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Application of rock mechanics principles to tunnelling in China
h~t. J. Rock Mech. Min. Sci. & Geomech. Ahstr. Vol. 31, No. 6, pp. 749-754, 1994
Elsevier Science Ltd. Printed in Great Britain
Pergamon
0148-9062(93)E0028-M
Technical Note Application of Rock Mechanics Principles to Tunnelling in China LI SHIHUI#
INTRODUCTION Tunnelling projects play an increasingly important role in the construction of the national economy, and they have drawn extensive attention internationally. China is vast and it has complicated terrain and geological conditions. Tunnelling has developed rapidly for the large scale construction in China. From 1949 to the early eighties, the total length of tunnels for water power was in excess of 200 km; for railways, 2500 km; and, for mines from 1966 to 1981, 7000km. Experience with construction of tunnelling was also obtained in practice, which promoted the development of rock mechanics. The characteristics of tunnelling projects are as follows: the tunnels have a large axial length, simple and consistent cross-sections; the orientations of tunnels are dependent upon their functions; there can be complicated and diversified geological conditions and there may be little possibility to make any choice; the area for geological reconnaissance is large, and there may be limited funds and technical personnel. In tunnelling, a number of unexpected geological conditions may be encountered, for example, faulted zones, junctions of faults, soft partings, water inrush, rock and gas outbursts, etc. Although in situ measurement of the strength and deformation of rocks, the stress fields of rocks (ground stress field and seepage field) can be made, and parameters of rock mechanics be provided for the design, due to limitation of funds, materials and technical conditions, for most tunnels in situ measurements cannot be afforded. Even for some key tunnelling projects, in situ measurements cannot be undertaken frequently, because of their length. Usually, engineering geological investigation is started with rock mass classification, and then parameters of rock mechanics are measured in typical geological units. Finally, some typical cross-sections are chosen, and rock stability is analysed by using non-linear numerical analysis of rock mechanics [i]. This commonly used method is only applicable to systems in which the inter-relations of all the factors are simple. For example, when the rock mass is competent and massive, tEngineering Geomechanics, Institute of Geology, Academia Sinica, Beijing, 100029, People's Republic of China. RMMS 31/6~L
749
it can be effectively used for measuring parameters of rock mass mechanics. The new Australian tunnelling method (NATM) brought about epochal change in tunnelling. Now, the applications of systems sciences, expert systems and computer science has brought a bright prospect for rock stability analysis. In recent years, Professor J. A. Hudson [2] believed that rock engineering involved a great number of inherent and external factors. For example, in situ stress, structure and strength of the rock mass, deformation of the rock mass, mechanisms of rock failure, and permeability, etc. are inherent factors, and the activity of underground water, the dimension effect of a sample, the shape and size of the tunnel, construction and lining are external factors that affect the changes of rock mass properties. The interaction and coupling action among these factors can be expressed by a matrix (rock engineering mechanism information technology, REMIT). The most important part of rock engineering is the investigation of coupled mechanisms between factors in the matrix. The investigation starts with the single factors, the interaction of all the factors, and finally all the aspects of the complete project, such as economic, cultural, environmental and social problems. This is the REMIT procedure proposed by Professor Hudson in which all the problems of rock mechanics can be solved at three levels. He also pointed out that attention should be paid to application of current new technology and new methods [2] in addition to expert systems, from which engineers can absorb experience from others. There is no doubt, all these viewpoints and methods have promoted the development of rock mechanics and have given guidance to the research as well as to the solutions of practical problems in rock engineering. Up to now, few people have realized that rock mechanics is a comprehensive science. Any problem in rock engineering is a combination of mechanics and geology, and also a problem of knowledge engineering. From the viewpoint of systems sciences, it is, in fact, an open complex giant system [3]. Theoretical research and practical experience have shown that such an open complex giant system cannot be solved by simply using the mathematical methods of applied mechanics, nor by
750
[.I SttlHUI: I~ECHNI(.ALNO][
conventional expert systems, nor by monitoring measurements. The only method that can be applied right now is the meta-synthesis engineering method which extends qualitative analysis to quantitative analysis. The essence of this method is to combine together theories of all the disciplines, empirical knowledge of experts, reliable information and computer science and form a system. In application, usually, a hypothesis (judgement or conjecture) is made, and it is then checked and revised by empirical data [3,4]. The author introduces the principles and method of systems sciences in this note. The author studies the macroscopic coupling of all the factors that affect rock stability in excavation and lining of the tunnels and the controlling mechanism by combining analysis of rock mechanics and the integral viewpoint of system science. The author proposes a semi-theoretical and semi-empirical analysis method which incorporates NATM, classification of rock masses and back-analysis technique. This has been used for many projects in the past few years. It was preliminarily applied and popularized for the prediction of rock stability in tunnelling in China.
