J. Cent. South Univ. Technol. (2009) 16: 0827-0834

DOI: 10.1007/s11771-009-0137-9

Analytical approach and field monitoring for mechanical behaviors of

pipe roof reinforcement

WANG Hai-tao(王海涛), JIA Jin-qing(贾金青), KANG Hai-gui(康海贵)

(State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology,

Dalian 116024, China)

Abstract: Considering the delay effect of initial lining and revising the Winkler elastic foundation model, an analytical approach based on Pasternak elastic foundation beam theory for pipe roof reinforcement was put forward. With the example of a certain tunnel excavation, the comparison of the values of longitudinal strain of reinforcing pipe between field monitoring and analytical approach was made. The results indicate that Pasternak model, which considers a more realistic hypothesis in the elastic soil than Winkler model, gives more accurate calculation and agrees better with the result of field monitoring. The difference of calculation results between these two models is about 7%, and Pasternak model is proved to be a better way to study the reinforcement mechanism and improve design practice. The calculation results also reveal that the reinforcing pipes act as levers, which increases longitudinal load transfer to an unexcavated area, and consequently decreases deformation and increases face stability.

Key words: tunnel heading; pipe roof reinforcement; Pasternak elastic foundation beam; field monitoring

1 Introduction

Several pre-reinforcement methods of heading have been developed in order to overcome the significant difficulties encountered while tunneling in weak ground. One of such methods is the pipe roof reinforcement method. This method consists on installing, prior to the excavation of a length of tunnel, a series of pipes, either parallel to the tunnel axis or at a certain angle with it. By injecting grout through the pipes, the ground between the pipes is stiffened and the pipes are connected, creating a kind of ‘umbrella’ above the area to be excavated. This arrangement creates a stiff layer of ground and allows safe excavation even in poor ground conditions.

In recent years, there have been numerous studies on the behaviors of pipe roof reinforcement. IBRAHIM [1] and ZHONG [2] reported the field monitoring results from various tunneling projects involving pipe roof reinforcement technique. They found that by using pipe roof reinforcement, the stability of the tunnel face in a poor geotechnical condition is improved and the ground movement can be reduced effectively. CHANG [3] proposed an analytical design method for the pipe roof reinforcement based on Winkler elastic foundation beam theory. Later, ZHANG et al [4] calculated the important design parameters such as the pipe length, pipe diameter and pipe space, using loading-structure model, and obtained a perfect result for the design and construction of the pipe roof reinforcement in line Fuxingmen to Bawangfen of subway in Beijing.

Research on tunnel face pre-reinforced with sub- horizontal pipes has gained great progress in recent years. The fundamental working mechanism of the pipes is rather similar to that of the pipe roof reinforcement in terms of applicability and functionality. PEILA [5] conducted a three-dimensional finite element analysis to study the behavior of tunnel face reinforced with horizontal fiber glass pipes. He found that the pipes had a positive reinforcing effect on the face stability in the form of a reduction of the displacement and the plastic zone extension. In addition, YOO [6] conducted a parametric study on the effect of reinforcing layouts on the deformation behavior of the tunnel face and drew a conclusion that there existed an optimum reinforcing layout to reduce the deformation of the tunnel for a given tunnel geometry and ground condition.

Physical modeling has played an important role in studies related to excavation of tunnels. A variety of modeling techniques have been developed by researchers all over the world to study ground response to tunneling [7]. These techniques range from the two-dimensional trap door tests to the miniature tunnel boring machines that simulate the process of tunnel excavation and lining installation in a centrifuge. KAMATA and MASHIMO [8] performed a series of centrifuge tests and studied the strengthening effects of typical auxiliary bolting methods such as face bolting, vertical pre-reinforcement bolting and fore poling on tunnel faces. The test results showed that each bolting technique has an optimum length and arrangement to perform effectively. HISATAKE and OHNO [9] conducted a series of centrifuge tests to clarify the effects of pipe roof supports and the excavation method on the displacements above a tunnel face. The results of the model tests show the quantitative effects of the ring-cut excavation method and clarify that the method decreases the ground displacements remarkably. The model tests also indicate that the maximum settlement of a ground excavated by the full-face excavation method with pipe roof supports is one fourth of that without them. Recently, SHIN et al  [10] have performed a large scale model testing for the pipe-reinforced tunnel heading in a granular soil to study reinforcing mechanism and improve design practice. The mechanical behaviors of ground and pipes were instrumented during tunneling. They found that the pipe reinforcement of heading increased longitudinal load transfer to an unexcavated area, and consequently decreased deformation and increased face stability.

