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Геомеханика
Вместе с тем, скачкообразное изменение и концентрация тангенциальных напряжений на внутреннем контуре спинки тюбингов наблюдается при любых значениях коэффициента бокового распора, в том числе и при X = 1. Выявленные закономерности изменения тангенциальных напряжений на внутреннем контуре обделки нужно учитывать при расчете прочности её элементов.
Список литературы
1. Н.С. Булычев, Б.З. Амусин, А.Г. Оловянный. Расчет крепи капитальных горных выработок. М.: Недра, 1974. 319 с.
A. Protosenya, M. Karasev, E. Karasev
3d model of cast-in-place tubing lining interaction with soil massive
The new analysis method of stress and strain formation in cast-in-place tubing lining is suggested. Variation of tangential and radial stresses on the inner and outer lining boundary is found.
Key words: model, tubing, soil, stress, modulus, back, rib.
Получено 22.09.10
УДК 552.2
P. Рахманнеджад, Ph.D., доц., г rahmanneiad@hotmail.com (Иран, Керман, Kerman University)
ЧИСЛЕННАЯ КЛАССИФИКАЦИЯ ГОРНЫХ ПОРОД
Предлагается новый подход к классификации горных пород, основанный на обработке результатов большого количества численных экспериментов. Исходными данными для этой системы классификации являются глубина заложения тоннеля, коэффициент бокового давления пород, площадь поперечного сечения тоннеля, отношение эффективных модулей деформации массива пород и бетонной обделки, отношение толщины обделки к пролету выработки. На выходе определяется коэффициент запаса несущей способности бетонной обделки.
Ключевые слова: классификация горных пород, тоннель, поперечное сечение, бетонная обделка, численный метод, факторный анализ.
Generally, for preliminary design in tunneling is used the engineering classification systems such as Q [1] and RMR [2]. The existing rock mass classifications have empirical character i.e., based on the experience of constructed tunnels and are used for different geological-engineering conditions. Therefore, these cannot cover the especial characters of underground constructions in different areas of industry. For example, for hydraulic tunnels the effect of water in tunnel and the shape of cross section are main and didn’t include in these systems that have common character.
In this paper is shown the theory-based activities for creation of a classification system for analysis of stability of non-pressurized water tunnel. These classifications based on scientific calculations (numerical method and factor analysis). By use of the ideas and results of this method, it is possible to fast and precisely determine the safety factor of lining, including type and thickness of concrete in different conditions.
The interaction of the system of underground structure-rock mass depends on many factors. The most important of which are initial stress state, orientation in respect to principle stresses, size and shape of tunnel and joint parameters.
We consider Semi-hard rocks (strength coefficient (f) varies from 4 to 8 according to the classification by M.M. Protodiyakonov) [3].
In this analysis, the three most frequently shapes modeled: a square with semicircular roof -No. 1, the box shape -No.2 and circular No. 3 (fig. 1) [3].
Fig. 1. Analysed shapes of cross section in semi-hard rocks
As important factors, effecting in the stability state of water tunnel we selected 5 factors: S/So - working cross sectional area of tunnel (So=1); Eef/Econ
- the ratio of the effective deformation modulus of rock mass to the effective elastic modulus of concrete; t/r - the ratio of concrete lining to the tunnel radius; H/Ho - depth of tunnel (Ho = 1) and X - coefficient of lateral pressure. Table gives the variation ranges for mentioned factors.
Range of variation of the factor
Factor Factor number Variation ranges
S Xi 20-120
Ee/Econ X2 1-5
t/r X3 0.1-0.15
H X4 50-500
X X5 0.2-1
The semi-hard rocks are usually jointed, which is incorporated in the scheme by the assumption that the rock mass is weakened by two mutually perpendicular joint systems having dip angles equal to 450. The joints are reproduced in finite element mesh around the excavation in a region whose size corresponds to half span of the tunnel b/2; outside it. The rocks were simulated as a continuous homogeneous medium having an effective elastic modulus that incorporates the effects of the cracks.
To simulate the rock, were used four-node isoparametric elements while, the joints were simulated by means of special contact [4]. In figure 2 show the grid of finite elements for cross section No. 1 is shown.
j.j.V-1 y
|— h :■ = ■ -■ h ■ ■■ ! ■ r 1— —H — — i— i— ■1
-1 ■- -5 —-
P V -,
1î r> « rr.
— G ' - - ■ i .'i— — P— J
* ■ 1.
IJ V-! y 1
- » ■ « f
—1— "k v ■!
Fig.2. Grid of finite elements for cross section No. 1
A linear elasto-plastic treatment for the condition of planar strain were used for the above three form of tunnels [5] and the Mohr-Coulomb equation was used as the criterion of plasticity.
The calculations were performed for B15 class of concrete [3]. Compressive strength oc = 8.5 MPa, tensile strength ot = 0.8 MPa, elastic modulus Econ = 0.7x 23000 = 16000 MPa. Factor 0.7 is introduced to correct the decrease in strength of concrete after passing the limit state (when cracks are formed in the concrete).
The lining thickness [3]
t = (0,1 - 0,15)r. (1)
Where r is the inside radius of the tunnel.
For calculation of stress-strain state of rock mass, surrounding tunnel is considered the stages of opening of cross section.
The number and conditions of numerical experiments were defined in accordance with the matrix of experimental planning [6].
To compare the three shapes, were used the safety factor - M, which is the ratio of the calculated resistance of the concrete- R to the stress acting in the lining - o.