TYPICAL ANALYSIS The typical analysis is a summary and an improvement of the conventional tunnelling experience obtained from underground excavations and application of the latest sciences. First of all, one finds out the actual needs of a tunnel project and the possible conditions. The merits and disadvantages of all the relevant theories and methods at home and abroad have been investigated and the results of their application have been studied carefully. Among them three methods have been chosen and have formed a new system. They are: rock mass classification, information obtained from typical tunnelling projects, and non-conventional numerical analysis of rock mechanics represented by back-analysis of displacement (as well as relevant computer sciences). The typical analysis is, in fact, an application of meta-synthesis engineering to the specific conditions of the Chinese tunnels. The success of its application does not depend on the breakthroughs of individual techniques, but on the advantages of the integral system. The functions and inter-relation of these three subsystems of the typical analysis are as follows: 1. The major geological factors of the input parameters for mechanical analysis based on the theory of engineering geomechanics are identical to the major geological factors of rock mass classification systems. Therefore, the rock mass classification system can provide typical geological environment (and corresponding constructional factors) for rock stability analysis, and synthetic parameters of major geological factors can be input. 2. The in situ measurement data, obtained from typical tunnels, as an indication of inter-coupling of major geological factors in the integral stab-
ility of the rock mass, represent quantitalively the degree of synthesis. That i~, to say, the measured peripheral displacement of the tunnels, as a reference, can be fed back to correct the program of numerical analysis (currently, it is a linear elastic analysis program), so that the resuits of analysis are sufficiently close to the data of typical projects (therefore, this program is no longer a linear elastic one), and a special channel is formed. It is a rough semi-theoretical and semi-empirical model for analysis, not a non-linear medium model of rock mechanics with input of in situ measured parameters of rock mechanics. However, it can meet the requirements of general tunnels. 3. The routine portion of the numerical analysis of rock mechanics describes the influence of the structural conditions, such as the shape of the tunnel, lining, depth, etc. on the stability of the rock mass; and the non-routine portion, namely, the portion corrected by individual typical projects, describes the influence of the geological environment (and corresponding operational conditions) on the integral stability of the rock mass. The latter is and will be locally checked and adjusted to expand its scope of application. The typical analysis, like meta-synthesis, is an empirical assumption; and its determination can only be checked by a great number of proiects in application and by empirical statistics. The three components of a typical analysis and their relation are shown in Fig. 1. From the knowledge acquisition and knowledge representation points of view, the typical analysis is only an outline of the thinking method of expert consultancy for prediction of rock stability in tunnels. The entire process is in conformity with the expert consultancy in this field. First of all, it is necessary to determine the class of rock mass in the project; to retrieve typical cases of similar rock masses by using the rock classification system as a bridge, and
Fig. I. Three components of the typical analysis and their relation.
LI SHIHUI: TECHNICAL NOTE
751
Site investigation lline and orientation IRock classification General tunnel I | Major underground Projects I I Projects I I ~ Gr°und characteristics: ~ i Primary stress, strength, -- water,fissures,anistropy, etc.
[..
Statical system analysis, rock mechanics model
Mechanical model
N o . N O V'~
Safety concept failure hypotheses Yes
I Contractual aspectsI I Driving the tunnels I "[ and lining N
Risk assessment
I
I
Reinforcing
~
Field measurement .
I
Geotechnical investigation Experience estimation
(~ ~ Excavation method ~ _ structuralelements I ,~ i I
Technical model Statical analysis .... in typical analogic analysis
Geology
4
-t
I
.
.
.
j
For the actual state only Unknown safety measurement
Fig. 2. Typicalanalogicanalysisin the designprocessfor tunnelling.Note: dotted lineshowsbranch processof TypicalAnalogic Analysis.
these will be used as the closest and most reliable references for the analysis. In the analysis, it is usually assumed that the constructional method used in this project is very close to typical projects; to compare the structural conditions of the projects with the typical projects and their effect on rock stability; simple means will be used for mechanical analysis, in the most simplified conditions (in typical engineering geological environment and operational conditions to analyse the specific structural conditions of the project). The deformation behaviour and failure of the rock mass in the project can be predicted with some certainty, and qualitative and rough quantitative prediction can be made as in consultancy. APPLICATION The position and function of the typical (analogic) analysis is shown in Fig. 2 in the design program of a project. In the figure the additions and amendments were made according to the practice in Chinese tunnels. The portion with a dotted line was added as a branch of the
flow sheet [1], and the other portion with a solid line was taken from the literature [6]. In order to check the effectiveness of the typical analysis in tunnelling projects, a BMP84 boundary element method (BEM) program was developed in 1985. The main points of this technique are: . The merits of 2 D linear elastic BEM program are: ease of data input and output, and simple in application. . When the BEM program is applied for calculating several media, such as, surrounding rocks with a sprayed layer of shotcreting and roof bolts, etc, the required internal memory and running time increases rapidly. Shear wedge theory, developed by Professor L. V. Rabcewicz, was introduced to calculate the equivalent normal resistance force of rock-bolting and shotcreting, Pi and its application was expanded to calculate stresses and displacements under conditions of different confined pressure coefficient, ;t ratio of height to length (H/L) and
752
l.I SHtHUh 13 25 37
49
TECHNICAL NO'fF
6173 85 97109121133145 Element No.