Overview of the previous studies indicates that although these studies give insights into the working mechanism of pipe roof reinforcement technique, the majority of the studies focus on the general effect of reinforcement distribution on face deformation and ground surface settlements are limited. There are few attempts to analyze the mechanical behaviors of the reinforcing pipes [11-13]. Therefore, in this work, an analytical approach based on Pasternak elastic foundation beam theory for pipe roof reinforcement was put forward. The corresponding deformation equations and internal force formula were deduced, and the solutions of this model were given. Then with the example of a certain tunnel excavation, the comparison of the results between field monitoring, Winkler model and Pasternak model was made.

2 Analytical analysis

2.1 Analytic model

In a typical excavation procedure, the pipe roof reinforcement can be divided into four sections according to the stress status in different sections: supported section (OA), unsupported section (AB), disturbed section (BC) and undisturbed section (CD). Fig.1 illustrates a typical excavation procedure of pipe roof supported tunnel. To establish the mechanical model,

Fig.1 Schematic view of pipe roof supported tunnel

some key assumptions are made in the idealized pipe roof reinforcement and listed as follows.

 (1) It is assumed that the steel pipe works as a beam embedded in a Pasternak elastic foundation bearing uniform load q(x). This model was developed by Pasternak and considered a more realistic hypothesis in the elastic soil than Winkler model. Fig.2 shows the beam embedded in a Pasternak elastic foundation. In this model, load p(x) and vertical displacement ω(x) at an arbitrary point of the lower boundary of a beam hold the following relation.

                     (1)

where  k and G_p represent the elastic characteristics of the soil.

Fig.2 Geometry of Beam on Pasternak elastic foundation

(2) The overburden pressure at the top of a steel pipe can be calculated by Terzaghi theory. Equations used in estimation of q(x) are as follows:

                        (2)

q(x)=Pδ                                     (3)

where  B₁=B+htan(45?+φ/2), B is half of excavation width, γ is the unit weight of geologic formation, K₀ is the coefficient of earth pressure at rest, H is the cover depth, h is the height of excavation, is the cohesion of soil, φ is the friction angle of soil, q(x) is the surcharge load, and δ is the distance between pipes.

(3) Active failure condition is assumed at the tunnel face, so the length of pipe bearing overburden pressure ahead of the tunnel face (d) equals htan(45?+φ/2).

(4) Considering the delay effect of initial lining, the supported area (OA) is simplified to a fixed end with ω₀ vertical displacement at 0.5a before point A, where ω₀ is the tunnel crown settlement at this point.

Thus two kinds of the mechanical models established for pipe roof reinforcement according to different stress conditions are shown in Fig.3, including type A and type B. The two kinds of models are defined as follows.

Type A: Generally, the length of steel pipe ahead of the tunnel face (d′) is greater than the distance between the tunnel face and failure line (d) during tunnel excavation, so the steel pipe is assumed to a semi-infinite long beam embedded in a Pasternak elastic foundation in this case. The mechanical model is shown in Fig.3(a).

Type B: When the length of steel pipe ahead of the tunnel face (d′) is less than or equal to the distance between the tunnel face and failure line (d), the steel pipe is assumed to a finite long beam embedded in a Pasternak elastic foundation. The mechanical model for this case is shown in Fig.3(b).

