transverse pilot tunnel on the surface subsidence and the pipe curtain deformation was first studied through numerical simulation, followed by the analysis of the impact of the excavation of the transverse pilot tunnel on the deformation characteristics of the pipe curtain through on-site monitoring. The results show the following: the excavation of the middle pilot tunnel is the key stage of the construction. The excavation sequence of H2 and H4 and H6 → H1 and H3 → H5 and H7 caused the least surface subsidence. Increasing the grouting width and improving the strength of the initial support can control the pipe curtain deformation very well, and it is reasonable to choose 1.5 m as the grouting width.

Estimation Method for an In Situ Stress Field along a Super-Long and Deep-Buried Tunnel and Its Application

Aiming at some stress-induced failure phenomena in surrounding rock that occur during the construction of super-long and deep-buried tunnels, a method for estimating the in situ stress in the tunnels based on multivariate information integration is proposed, which uses a small amount of in situ stress measurement, stereographic projection technology, and a numerical simulation method. Firstly, by conducting a macroscopic analysis of the regional geological structure, topography, and pre-excavated small tunnels (such as exploration of adits and pilot tunnels), the strength of the tectonic stress field and the orientation of the principal stresses in the tunnel sections are preliminarily determined. Secondly, the reliability of the in situ stress measurement data were analyzed using full-space stereographic projection and the plane stress projection method. Then, some representative measurement points that reflected the distribution characteristics of in situ stress in the project area, on the whole, were determined. Thirdly, the finite difference (FDM) and multiple regression analysis (MRA) methods were used to inverse the in situ stress field in the project area. The proposed method was applied to a super-long and deep-buried tunnel project in Qinling, and the in situ stress distribution characteristics of the tunnel sections at different mileages were obtained. The results show that both the calculated principal stress values and the azimuth angle of the maximum horizontal principal stress are in good agreement with the measured ones, indicating that the method used in this study is reasonable. Finally, the typical surrounding rock failure phenomena encountered during the excavation of the project were investigated, and targeted treatment measures were proposed. The research results can provide references for support design and disaster management of surrounding rock in deep-buried long tunnels.

Research on large deformation control technology of highly weathered carbonaceous slate tunnel

Abstract In order to further explore the large deformation control technology of high ground stress soft rock tunnel, this study takes the highly weathered carbonaceous shale section of Muzhailing tunnel as the research background, the large deformation control effect of scheme 1 “three-step method” and scheme 2 “pilot tunnel expansion method” are compared and analysed by field test and numerical simulation. The results show that the numerical simulation results are consistent with the field test, and the deformation trend of the tunnel is the same. The maximum deformation of the tunnel occurs at the middle step. From the perspective of tunnel deformation, control effect is reduced by about 10% compared with scheme 1, and the deformation of both schemes does not exceed the reserved deformation (400 mm). From the perspective of construction efficiency, the construction efficiency of scheme 2 is 23.07% lower than that of scheme 1. Taking into account the deformation control effect and construction efficiency, it is recommended that the three-step method should be adopted in the construction of this section, and the research results can provide a reference for the construction of the carbonaceous slate section of the tunnel.

Study on the Mechanical Characteristics and Ground Surface Settlement Influence of the Rise–Span Ratio of the Pile–Beam–Arch Method

The pile–beam–arch method (PBA) method is increasingly being used in the construction of metro stations with complex traffic conditions. The rise–span ratio of the arch not only affects the height of the station, but also affects the rationality of the design of subway stations and the safety of construction. The mechanical response of steel pipe piles with different rise–span ratios and the effect of controlled surface settlement have been investigated in the interactions involved in pile–soil system. In this paper, the finite element model of each rise–span ratio was established, and the rationality of the model was demonstrated by comparing the numerical simulation calculation with the field surface settlement monitoring data. The mechanical characteristics and influence analysis of the surface deformation during the excavation of the cave pile method were investigated. The results show that the maximum axial force of the central pile first decreases and then increases with the increase in the rise–span ratio. The maximum bending moment of the arch decreases as the rise–span ratio increases, and the maximum axial force of the arch is negatively correlated with the rise–span ratio. The maximum axial force of the central pile is located at the bottom plate. Due to the symmetry of the structure, the bending moment of the centre pile is small, but the maximum bending moment of the whole station is located at the side wall of the bottom plate. As the rise–span ratio increases, the surface settlement first decreases and then increases. The construction of the pilot tunnel and the upper arch is the most important factor leading to the surface settlement, so it is necessary to strengthen the soil layer.