. . . . . . . . .
Element length i{1.5
12.0 ~4.0
24.0 1.0 22.0 20.5 21.0 Y -
2.0
Aa
Py
ZXor
(Aar)ar
Relative normal
Px
stress i n c r e m e n t ~x a r
o f the r o e k m a s s
. x
H L
- -
ul
J.-4.0,
2.0 2.0 , 1 . 0 ,
0.5
Fig. 3. Distribution of relative stress increment in the rock masses with different confined pressure coefficients along the periphery of the tunnel.
the shape of the tunnel. To be more specific, the FEM was introduced to calculate 312 cases in different conditions, and the empirical function expression P~ (2, H/L ) was obtained by statistics. (The examples are shown in Figs 3 and 4.) After checking and correction, they were incorporated into the BEM program. . The measured data are input, and then numerical analysis of typical projects is made. The measured values of convergence (displacement) are fed back for correction of P~(2, H/L ), so that the results are sufficiently close to those of typical projects, and a comprehensive correction coefficient, Kc is obtained; and this is used to
o,1
0.505 0.596
H --
L
-1.0
1.0 -
1.25
1.270
1.5 1.523
2.0
t
1.911
2 - 1.0
H
Aar Fig. 4. Distribution of relative stress increment of rock mass along the periphery of tunnel at different ratios of H/L.
establish a special channel for classification of the rock mass in the tunnel. . After being corrected by a typical project, the results of the analysis are equivalent to the deformation at a given moment (that is the moment when the last measurement of the convergence value is made for feedback correction) of the non-linear and rheological rock mass of the project; and the limit equilibrium force derived from shear wedge theory is also converted into the designed bearing capacity for a safety factor close to the typical project. Thus, it can be applied directly in the design and construction. The method of checking tensile cracks on the periphery of tunnel is used to prevent P, (2, H/L ) from becoming the active force. Kc values for all classes of rock masses are checked and partially corrected in application so as to extend the scope of application and reliability of the program. Before the BMP84 BEM program is checked by a project, it is first checked by engineering data. Representative and reliable data were collected from 26 measuring sections of 18 tunnels (mainly soft rock projects). The calculated data were then compared with the measured data. The degree of closeness was much better than the design figures. From 1989 to 1990, two workshops were organized to popularize the BMP84 program, with 98 participants, coming from 77 units of water conservancy, hydro-power, railway, highway, tunnelling, coal and metal mines, national and civil defence, bringing with them information collected from 86 cross-sections of projects being designed or under construction. The checked results were quite satisfactory. The rates of satisfaction were 91.4 or 94.1% respectively. The revised BMP84 BEM program was published in a book entitled Systems Analysis of Tunnel Rock Stability in 1991, which provided a technical methodology for extensive application and popularization [1].
Li SHIHUI:
TECHNICAL NOTE
The efficiency of the BMP84 BEM program was about 10-100 times higher than the conventional method. Its major technical functions are as follows: 1. Data input is simple, on average 70 inputs. All the figures except the control instructions, are taken from the design drawings. 2. Generally, it takes less than 3 min for a 386 type micro-computer to calculate the figures of a cross-section, and it is easy for ordinary technical personnel to learn how to calculate. 3. The precision of calculation can meet the requirements of the project. The reliability ratio of the calculated to the measured convergence is in the range of 1/3 to 3; and the statistical value of cases is over 80%. It can reach the level of an expert in this field. The following are case studies of three projects:
(1) Comparison of proposals for the Qinling railway tunnel Qinling tunnel on the railway line from Xi'an to Ankang is about 19 km in total. It is the longest railway tunnel in China. The rock that Qinling railway tunnel passes through is metamorphosed granite, with high ground stress and complicated geological conditions. In the selection of various proposals, Mr Zhang Jinrong made calculations of about 30 cross-sections of single and double lane tunnels at a depth varying from 200 to 1600 in Class V rocks or (Class II and VI rocks according to the classification system used by the railway), using both the elasto-plastic finite element analysis program developed by a university and the BMP84 program, one after the other. The results obtained were quite close to each other and can meet the design standards, i.e. the ratio of displacement along the periphery of the tunnel averaged 0.90, varying from 0.51 to 1.57; the ratio of maximum main stresses was 1.05 on average, varying from 0.43 to 1.94. The shape in the plastic zone and in the tensile stress zone is about the same. However, when the BMP84 program is compared with the finite element method, the BMP84 program takes less than 1/80 of the time for preparing the data and less than 1/20 of the time for calculation (BMP84 program using PC/XT machine, and finite element program using a 386 machine).