Fig.3 Mechanical models of pipe roof reinforcement during tunnel excavation: (a) Type A; (b) Type B

2.2 Solution of differential equations

According to the two mechanical models, the differential equation of the vertical deformation for steel pipe can be obtained based on elastic foundation theory:

       (4)

where  b*=b[1+(G_p/k)^1/2/b], b is the beam width in Pasternak elastic foundation, E is the elasticity modulus of steel pipe, I is the inertia moment of steel pipe.

2.2.1 Type A

In this type, the differential equations of steel pipe in different sections are summarized as follows:

Section A′B:

                             (5)

Section BC:

                       (6)

Section CD:

                       (7)

The solutions of the differential equations are as follows.

Section A′B:

         (8)

Section BC:

 (9)

with

(10)

Section CD:

  (11)

where  C₁-C₈ are the undetermined coefficients, α₁= [1-(G_pλ²/k)]^1/2, λ⁴=kb/(4EI) and ω₂^* is the particular solution of the differential equation under boundary conditions: ω₂|_x=s+d=ω₃|_x=s+d, ω⁽¹⁾₂|_x=s+d=ω⁽¹⁾₃|_x=s+d.

The boundary conditions in this case are: ω₃|_x→∞=0, θ₃|_x→∞=0 because the vertical displacement and the rotation angle at point A′ are ω₀ and 0, respectively. The boundary conditions at this point are: ω₁|_x=0=ω₀, θ₁|_x=0=ω⁽¹⁾|_x=0=0, and the continuity conditions at point C must be satisfied. So the boundary conditions at this point are: ω₁|_x=s=ω₂|_x=s=0, ω₁⁽¹⁾|_x=s=ω₂⁽¹⁾|_x=s=0, ω₁⁽²⁾|_x=s=ω₂⁽²⁾|_x=s=0, ω₁⁽³⁾|_x=s=ω₂⁽³⁾|_x=s. Applying Eqs.(8)- (11) and the boundary condition, the equation set is derived as follows:

       (12)

where

The undetermined coefficients C₁, C₂, C₇ and C₈ can be determined from Eq.(12). Then substituting them into Eqs.(8)-(11), the deformation equations of steel pipe in each section can be obtained. The subgrade reaction can be derived from Eq.(1). The rotation angle, the bending moment and the shear force of the steel pipe can also be derived from the following equations:

                               (13)

                         (14)

                 (15)

2.2.2 Type B

In this type, the differential equations for sections A′B and BC are the same as those in type A, the solutions of the differential equations for these sections are equal to Eqs.(8) and (9), respectively.

Because the vertical displacement and the rotation angle at point A′ equal ω₀ and 0, respectively, the boundary conditions at this point are: ω₁|_x=0=ω₀, θ₁|_x=0=ω⁽¹⁾|_x=0=0, and the continuity conditions at point B must be satisfied. So the boundary conditions at this point are: ω₁|_x=s=ω₂|_x=s, ω₁⁽¹⁾|_x=s=ω₂⁽¹⁾|_x=s, ω₁⁽²⁾|_x=s=ω₂⁽²⁾|_x=s, ω₁⁽³⁾|_x=s=ω₂⁽³⁾₂|_x=s. As point C is the free end of steel pipe, the boundary conditions at this point are: ω₂⁽²⁾|_x=s+d=0, ω₂⁽³⁾|_x=s+d=0.

Applying the above equations and the boundary conditions, the equation set is derived as follows:

(16)

where

The undetermined coefficients C₁, C₂, C₅-C₈ can be determined from Eq.(16). Then substituting them to Eqs.(8) and (9), the deformation equations of pipe roof in each section can be obtained. The subgrade reaction, the rotation angle, the bending moment and the shear force of the steel pipe can also be derived from Eqs.(1) and (13)-(15).