Settlement Prediction Method of Extra-Large Diameter Tunnels in Soft Rock Strata

This research was undertaken to predict the result of vault settlement during the excavation of super-large-span tunnels in soft rock strata, which are prone to deformation and hard to predict aftermaths. Numerical simulation was applied to tackle with vault problems during excavation of super-large-span soft rock tunnels such as proneness to deformation and hard prediction on vault settlement. As a result, a model for continuous prediction of vault settlement as the tunnel face keeps advancing was proposed, with influencing factors such as excavation span and tunnel depth taken into consideration, and put forward the optimization of super-large-span variable-section tunnels construction scheme. The results show that the vault settlement becomes fast at the beginning of the excavation because its surrounding rocks are characterized by weakness, incompleteness, and poor stability. At the initial stage of excavation, the varying tunnel depth had a greater impact on vault settlement, indicating that the primary support has to be enhanced at the beginning of the excavation of a vault with weak surrounding rocks. As the excavation of pilot tunnels proceeds, the high-stress zone transfers to the deep part of the surrounding rocks. The tunnel vault settlement model is capable of rapidly predicting the vault settlement at locations other than the observation points. The final settlement amount is affected by the excavation span, the tunnel depth, and the basic mechanical parameters of surrounding rocks. The key to the construction of a super-large-span and variable cross-section tunnel lies in the cross-section varying parts where the stress is concentrated, thus requiring reinforcement and frequent monitoring. The research methods and analysis may provide basic data and technical means for the control of the vault settlement of large-span tunnels in soft rock strata.

Influence of the Large-Span Pile-Beam-Arch Construction Method on the Surface Deformation of a Metro Station in the Silty Clay–Pebble Composite Stratum

The Pile-beam-arch (PBA) method is a new and effective construction method for the urban metro station. It is the key to ensuring the safe construction of the station to clarify the influence of PBA method construction on surface deformation under unfavorable geological and large span conditions. Based on a station of Beijing subway, this paper studies the surface deformation law of the large-span PBA method in different construction stages under silty clay-pebble composite stratum by means of FLAC 3D numerical analysis and field monitoring of level. Then the influence of the excavation scheme of the pilot tunnel and the construction scheme of the secondary lining of the arch on the surface deformation is simulated and analyzed. The results show that, through numerical simulation, the ratio of pilot tunnel excavation: pile-beam construction: vault initial support construction: vault secondary lining construction is about 5:1.1:3.3:0.6. The settlement deformation mainly occurs in the excavation stage of the pilot tunnel. Through the comparative analysis of the field monitoring results and the numerical simulation results, it can be seen that the two results are highly consistent, which verifies the accuracy of the numerical simulation results. The pilot tunnel excavation scheme of excavating the middle first and then excavating both sides, first through the upper layer and then through the lower layer, and the scheme of one-time construction of the secondary lining of the arch are better. The research results promote the further maturity and perfection of large-span PBA method construction under unfavorable geology and provide reference for similar projects.

Field test on deformation control of weathered carbonaceous slate tunnel in high geostress

The problems of large deformation often occur in strongly weathered carbonaceous slate tunnels with high geostress. In order to control large deformation in the process of tunnel construction, an advanced drilling measure and an advanced pilot tunnel measure are proposed, then relevant field tests are carried out to verify their results. Compared with conventional support measures, the advanced pilot tunnel measure has a better control effect on horizontal convergence and vault settlement, which are reduced by 29.70% and 75.81%, respectively. In addition, the advanced drilling measure provides more advantages in controlling the maximum surrounding rock stress and the maximum steel frame stress, which are reduced by 77.44% and 23.12%, respectively. The results show that the large deformation of a strongly weathered carbonaceous slate tunnel in high geostress cannot be effectively solved by conventional support measures, but the two advanced stress-control measures can effectively reduce deformation of the surrounding rock of the tunnel and decrease the stress of the tunnel's steel frame and surrounding rock.

Study on the Influence Mechanism of Soil Deformation Induced by Shield Tunnel Construction

The construction of shield tunnel will adversely affect the surrounding soil and is prone to safety accidents. This paper focuses on the problem of soil deformation induced by shield tunnel construction. Based on the theoretical mechanics Mindlin solution, the soil deformation caused by the frontal thrust, friction force and formation loss of the shield is linearly superimposed, and the accurate calculation formula of soil deformation caused by shield is derived in time and space. Relying on the finite element software Midas GTS NX, the three-dimensional dynamic simulation of soil deformation induced by the double-line tunnel was carried out, the law of stratigraphic deformation during the construction of the double-line tunnel was obtained, and the influence mechanism of different tunnel burial depths on the surrounding soil deformation was studied. Finally, it was proved that the settlement curves of the surface and soil layer during the continuous excavation and unloading of the double-line shield tunnel were consistent with the settlement curves of the double-line Peck, and the settlement extremes of the pilot tunnel were slightly larger than those of the latter tunnel.