(2) Displacement back analysis of Pandaoling tunnel Pandaoling tunnel is 15.723 km long, and is located in the main irrigation channel of a project which leads to Datong River into Zhuanglang River for irrigation of Qinwangchuan land. It is one of the top ten longest such tunnels in the world. This tunnel was constructed by a Japanese contractor, Kumagai Gumi Co. Ltd. It has a round arch, straight sides and an invert. The gross span of the tunnel is 5 m with a height of 5.2 m. The depth of
tLiu Yongxue et al. Preliminary application of feedback of measured information for design of Pandaoling tunnel in a water irrigation system. Underground Engineering Technique (1992).
753
the portal section is 110 m. The rock it passes through is tertiary intercalated sandstone and sandy mudstone, with a uniaxial compressive strength of 0.3-5.9 MPa. The elastic modulus of the rock mass is 182.4MPa. According to the report of the geological investigation, the FEM report believed that the confined pressure coefficient should be calculated in accordance with the gravity field, and is 0.43. In 1989 the author and Mr. Wang Zhongjing made a back-analysis together, using horizontal displacement and roof convergences measured at 9 cross-sections in the portal section (No. 77 + 954--78 + 020.5) at similar depth and rock type. The confined pressure coefficient obtained by the BMP84 program is 0.9-1.2, which almost doubled the figures in the original design. In 1992, based on the back-analysis of displacement with a two-media model of the tunnel, and a report of the measured data with a hydraulic stress meter, the confined pressure coefficients were all close to 1.0.t This proved the figures of the above-mentioned back-analysis published in the literature [1] to be correct.
(3) Checking the design of a diversion tunnel at Ertan hydro-electric project Ertan power station is located in the lower reaches of Yalong River, with an installed capacity of 3.30 million kW, which is the largest hydro-power station ever built in China. There are two diversion tunnels, one on each bank of the station. The size of the excavated section is 20.5 m × 25.5 m. They are both about 1100 m long. The rock type is syenite, basalt and sandy shale. It is in the high stress zone. In the construction period, cave-in happened in the soft rock and rockbursts in the hard rock. The geological conditions are very complicated. In September 1991 the foreign contractor submitted a transmittal with a report of BEM results for approval of the proposed rock support methods. It was proposed in order to keep stability of the rock mass, 1000 N pre-stressed anchors 15 m long each should be added to the side walls every 16 m 2 in the section in E class rock mass (equivalent to Class IV rocks in tunnels for the hydro-power station in China). The price of one piece of anchor was RMB 35,000 Yuan in the contract. The time for the action required was November in the same year. At that time only 4 weeks were left for checking this transmittal by numerical analysis of the rock mechanics. It would have been very difficult if conventional analysis was to be used. Chengdu Hydroelectric Investigation and Design Institute finished the checking in a short period of time by using the BMP84 program. The results of the checking proved the original design to be rational, and proved that the parameters provided by the contractor were not adequate. It was decided to keep the original design. In October 1992, when the author visited the site, the diversion tunnel in the section of Class IV rock was mostly finished without a single pre-stressed anchor being installed. The rock mass remained stable after the preliminary lining was applied; and this check-up saved nearly RMB 2 million Yuan for the state.
754
L! SHIHUI: TECHNICAL NOTE CONCLUSIONS
Numerical analysis for the preliminary prediction o f rock stability has been applied and popularized for the first time in Chinese tunnelling projects based on the theoretical research and practice o f typical analogic analysis. The advantages o f the BMP84 BEM p r o g r a m and its social and economic benefits have proved that the thinking and method o f typical analogic analysis are suitable for the very complicated conditions o f tunnels, and are scientific and rational. The key to the success o f typical analogic analysis is the application o f metasynthesis engineering in tunnelling. The BMP84 program is still not perfect. It remains to be further checked and improved in the practice o f tunnelling. Acknowledgement--The author would like to thank those who pro-
vided assistance in the development of the method. The name list is too long to be included, see postscript of the literature [1].
Accepted for publication 27 October 1993.
REFERENCES
I. Li Shihui. Systems Analysis of Tunnel Rock Stability. China Railway Publish House, Beijing (1991). 2. Hudson, J. A. Principles of rock mechanics and engineering. Chinese J. Rock Mech. Engng 8, 252-268 (1989). 3. Qian Xuesen, Yu Jingyuan and Dai Ruwei. A new discipline of science--the study of an open complex giant system and its methodology. Nature J. 13, 1-10 (1990). 4. Dai Ruwei. Meta-synthesis engineering developed from qualitative analysis to quantitative analysis. Pattern Recogn. Artific. Intell. 4, 5-10 (1991). 5. Gu Dezhen. Fundamentals of Rockmass Engineering Geomechanics. Publishing House of Sciences, Beijing (1979). 6. Heinz Duddeck. Guideline for the design of tunnels "new developments of underground space use". Proc. 3rd Int. Conf. on Underground Space and Earth Sheltered Buildings, Shanghai, China, pp. 180-188 (1988).