3 Mechanical behavior of reinforcing pipe

3.1 Field monitoring research

In this work, the example of a certain tunnel excavation, i.e. Erlangshan tunnel in Chuanzang highway, was adopted [3]. The length of this tunnel was 4 160 m. At the tunnel entrance section, the difficult ground condition was encountered. The tunnel was driven through unconsolidated ground with small ground cover. In order to secure the stability of tunnel, pipe roof reinforcement method was used, and the stability of the pipes was provided by the installation of steel ribs at a spacing of 1 m. The tunnel had 7 m of excavation height and the soil cover was 10 m. In this tunneling case, the tunnel excavation rate was 1.5 m/d. The unsupported span length was 1.5 m. Steel pipes used for umbrella arch had outer diameter of 102 mm, length of 30 m and thickness of 10 mm. The distance between the pipes was 40 cm and each section contained 28 steel pipes. Some holes were opened at pipe’s edge in order to surround pipes surfaces and fill the cracks in rock by injection with cement/water ratio of 1/0.5 (mass ratio) which was injected under 0.5-1.0 MPa pressure. The elastic modulus of steel pipe was 200 GPa. The arrangement plan of pipe roof reinforcement in Erlangshan tunnel is shown in Fig.4.

Fig.4 Plan of pipe roof reinforcement (Unit: cm)

In order to understand the mechanical behaviors of the reinforcing pipes, the longitudinal strain of two pipes (M₁ and M₂) was monitored during tunnel excavation. The transducers were made of the same material as reinforcing pipes, and had outer diameter of 80 mm, length of 150 mm and thickness of 5 mm. Pipes M₁ and M₂ had five and three monitoring points, respectively. Fig.5 shows the arrangement plan of monitoring points along reinforcing pipe. Before installation of the reinforcing pipes, four strain gauges were symmetrically installed along the pipe interior wall at each point. As the cement paste would be injected through pipes during construction, the strain gauges being damp-proofing and insulating is very important. However, monitoring the longitudinal strain of the pipes was not satisfactory. The transducers installed seemed to be affected during tunnel construction. Only the data for longitudinal strain of pipe M₁ were available. The monitoring data were checked and analyzed to evaluate the sufficiency of tunnel support and fed back to management of construction procedure. The monitoring data of pipe M₁ during tunnel excavation are shown in Fig.6.

Fig.5 Plan of monitoring points along reinforcing pipe

Fig.6 Monitoring results of longitudinal strain of pipe M₁

3.2 Analytical research

Taking the Erlangshan tunnel as a calculation case, the analytical approach based on Pasternak elastic foundation beam theory was used to analyze the mechanical behaviors of the reinforcing pipes. The comparison of the results between field monitoring, Winkler model and Pasternak model was made. In the analysis, the major calculation parameters are listed in Table 1. A unit weight of γ=22 kN/m³ was monitored for soil with a friction angle of 30?. The initial vertical displacement ω₀ was assumed to be 14 mm, the founda- tion shear modulus G_p was 10 MN/m and the coefficient of bedding k was 20 MN/m³. Using the Matlab program, the subgrade reaction, the flexivity and bending moment of the steel pipe were obtained by analytical approach. According to the beam flexure theory, the longitudinal strain of steel pipe can also be obtained by the following

equation: ε(x)= where D is the pipe diameter and t is thickness of pipe.

Table 1 Calculation parameters of reinforcing pipe

3.3 Results and discussion

In this work, considering the excavation condition of tunnel face at x=6 m, the mechanical behaviors of reinforcing pipes in this situation were analyzed.

From Fig.7, we can confirm that the measured values of longitudinal strain of pipe are larger than the calculated values. The general trends of decreasing longitudinal strain with increasing distance from the tunnel face for analytical approach and field monitoring are also different. The calculated values of longitudinal strain reduce faster than measured values. This phenomenon may be due to the assumption of elastic material in theoretical calculation. It is well known that when a tunnel is excavated in weak rocks, the state of plastic and failure may appear in the surrounding rocks. In the plastic state, the relationship between load (stress) and deformation (strain) is no longer linear. Therefore, the assumption of linear elastic material in this analysis has some precision errors.

