Collapse Analysis of Tunnel Portal Based on Catastrophe Theory

Zuo Zhuo1 Zhang Jianren2 Fu Helin3 Peng Wenxuan4 1,2 Changsha University of Science and Technology, 410007 3,4 School of Civil Engineering e of Central South University Changsha 41007 China e-mail: [email protected]

ABSTRACT Landslide prevention is a technical problem of tunnel construction. In this paper, catastrophe theory is used to predict the possibility of tunnel collapse. The prediction results show that the collapse is possible in the case of bare rock. It is necessary to adopt the methods of temporary support and temporary support, reasonably arrange the excavation sequence and control the excavation step distance, and strengthen the monitoring quantity and information feedback under the premise that the two liners are closely followed, so as to ensure the safety of the tunnel construction.

KEYWORDS: catastrophe theory /tunnel/ excavation/ predict /collapse

INTRODUCTION

The instability of tunnel surrounding rock is mostly steady or slow failure, which is often regarded as a continuous process. The actual situation often happens suddenly, sometimes the disk is huge and the energy is released. Therefore, if the situation is considered as a continuous process and interpreted with the traditional continuum theory, it must be unreasonable, and other solutions must be sought.

Catastrophe theory, a branch of mathematics, it belongs to the study of discontinuous phenomenon, it Puxue, extension of singularity theory as the main mathematical tools, the French mathematician R.Thom founded in 1972. Since the establishment of the theory, the traditional integral method cannot describe the instability of the tunnel surrounding rock, landslide, collapse, earthquake and other discontinuous phenomena, and mutation theory has played a significant role. It uses proper mathematical descriptions to study the abrupt changes that may occur in a smooth system. Therefore, using the catastrophe theory, the phenomenon of tunnel collapse and its mechanism can be analyzed, thus providing a theoretical basis for tunnel support.

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TUNNEL EXCAVATION CONDITION

Liangjiayuanzi tunnel located in Huaihuai district of Hunan Province, with the split, in a curve shape distribution, the overall direction of the tunnel axis is about 106 degrees; the left tunnel length 3450m, the maximum depth of about 531.8m, is located at ZK21+200; the right tunnel length 2276m, maximum depth of about 513.6m, located in K21+180. Review of engineering geological conditions 1) Topography and geomorphology: The tunnel belongs to tectonic denudation low Zhongshan landform, undulating terrain. The tunnel site is narrow and the traffic conditions are poor. 2) Stratigraphic lithology The stratigraphic distribution of the tunnel site is described from the old to the new: Quaternary Pleistocene series (QPdl) A and silty clay are mainly distributed in the slope of Yongshun tunnel at the end of tunnel. Layer thickness 1.5m-2.4m. B and crushed stone (QPdl) are mainly distributed at the Longshan end of the tunnel, the entrance of the mouth and the slope of the body, and the thickness is 7.5m-16.3m. Middle Cambrian Maoping formation (∈2m) C (∈2m), dolomite and -1 thickness 6.9m. D (∈2m), dolomite and -2 thickness 3.0m-9.4m. E (∈2m), limestone and -1 thickness 2.6m. F (∈2m), limestone and -2 thickness 6.1m-130.3m. RQD=5-70%. Lower Cambrian Ming Temple group (1m) G, carbon siltite (∈1m) 5 -1 thickness 3.0m. H, carbon siltite (∈1m). -2 is mainly distributed in the mountain tunnel area end entrance, thickness of 7.2m-25.5m. I, carbon siltite (∈1m). -3: black, weathered, sandy, muddy cementation, thick layered structure, joint fissure, fissure disseminated by iron and manganese, core is short column, long column, hard rock, rock intact. This layer is mainly distributed in the Longshan end of the tunnel site, and the thickness is 3.5m-17.5m. RQD=50-80%. J, carbargilite (∈1m) the thickness of 7.0m. K, siltite (∈1m) -1 thickness 7.3m. L, siltite (∈1m) -2 thickness 63.4m. M, siltite (∈1m, -3) and the thickness of 8.5m-326.3m, RQD=50-70%. According to the preliminary exploration of shallow seismic reflection survey, covering layer and weathered layer of elastic wave velocity VP=600-1600m/s, strong weathering carbon containing silty sand, silty sandstone Vp=1700-2300m/s, weathered pelitic siltstone Vp=2100- 3600m/s. Middle weathered limestone and dolomite Vp=2500-4100m/s. 3) Geological structure The geological structure of the tunnel is relatively simple, and there is no unfavorable geological structure development, and the regional geology is relatively stable. Vol. 22 [2017], Bund. 13 5133