Elsevier Science Ltd. Printed in Great Britain
Pergamon
0148-9062(93)E0028-M
Technical Note Application of Rock Mechanics Principles to Tunnelling in China LI SHIHUI#
INTRODUCTION Tunnelling projects play an increasingly important role in the construction of the national economy, and they have drawn extensive attention internationally. China is vast and it has complicated terrain and geological conditions. Tunnelling has developed rapidly for the large scale construction in China. From 1949 to the early eighties, the total length of tunnels for water power was in excess of 200 km; for railways, 2500 km; and, for mines from 1966 to 1981, 7000km. Experience with construction of tunnelling was also obtained in practice, which promoted the development of rock mechanics. The characteristics of tunnelling projects are as follows: the tunnels have a large axial length, simple and consistent cross-sections; the orientations of tunnels are dependent upon their functions; there can be complicated and diversified geological conditions and there may be little possibility to make any choice; the area for geological reconnaissance is large, and there may be limited funds and technical personnel. In tunnelling, a number of unexpected geological conditions may be encountered, for example, faulted zones, junctions of faults, soft partings, water inrush, rock and gas outbursts, etc. Although in situ measurement of the strength and deformation of rocks, the stress fields of rocks (ground stress field and seepage field) can be made, and parameters of rock mechanics be provided for the design, due to limitation of funds, materials and technical conditions, for most tunnels in situ measurements cannot be afforded. Even for some key tunnelling projects, in situ measurements cannot be undertaken frequently, because of their length. Usually, engineering geological investigation is started with rock mass classification, and then parameters of rock mechanics are measured in typical geological units. Finally, some typical cross-sections are chosen, and rock stability is analysed by using non-linear numerical analysis of rock mechanics [i]. This commonly used method is only applicable to systems in which the inter-relations of all the factors are simple. For example, when the rock mass is competent and massive, tEngineering Geomechanics, Institute of Geology, Academia Sinica, Beijing, 100029, People's Republic of China. RMMS 31/6~L
749
it can be effectively used for measuring parameters of rock mass mechanics. The new Australian tunnelling method (NATM) brought about epochal change in tunnelling. Now, the applications of systems sciences, expert systems and computer science has brought a bright prospect for rock stability analysis. In recent years, Professor J. A. Hudson [2] believed that rock engineering involved a great number of inherent and external factors. For example, in situ stress, structure and strength of the rock mass, deformation of the rock mass, mechanisms of rock failure, and permeability, etc. are inherent factors, and the activity of underground water, the dimension effect of a sample, the shape and size of the tunnel, construction and lining are external factors that affect the changes of rock mass properties. The interaction and coupling action among these factors can be expressed by a matrix (rock engineering mechanism information technology, REMIT). The most important part of rock engineering is the investigation of coupled mechanisms between factors in the matrix. The investigation starts with the single factors, the interaction of all the factors, and finally all the aspects of the complete project, such as economic, cultural, environmental and social problems. This is the REMIT procedure proposed by Professor Hudson in which all the problems of rock mechanics can be solved at three levels. He also pointed out that attention should be paid to application of current new technology and new methods [2] in addition to expert systems, from which engineers can absorb experience from others. There is no doubt, all these viewpoints and methods have promoted the development of rock mechanics and have given guidance to the research as well as to the solutions of practical problems in rock engineering. Up to now, few people have realized that rock mechanics is a comprehensive science. Any problem in rock engineering is a combination of mechanics and geology, and also a problem of knowledge engineering. From the viewpoint of systems sciences, it is, in fact, an open complex giant system [3]. Theoretical research and practical experience have shown that such an open complex giant system cannot be solved by simply using the mathematical methods of applied mechanics, nor by
750
[.I SttlHUI: I~ECHNI(.ALNO][
conventional expert systems, nor by monitoring measurements. The only method that can be applied right now is the meta-synthesis engineering method which extends qualitative analysis to quantitative analysis. The essence of this method is to combine together theories of all the disciplines, empirical knowledge of experts, reliable information and computer science and form a system. In application, usually, a hypothesis (judgement or conjecture) is made, and it is then checked and revised by empirical data [3,4]. The author introduces the principles and method of systems sciences in this note. The author studies the macroscopic coupling of all the factors that affect rock stability in excavation and lining of the tunnels and the controlling mechanism by combining analysis of rock mechanics and the integral viewpoint of system science. The author proposes a semi-theoretical and semi-empirical analysis method which incorporates NATM, classification of rock masses and back-analysis technique. This has been used for many projects in the past few years. It was preliminarily applied and popularized for the prediction of rock stability in tunnelling in China.