Fig.7 Curves of longitudinal strain of reinforcing pipe

Though there are some differences between the results of analytical approach and field monitoring, general trends of the results are similar. We can also find that the calculation results of longitudinal strain of reinforcing pipe by employing Pasternak model agree better with the results of field monitoring than those by employing Winkler model. This may be the reason that Pasternak model considers a more realistic hypothesis in the elastic soil than Winkler model, and gives more accurate calculation. The difference of calculation results between these two models is about 7% as shown in Fig.7. The distribution pattern of longitudinal strain of reinforcing pipe indicates that the maximum longitudinal strain occurs around the tunnel face, but decreases rapidly with distance up to 10 m ahead of the tunnel face, after which there is a gradual decrease to zero. Such a distribution pattern suggests that the steel pipes act as levers, which increases longitudinal load transfer to an unexcavated area, and consequently decreases deformation and increases face stability.

The comparison of the flexivity of reinforcing pipe and subgrade reaction between Winkler model and Pasternak model can be seen from Figs.8 and 9. As expected, although the difference of calculation results between these two models is about 7%, the general trends of the results are very similar. From Fig.8, we can find that the maximum flexivity of reinforcing pipe is about 16 mm, and the noticeable flexivity changes are observed around the tunnel face. But the general trend of decreasing flexivity with increasing distance from the tunnel face is evident. From Fig.9, it can be seen that in the range of 0-2 m ahead of the tunnel face, the value of subgrade reaction is greater than the overburden pressure of reinforcing pipe, but decreases rapidly with distance up to 7 m ahead of the tunnel face, after which there is a gradual decrease to zero. This phenomenon confirms the lever role of reinforcing pipe once again, and agrees well

Fig.8 Calculation curves of flexivity of reinforcing pipe

Fig.9 Calculation curves of subgrade reaction

with the practical experience.

Fig.10 shows the bending moment of reinforcing pipe. The noticeable bending moment changes are observed around the tunnel face. In general, the trends are similar between the deformation and internal force of reinforcing pipe, showing a sharp decrease with increasing distance from the tunnel face up to the range of 7-10 m, after which there is a gradual decrease to zero. It is clear that the longitudinal influencing range of tunnel excavation is 1.0-1.5 times as large as the excavation height from the tunnel face. Therefore, the ring-cut excavation method should be applied to tunnel in weak ground when the pipe roof supports are installed. This method has a sufficient effect on the decrease of the influencing range, and consequently restraints the rock displacement ahead of the tunnel face.

Fig.10 Calculation curve of bending moment of reinforcing pipe

4 Conclusions

(1) The comparison of the results among field monitoring, Winkler model and Pasternak model indicates that the Pasternak model, which considers a more realistic hypothesis in the elastic soil than Winkler model, gives more accurate calculation and agrees better with the result of field monitoring. Pasternak model is proved to be a better way to study the reinforcement mechanism and improve design practice.

(2) The pipe roof reinforcement can be effectively used not only to improve the face stability but also to limit the surface settlements ahead of the tunnel face. Reinforcing pipes act as levers, which increases longitudinal load transfer to an unexcavated area, and consequently decreases deformation and increases face stability.

(3) The longitudinal influencing range of tunnel excavation is 1.0-1.5 times as large as the excavation height from the tunnel face. Therefore, the ring-cut excavation method should be applied to tunnel in weak ground when the pipe roof supports are installed. This method has a sufficient effect on the decrease of the influencing range, and consequently restraints the rock displacement ahead of the tunnel face.

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(Edited by YANG You-ping)

Foundation item: Project(IRT0518) supported by the Program of Innovative Research Team of Ministry of Education of China

Received date: 2008-10-26; Accepted date: 2009-03-05

Corresponding author: JIA Jin-qing, Professor; Tel: +86-411-84706027; E-mail: keyknown@163.net