4) Earthquake According to the code for seismic design of Highway Engineering (JTJ004-89), the tunnel shall be subject to seismic fortification in accordance with the relevant provisions. 5) Hydrogeological conditions Fissure water is the main part of the tunnel area, while fissure water is mainly supplied by meteoric water. The groundwater supply and discharge are fast and the water shortage is low. On the hillside of groundwater is not developed, because the joint carbonaceous argillaceous siltstone, siltstone and limestone, dolomite fractured poor connectivity, groundwater is not with the connectivity of fissure water, fissure water for local broken rock, and a small amount of water, no uniform groundwater level. The groundwater depth is 4.0m-65.4m, and the water inflow at the orifice is about 16.4L/min.

Determination of tunnel excavation method

In the slope due to the hole in the body, therefore, using the method of double side excavation tunnel. See figure 1. In order to ensure the safety of tunnel construction, this paper uses the catastrophe theory to predict the possibility of tunnel collapse, and provides the basis for the next step construction. CONSTRUCTION OF CUSP CATASTROPHE MODEL

The most commonly used mutation model is cusp catastrophe, as shown in figure 2. Potential function of cusp catastrophe:

（1）

In Formula(1), u and V are control variables, and X is state variable.

For the (1) derivation, a control equilibrium surface can be obtained:

（2）

Further derivation is available:

（3）

Find the differential expression of the root of equation (2):

In addition to the satisfying formula (2), the non isolated singular point set should also satisfy the formula (3). By (2) (3) elimination x, obtained:

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Figure 1: double side heading method construction

Figure 2: the cusp catastrophe model section map

Establishment of cusp catastrophe model for tunnel

excavation of slope surrounding rock mass

The surrounding rock is not excavated and disturbed in the tunnel. It is in a stable state of primary rock stress. When the tunnel is excavated, the surrounding rock stress redistribution occurs, and some stress concentration, leading to some surrounding rock in plastic state, and even destruction. Large scale landslide may occur in tunnel excavation of slope surrounding rock mass. Using the method of double side excavation tunnel 2. Based on catastrophe theory, a cusp catastrophe model of tunnel portal excavation is established to find the bifurcation set of catastrophe model and to determine the critical condition of surrounding rock collapse. The branch set is the set of the energy released and supplied by the excavation of the tunnel crown rock system, which is equal to the energy absorbed by the collapse and collapse center of the tunnel. The mechanical model of collapse induced by instability of tunnel surrounding rock is established, as shown in Figure 3 and Figure 4.

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Figure 3: The rock mass structure Figure 4: Tunnel surrounding rock instability tunnel Collapse collapse mechanical schematic diagram

Can be seen from Figure 3, after the excavation of Tunnel Temporary rock pillar load bearing. If the temporary rock column has been crushed and the bearing capacity is low, the deformation will increase continuously. Because the surrounding rockmass slope body is easy to collapse, the formation of caving arch, the Platts caving arch height, then figure 3 can be simplified as three hinge system in figure 4. In order to conform to the actual situation, when the surrounding rock of the vault is turned 1 and 2, the instability of surrounding rock caused by K and H is induced, and the amount of the landslide is the damage variable A.