TYPICAL ANALYSIS The typical analysis is a summary and an improvement of the conventional tunnelling experience obtained from underground excavations and application of the latest sciences. First of all, one finds out the actual needs of a tunnel project and the possible conditions. The merits and disadvantages of all the relevant theories and methods at home and abroad have been investigated and the results of their application have been studied carefully. Among them three methods have been chosen and have formed a new system. They are: rock mass classification, information obtained from typical tunnelling projects, and non-conventional numerical analysis of rock mechanics represented by back-analysis of displacement (as well as relevant computer sciences). The typical analysis is, in fact, an application of meta-synthesis engineering to the specific conditions of the Chinese tunnels. The success of its application does not depend on the breakthroughs of individual techniques, but on the advantages of the integral system. The functions and inter-relation of these three subsystems of the typical analysis are as follows: 1. The major geological factors of the input parameters for mechanical analysis based on the theory of engineering geomechanics are identical to the major geological factors of rock mass classification systems. Therefore, the rock mass classification system can provide typical geological environment (and corresponding constructional factors) for rock stability analysis, and synthetic parameters of major geological factors can be input. 2. The in situ measurement data, obtained from typical tunnels, as an indication of inter-coupling of major geological factors in the integral stab-
ility of the rock mass, represent quantitalively the degree of synthesis. That i~, to say, the measured peripheral displacement of the tunnels, as a reference, can be fed back to correct the program of numerical analysis (currently, it is a linear elastic analysis program), so that the resuits of analysis are sufficiently close to the data of typical projects (therefore, this program is no longer a linear elastic one), and a special channel is formed. It is a rough semi-theoretical and semi-empirical model for analysis, not a non-linear medium model of rock mechanics with input of in situ measured parameters of rock mechanics. However, it can meet the requirements of general tunnels. 3. The routine portion of the numerical analysis of rock mechanics describes the influence of the structural conditions, such as the shape of the tunnel, lining, depth, etc. on the stability of the rock mass; and the non-routine portion, namely, the portion corrected by individual typical projects, describes the influence of the geological environment (and corresponding operational conditions) on the integral stability of the rock mass. The latter is and will be locally checked and adjusted to expand its scope of application. The typical analysis, like meta-synthesis, is an empirical assumption; and its determination can only be checked by a great number of proiects in application and by empirical statistics. The three components of a typical analysis and their relation are shown in Fig. 1. From the knowledge acquisition and knowledge representation points of view, the typical analysis is only an outline of the thinking method of expert consultancy for prediction of rock stability in tunnels. The entire process is in conformity with the expert consultancy in this field. First of all, it is necessary to determine the class of rock mass in the project; to retrieve typical cases of similar rock masses by using the rock classification system as a bridge, and
Fig. I. Three components of the typical analysis and their relation.
LI SHIHUI: TECHNICAL NOTE
751
Site investigation lline and orientation IRock classification General tunnel I | Major underground Projects I I Projects I I ~ Gr°und characteristics: ~ i Primary stress, strength, -- water,fissures,anistropy, etc.
[..
Statical system analysis, rock mechanics model
Mechanical model
N o . N O V'~
Safety concept failure hypotheses Yes
I Contractual aspectsI I Driving the tunnels I "[ and lining N
Risk assessment
I
I
Reinforcing
~
Field measurement .
I
Geotechnical investigation Experience estimation
(~ ~ Excavation method ~ _ structuralelements I ,~ i I
Technical model Statical analysis .... in typical analogic analysis
Geology
4
-t
I
.
.
.
j
For the actual state only Unknown safety measurement
Fig. 2. Typicalanalogicanalysisin the designprocessfor tunnelling.Note: dotted lineshowsbranch processof TypicalAnalogic Analysis.
these will be used as the closest and most reliable references for the analysis. In the analysis, it is usually assumed that the constructional method used in this project is very close to typical projects; to compare the structural conditions of the projects with the typical projects and their effect on rock stability; simple means will be used for mechanical analysis, in the most simplified conditions (in typical engineering geological environment and operational conditions to analyse the specific structural conditions of the project). The deformation behaviour and failure of the rock mass in the project can be predicted with some certainty, and qualitative and rough quantitative prediction can be made as in consultancy. APPLICATION The position and function of the typical (analogic) analysis is shown in Fig. 2 in the design program of a project. In the figure the additions and amendments were made according to the practice in Chinese tunnels. The portion with a dotted line was added as a branch of the
flow sheet [1], and the other portion with a solid line was taken from the literature [6]. In order to check the effectiveness of the typical analysis in tunnelling projects, a BMP84 boundary element method (BEM) program was developed in 1985. The main points of this technique are: . The merits of 2 D linear elastic BEM program are: ease of data input and output, and simple in application. . When the BEM program is applied for calculating several media, such as, surrounding rocks with a sprayed layer of shotcreting and roof bolts, etc, the required internal memory and running time increases rapidly. Shear wedge theory, developed by Professor L. V. Rabcewicz, was introduced to calculate the equivalent normal resistance force of rock-bolting and shotcreting, Pi and its application was expanded to calculate stresses and displacements under conditions of different confined pressure coefficient, ;t ratio of height to length (H/L) and
752
l.I SHtHUh 13 25 37
49
TECHNICAL NO'fF
6173 85 97109121133145 Element No.