Field test and numerical simulation of ground settlement in super shallow buried station excavation supported by transverse pipe roof

The pipe roof is an effective means to control the surface settlement during the construction of the super-shallow buried subway station. The transverse pipe roof method can not only reduce the construction work surface, but also improve the construction efficiency by multi-stage flow construction. Based on the transfer station project of the Olympic Sports Center of Jinan Rail Transit Line 3, the ground settlement law caused by the excavation of ultra-shallow buried subway station under the action of transverse pipe roof is analyzed through field measurement. The mechanism of pipe roof controlling ground settlement and the influence of steel pipe spacing and steel pipe length on the bearing mechanism of pipe roof are analyzed by numerical simulation. The following conclusions are drawn. 1) The surface settlement curve caused by the excavation of the small pilot tunnel in the lateral direction of the station is a wavy U-shaped, and the surface settlement curve becomes a smooth U-shaped after the soil is broken. In the longitudinal direction of the station, the surface settlement is jagged, and the surface settlement above the pipe roof is less than the surface settlement between the pipe roofs. 2) After soil excavation, pipe roof can bear the load of surrounding rock and restrain the settlement of soil above, and soil arch effect is formed between pipes to restrain the relaxation of soil between pipes. With the increase of the spacing of the steel pipe, the height of the soil arch increases. After exceeding a certain spacing, the micro-soil arching effect disappears and the surface settlement increases. 3) The length and stiffness of pipe roof will affect the bearing capacity of pipe roof and there is an upper limit. When it exceeds the upper limit, increasing the length or stiffness of pipe roof has little effect on the control effect of ground settlement. The research can provide reference for shallow buried excavation station and other projects.

Construction of subway station using the small pipe roof-beam method: A case study of Shifu Road station in Shenyang

A case study of the Shifu Road station of Shenyang Metro Line 4 in China, which was constructed using the small pipe roof–beam method, is presented herein. The minimum buried depth of the Shifu Road station is only 4.2 m, and numerous urban and high-rise buildings are constructed above the station. The location, surroundings, geological conditions, design, and construction process of the Shifu Road Station is described herein. The settlement of the pipe roofs, beams, intermediate columns, and side piles; the vault settlement and horizontal convergence of the pilot tunnels; and the surface settlement are monitored. Subsequently, the station is compared with similar metro stations in terms of surface settlement and construction period. The results indicate that the excavation of the transverse pilot tunnel and the negative layer significantly affect the pipe-roof settlement above the intermediate column and the surface settlement of the station center, which constitutes more than 75 % of the total settlement. The surface settlement above the Z3 pilot tunnel is affected significantly by the excavation of the longitudinal pilot tunnel and constitutes approximately 80 % of the total settlement. The vault settlement and horizontal convergence of the pilot tunnels as well as the settlement of the beams, intermediate columns, and side piles exhibit staged changes throughout the construction period. Compared with the surface settlement of similar metro stations, that of the station investigated is approximately 63 % owing to the adoption of the small pipe roof–beam method, thus reducing the construction period by six months at the least. The results obtained show that the proposed method is advantageous for constructing shallow buried large-span metro stations and that it can serve as a reference for various applications.

The Influence of Pile-Beam-Arch Construction on the Stratum and Station Support Structure

The PBA construction method is suitable for urban subway construction in situations with dense traffic and many surrounding buildings and can effectively reduce surface disturbance and control surface subsidence. Based on field-measured data, this study creates numerical finite element models of 3D stratum-structure, studies the influence of each process conversion on the subsidence of the ground surface and the force of the station supporting structure during the construction of the PBA station, and clarifies the optimal construction parameters. The research results show that the consistency between the field monitoring data and the simulation data is more than 80%, which verifies the correctness of the model. It is concluded that the formation of the pile-beam-arch is the main part of the supporting structure and that digging the pilot tunnel and the formation of the beam arch are the control factors of surface settlement. Based on this, the best sequence of pilot tunnel excavation and arch buckle of the two-story two-span station is obtained, and the optimal pilot tunnel excavation scheme of first the middle and then the side, first the upper and then the lower, and the best arch buckle scheme of the synchronous arch buckle on both sides is determined. The results of the research can serve as a guideline when selection the construction parameters for similar PBA stations.

Influence of Pipe-Jacking Reaction on Earth Pressure of Back Wall of Pilot Tunnel of Subway Station

The study of the distribution form and calculation method of the earth pressure on the back wall of a pilot tunnel under a jacking reaction is very important to ensure the safety and smooth construction of the pipe jacking. Based on a metro station in Shenyang, this paper firstly investigates the effects of the changes in the jacking reaction parameters, such as the loading intensity, loading position, and loading area on the earth pressure and the displacement of the back wall in a pilot tunnel through numerical simulation, and then proposes a formula for calculating the soil reaction on the back wall and verifies it by comparison with the FEA (finite element method) results. The results show that the earth pressure distribution pattern of the back wall is similar to the normal distribution curve under the action of the jacking reaction. The horizontal displacement and earth pressure of the back wall will gradually increase with the increase in the jacking reaction. The horizontal displacement of the back wall is greatest when the load is applied to the middle wall, followed by the top wall and the bottom wall. The maximum horizontal displacement is reduced by approximately 24.25% when the loading position changes from the middle to the bottom. As the loading area increases, the maximum horizontal displacement of the back wall decreases, in the order of 11.8% and 14.45% relative to the previous level. The earth pressure of the back wall also decreases, in the order of 17.92% and 22.76% relative to the previous level. The equations presented are applicable to the calculation of the soil reaction in the limit state.