The total energy or potential energy function of the collapse system 2 F(θ ) = 2Aθ + 2PLsinθ − Q p sinθ − 2µ(1− cosθ ) （5） = 2Aθ 2 + Bsinθ − 2µ(1− cosθ ) Here，B=2PL-QP; L--distance between H and J；P—Average pressure of tunnel vault ；µ-- Stiffness of surrounding rock of roof ；QP---Residual strength of intermediate rock column

（6）

（7）

Here assume B=0，so in balance position will lead 。

In formula（7），when ，only on solution exists，。 when , solution

, Instability Will occur，when is also instable. When Bis unequal to 0，

Closed results cannot be obtained .So ， will be transferred in taylor series

θ = θ − µ − θ 2 + θ 2 + µθ 4 + θ 5 F( ) B ( 2A) 1/ 6B 1/12 0( ) （8） Formula (8) is a cusp catastrophe model for tunnel excavation of slope surrounding rock mass.

Assume ，then

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The standard potential function of cusp catastrophe is:

（9） The corresponding bifurcation equation is:

（10） Here ，，enter into formula（10）, then：。 In QPOµ the coordinate plane, the bifurcation set of the potential function (9) is shown in figure 5.

Figure 5: mutation model three hinge arch bifurcation set

From Figure 5，The parameters of the three hinged arch system are QP，µ。， the sufficient conditions for the system equilibrium QP，µare obtained to satisfy formula (10)。To QP，µ，Change the different paths, three hinge arch has two different failure modes, namely: first, control points along the 1-2-3 path change will lead to steady destruction; the 1-3 along the path of change will lead to structural failure suddenly, collapse, accompanied by huge energy release, threaten the mine production and the safety of surface buildings. Informula（10)，when µ-2A=0，QP=2PL, sign as(Qp)。Therefore, based on the special case of catastrophe theory, the critical value of three hinged arch collapse can be obtained.

PREDICTION OF EXCAVATION COLLAPSE AT THE

ENTRANCE OF LIANGJIAYUANZI OLL TUNNEL

From above analysis, whenµ-2A=0，QP=2PLthe critical value of three hinged arch collapse, sign as（QP）0。when（QP）>（QP0），collapse will occur。The surrounding rock mass of the tunnel at the entrance of the Liangjiayuanzi tunnel is a slope accumulation, and its strength is 0.5-0.8MPa. Using the method of double side excavation tunnel, tunnel span is 5m, and the tunnel in the shallow buried section, stress for the corresponding tunnel entrance at the top of the unit area: Vol. 22 [2017], Bund. 13 5137

gH 2 q = Q / 2a = gH − tg 2 (450 −ϕ / 2)tgϕ 1 2a f f 1 r=2.7t/m3, H=11m, ¢f=250, 则（QP）0=q×L=0.62MPa，Close to the strength of surrounding rock. Therefore, when the tunnel is excavated in shallow section, the instability of surrounding rock leads to the collapse. In order to avoid the collapse phenomenon, recommended surface steel pipe, surrounding rock reinforcement, improve the surrounding rock strength; can also take strong reinforcement, such as encryption, to increase the diameter of pipe roof joist spacing, and in tunnel excavation as soon as possible closure. CONCLUSION

In this paper, the theoretical analysis model of the tunnel excavation of the slope tunnel is established, and the possibility of the collapse is predicted. The results show that the possibility of collapse exists when the surrounding rock is bare rock. It is necessary to adopt the methods of temporary support and temporary support, reasonably arrange the excavation sequence and control the excavation step distance, and strengthen the monitoring quantity and information feedback under the premise that the two liners are closely followed, so as to ensure the safety of the tunnel construction.

ACKNOWLEDGEMENT This paper are sponsored by Project supported by China Natural Foundation (No.51538009, No.51578550) and Project of Chang Science Bureau, here we thank them.

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Editor’s note. This paper may be referred to, in other articles, as: Zuo Zhuo, Zhang Jianren, Fu Helin, Peng Wenxuan: “Collapse Analysis of Tunnel Portal Based on Catastrophe Theory” Electronic Journal of Geotechnical Engineering, 2017 (22.13), pp 5131-5138. Available at ejge.com.