. . . . . . . . .
Element length i{1.5
12.0 ~4.0
24.0 1.0 22.0 20.5 21.0 Y -
2.0
Aa
Py
ZXor
(Aar)ar
Relative normal
Px
stress i n c r e m e n t ~x a r
o f the r o e k m a s s
. x
H L
- -
ul
J.-4.0,
2.0 2.0 , 1 . 0 ,
0.5
Fig. 3. Distribution of relative stress increment in the rock masses with different confined pressure coefficients along the periphery of the tunnel.
the shape of the tunnel. To be more specific, the FEM was introduced to calculate 312 cases in different conditions, and the empirical function expression P~ (2, H/L ) was obtained by statistics. (The examples are shown in Figs 3 and 4.) After checking and correction, they were incorporated into the BEM program. . The measured data are input, and then numerical analysis of typical projects is made. The measured values of convergence (displacement) are fed back for correction of P~(2, H/L ), so that the results are sufficiently close to those of typical projects, and a comprehensive correction coefficient, Kc is obtained; and this is used to
o,1
0.505 0.596
H --
L
-1.0
1.0 -
1.25
1.270
1.5 1.523
2.0
t
1.911
2 - 1.0
H
Aar Fig. 4. Distribution of relative stress increment of rock mass along the periphery of tunnel at different ratios of H/L.
establish a special channel for classification of the rock mass in the tunnel. . After being corrected by a typical project, the results of the analysis are equivalent to the deformation at a given moment (that is the moment when the last measurement of the convergence value is made for feedback correction) of the non-linear and rheological rock mass of the project; and the limit equilibrium force derived from shear wedge theory is also converted into the designed bearing capacity for a safety factor close to the typical project. Thus, it can be applied directly in the design and construction. The method of checking tensile cracks on the periphery of tunnel is used to prevent P, (2, H/L ) from becoming the active force. Kc values for all classes of rock masses are checked and partially corrected in application so as to extend the scope of application and reliability of the program. Before the BMP84 BEM program is checked by a project, it is first checked by engineering data. Representative and reliable data were collected from 26 measuring sections of 18 tunnels (mainly soft rock projects). The calculated data were then compared with the measured data. The degree of closeness was much better than the design figures. From 1989 to 1990, two workshops were organized to popularize the BMP84 program, with 98 participants, coming from 77 units of water conservancy, hydro-power, railway, highway, tunnelling, coal and metal mines, national and civil defence, bringing with them information collected from 86 cross-sections of projects being designed or under construction. The checked results were quite satisfactory. The rates of satisfaction were 91.4 or 94.1% respectively. The revised BMP84 BEM program was published in a book entitled Systems Analysis of Tunnel Rock Stability in 1991, which provided a technical methodology for extensive application and popularization [1].
Li SHIHUI:
TECHNICAL NOTE
The efficiency of the BMP84 BEM program was about 10-100 times higher than the conventional method. Its major technical functions are as follows: 1. Data input is simple, on average 70 inputs. All the figures except the control instructions, are taken from the design drawings. 2. Generally, it takes less than 3 min for a 386 type micro-computer to calculate the figures of a cross-section, and it is easy for ordinary technical personnel to learn how to calculate. 3. The precision of calculation can meet the requirements of the project. The reliability ratio of the calculated to the measured convergence is in the range of 1/3 to 3; and the statistical value of cases is over 80%. It can reach the level of an expert in this field. The following are case studies of three projects:
(1) Comparison of proposals for the Qinling railway tunnel Qinling tunnel on the railway line from Xi'an to Ankang is about 19 km in total. It is the longest railway tunnel in China. The rock that Qinling railway tunnel passes through is metamorphosed granite, with high ground stress and complicated geological conditions. In the selection of various proposals, Mr Zhang Jinrong made calculations of about 30 cross-sections of single and double lane tunnels at a depth varying from 200 to 1600 in Class V rocks or (Class II and VI rocks according to the classification system used by the railway), using both the elasto-plastic finite element analysis program developed by a university and the BMP84 program, one after the other. The results obtained were quite close to each other and can meet the design standards, i.e. the ratio of displacement along the periphery of the tunnel averaged 0.90, varying from 0.51 to 1.57; the ratio of maximum main stresses was 1.05 on average, varying from 0.43 to 1.94. The shape in the plastic zone and in the tensile stress zone is about the same. However, when the BMP84 program is compared with the finite element method, the BMP84 program takes less than 1/80 of the time for preparing the data and less than 1/20 of the time for calculation (BMP84 program using PC/XT machine, and finite element program using a 386 machine).