M = R / a . (2)
The following parametric equation is used:
M = h+ bixi + byXSj . (3)
t=1 i=1 i=1
After doing numerical experiment in accordance to designed matrix of planning and statistical processing of the achieved parametric equations were determined the coefficients of equation b0, b and bij (xi and xj are the factors). For example for cross section № 1 the parametric equation is:
M = 2.713x5 + 202.497x3 + 0.116x1 +1.79x2 -
0.0125x1x2 -1.004x1x3 + 0.037x1x5 +16.16x2x3 -
1.706x2x5 - 118.1x3x5 + 0.0038x4 -12.1 - ( )
0.5x1x4 - 0.0035x2x4 - 0.223x3x4 + 0.029x4x5.
A graphic use of the given parametric correlation that is based on nomograms [7] is used for determining the safety factor m (fig. 3).
The procedure for determining m is as follows: we define the points of intersection for the x1-x2 and x1-x3 lines and measure the distance between them; from the point of intersection of the x4-x5 lines, we draw a horizontal line, whose length is equal to the measured distance. The end point shows the value of M.
Fig.3. Nomograms for determining safety factor - M [8]: A - region of using reinforced concrete lining, B - region of using concrete lining,
C - region of using schotcrete lining
These nomograms help to:
- examine how each factor x affects on safety factor;
- for given xi, select the cross section form having an acceptable M;
- one can specify M and vary the xi to obtain the best shape from the
economic point of view.
Example: consider a water tunnel that has shape No.1. The area of cross section is equal to 32 m2 (r =2.9 m) and the depth -300 m. The coefficient of lateral pressure of rock mass is equal to 0.4. The effective deformation modulus of rock mass is equal to 32000 MPa, therefore the ratio of Eef/Econ=2. The concrete thickness- t is equal to 45 cm.
From the nomogram (fig. 3), the value of M is equal to 5 and the concrete lining has a great safety factor. If the thickness of concrete is decreased to 30 cm, to M will be equal to 2.5.
This example shows how one can do fast analysis of the stability of concrete lining of tunnel and make the necessary decides.
The nomograms are in fact as a local graphical classification system. The input data are five above mentioned parameters that include geomechanical (depth, coefficient of lateral pressure and rock mass modulus) and technical (lining thickness, concrete elastic modulus, radius and cross sectional area of tunnel). The output is safety factor of lining.
1. For preliminary design in tunnelling usually is used the current engineering classification systems, that have empirical character and cannot cover the especial characters of underground constructions in different areas of industry.
2. Numerical methods coupled with the factor analysis can be an effective tool for the studies of interaction of underground construction-rock mass and for consideration of the main factors that affect on the behaviour of the rock mass-support system.
3. The proposed method can be applied for construction of local classification system for any fixed engineering-geological conditions.
References
1. Barton N., R. Lien and J. Lunde. Engineering classification of rock masses for the design of tunnel support// Rock Mech. 1974. No. 6. P. 189-236.
2. Bieniawski Z.T. Engineering classification of jointed rock masses, Transact. S. Afr. Ins. Civil Eng. 1973. No. 15. P. 335-342.
3. SNIP 2.06.09.84. Hydraulic tunnels, Moscow, 1985.
4. Oriekhov V.G., Zertsalov M.G. Fracture mechanics of constructions and rock mass. M.: ACB press, 1998.
5. Zertsalov M.G., Tolstikov V.V. Manual software “cracks”// Journal of fundaments and soil mechanics. 1988. No. 5.
6. Adler U.P. Design of experiments. M.: NauKa 1976. 279 c.
Геомеханика
7. Barisov S.N. Algorithms for nomograms. M.: RAN, 1999.
R. Rahmannedjad
Numerical rock mass classification
There are popular rock mass classifications such as Q, RMR, RSR. These engineering classifications are based on experience of constructed tunnels and other underground constructions. In this paper is introduced a new manner for creation of a classification system. This manner is based on passing of a large number of numerical experiments and processing of these. The input data of classification system are used the depth of tunnel, the coefficient of lateral pressure, the area of cross section of tunnel, the ratio of effective modulus of deformation of rock mass to modulus of deformation of concrete lining and the ratio of lining thickness lining to width of tunnel. The output datum of numerical rock mass classification is the safety factor of concrete lining.
Key words: rock mass classification, tunnel, cross-section, concrete lining, numerical method, factor analysis.
Получено 22.09.10
УДК 624.1.041:550.34
A.C. Саммаль, д-р техн. наук., проф., sammal@mm.tsu.tula.ru (Россия, Тула, ТулГУ),
Ю.И. Климов, канд. техн. наук., доц., sammal@mm.tsu.tula.ru (Россия, Тула, ТулГУ),
Н.А. Капунова, канд. техн. наук., доц., sammal@mm.tsu.tula.ru (Россия, Тула, ТулГУ)
РАСЧЕТ МНОГОСЛОЙНЫХ ПОДЗЕМНЫХ КОНСТРУКЦИЙ СО СЛОЯМИ ПЕРЕМЕННОЙ ТОЛЩИНЫ НА СТАТИЧЕСКИЕ НАГРУЗКИ И СЕЙСМИЧЕСКИЕ ВОЗДЕЙСТВИЯ ЗЕМЛЕТРЯСЕНИЙ
Излагается аналитический метод расчета многослойных подземных конструкций, слои которых в общем случае могут иметь переменные толщины по периметру поперечного сечения, на статические нагрузки, включающие гравитационные и тектонические силы в массиве пород, внешнее давление подземных вод, внутренний напор (прирассмотрении обделок гидротехнических туннелей), а также сейсмические воздействия землетрясений. В качестве иллюстрации рассмотрены конкретные примеры расчета.
Ключевые слова: многослойные конструкции, переменная толщина, расчет, статические нагрузки, сейсмические воздействия.
Сооружение уникальных объектов энергетического, транспортного и гидротехнического назначения в сложных горно - и гидрогеологических условиях, в том числе - в районах повышенной тектонической и сейсмической активности, предопределили создание новых видов подземных конст-