(2) Displacement back analysis of Pandaoling tunnel Pandaoling tunnel is 15.723 km long, and is located in the main irrigation channel of a project which leads to Datong River into Zhuanglang River for irrigation of Qinwangchuan land. It is one of the top ten longest such tunnels in the world. This tunnel was constructed by a Japanese contractor, Kumagai Gumi Co. Ltd. It has a round arch, straight sides and an invert. The gross span of the tunnel is 5 m with a height of 5.2 m. The depth of
tLiu Yongxue et al. Preliminary application of feedback of measured information for design of Pandaoling tunnel in a water irrigation system. Underground Engineering Technique (1992).
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the portal section is 110 m. The rock it passes through is tertiary intercalated sandstone and sandy mudstone, with a uniaxial compressive strength of 0.3-5.9 MPa. The elastic modulus of the rock mass is 182.4MPa. According to the report of the geological investigation, the FEM report believed that the confined pressure coefficient should be calculated in accordance with the gravity field, and is 0.43. In 1989 the author and Mr. Wang Zhongjing made a back-analysis together, using horizontal displacement and roof convergences measured at 9 cross-sections in the portal section (No. 77 + 954--78 + 020.5) at similar depth and rock type. The confined pressure coefficient obtained by the BMP84 program is 0.9-1.2, which almost doubled the figures in the original design. In 1992, based on the back-analysis of displacement with a two-media model of the tunnel, and a report of the measured data with a hydraulic stress meter, the confined pressure coefficients were all close to 1.0.t This proved the figures of the above-mentioned back-analysis published in the literature [1] to be correct.
(3) Checking the design of a diversion tunnel at Ertan hydro-electric project Ertan power station is located in the lower reaches of Yalong River, with an installed capacity of 3.30 million kW, which is the largest hydro-power station ever built in China. There are two diversion tunnels, one on each bank of the station. The size of the excavated section is 20.5 m × 25.5 m. They are both about 1100 m long. The rock type is syenite, basalt and sandy shale. It is in the high stress zone. In the construction period, cave-in happened in the soft rock and rockbursts in the hard rock. The geological conditions are very complicated. In September 1991 the foreign contractor submitted a transmittal with a report of BEM results for approval of the proposed rock support methods. It was proposed in order to keep stability of the rock mass, 1000 N pre-stressed anchors 15 m long each should be added to the side walls every 16 m 2 in the section in E class rock mass (equivalent to Class IV rocks in tunnels for the hydro-power station in China). The price of one piece of anchor was RMB 35,000 Yuan in the contract. The time for the action required was November in the same year. At that time only 4 weeks were left for checking this transmittal by numerical analysis of the rock mechanics. It would have been very difficult if conventional analysis was to be used. Chengdu Hydroelectric Investigation and Design Institute finished the checking in a short period of time by using the BMP84 program. The results of the checking proved the original design to be rational, and proved that the parameters provided by the contractor were not adequate. It was decided to keep the original design. In October 1992, when the author visited the site, the diversion tunnel in the section of Class IV rock was mostly finished without a single pre-stressed anchor being installed. The rock mass remained stable after the preliminary lining was applied; and this check-up saved nearly RMB 2 million Yuan for the state.
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L! SHIHUI: TECHNICAL NOTE CONCLUSIONS
Numerical analysis for the preliminary prediction o f rock stability has been applied and popularized for the first time in Chinese tunnelling projects based on the theoretical research and practice o f typical analogic analysis. The advantages o f the BMP84 BEM p r o g r a m and its social and economic benefits have proved that the thinking and method o f typical analogic analysis are suitable for the very complicated conditions o f tunnels, and are scientific and rational. The key to the success o f typical analogic analysis is the application o f metasynthesis engineering in tunnelling. The BMP84 program is still not perfect. It remains to be further checked and improved in the practice o f tunnelling. Acknowledgement--The author would like to thank those who pro-
vided assistance in the development of the method. The name list is too long to be included, see postscript of the literature [1].
Accepted for publication 27 October 1993.
REFERENCES
I. Li Shihui. Systems Analysis of Tunnel Rock Stability. China Railway Publish House, Beijing (1991). 2. Hudson, J. A. Principles of rock mechanics and engineering. Chinese J. Rock Mech. Engng 8, 252-268 (1989). 3. Qian Xuesen, Yu Jingyuan and Dai Ruwei. A new discipline of science--the study of an open complex giant system and its methodology. Nature J. 13, 1-10 (1990). 4. Dai Ruwei. Meta-synthesis engineering developed from qualitative analysis to quantitative analysis. Pattern Recogn. Artific. Intell. 4, 5-10 (1991). 5. Gu Dezhen. Fundamentals of Rockmass Engineering Geomechanics. Publishing House of Sciences, Beijing (1979). 6. Heinz Duddeck. Guideline for the design of tunnels "new developments of underground space use". Proc. 3rd Int. Conf. on Underground Space and Earth Sheltered Buildings, Shanghai, China, pp. 180-188 (1988).