THE CALCULATION OF MULTILAYER LINING OF TUNNELS, CONSTRUCTED IN A TECHNOLOGICALLY DIVERSE OF MASSIF SOIL

Addressing urban transport is a very timely matter, especially in the capital Hanoi and Ho Chi Minh City. In order to solve this problem, a solution has been proposed for the construction of overhead tram and subway lines. In fact, when constructing subway lines through historical sites, high population density, many surface structures, etc., the method of open construction is not feasible, it is necessary to use the method Underground construction. These areas are often weak soil, the physical parameters of the soil detrimental to the tunnel construction work; Such as small stickiness, small internal friction angle, high porosity, high permeability coefficient, high water saturation, short shear strength etc. These factors create complex geological conditions in Construction tunnel. With that in mind, the calculation of the selection of the tunnel casing structure is necessary, which is timely. This paper provides a solution to the problem of stress state of multilayer lining supporting the tunnel of circular cross-section, constructed in a technologically heterogeneous array. The tunnel lining and surrounding soil mass are considered as elements of a united deformable system.


Basic theoretical principles
In the task, the calculated diagram is shown in Fig. 1, multilayer concentric ring consisting of arbitrary number of layers, the boundaries of which consists of a circle with the center placed at the origin.The gravitational force in the layer ( * 1, 2,..., i = N ), which simulates the soil body (as in a natural state and exposed to the technological impact of the excavation of the tunnel), is modeled by the presence of the same component fields of initial stresses (3) We write the boundary conditions at the contact lines L i (i=1, 2, …, N) rings through the additional stresses and displacements in the General form: Use the additional views radial contact stresses as appropriate pressure and introducing new symbols q highlight from lining of any two adjacent layers, numbered respectively i and i+1 (i = 1, …, N-1), contact common edge L i (Fig. 2).
Use the additional views radial contact stresses as the relevant pressures and introducing new symbols highlight the bolting of two arbitrary adjacent layers, numbered respectively i and i+1 (i=1, ..., N-1), in contact at the common boundary of L i (Fig. 2).When considering the equilibrium of selected layers, the effect of the discarded layers will replace the normal pressures.On the outer contour of L i-1 has pressure p i-1 , simulating the effect of the discarded layers of S i (i=1, …, i-1).The effect of the discarded inner layers S j (j=i+1, …, N) is modeled by a uniform pressure p i+1 , distributed according to the internal contour L i+1 .
The displacements of points of the contours taking into account the fact that the outer circuit L i-1 each i-layer S i (i=1, …, N) in the general case of a loaded pressure p i- Applying formula (6), should be taken into consideration that: Then convert the expression (8) can be written as: Imagine the resulting equality in the form

p p q cc
From the last expression one can write The resulting expression can be represented as: The formula to determine the coefficients K i, i , K i, i-1 and free members Q i can be obtained by comparing expressions (10) and (11): where . The recurrence formula (11) with i = 1 can be written as the ratio which, taking into account the condition ( 7) is converted to the form: where we have used the notation: (15) Further, using the representation ( 14), (15), applying the recurrence formula (11), putting i = 2, we can write: where: So, when i = 3 we arrive to the expression: , (18) where: As a result, generalizing the representation ( 13)−(19) can write a General formula that allows to express all the unknown values p i through p 1 in the form: If to take into account the representation (15) and (12), formulas (21) completely determine included in the expression (20) the values of M i , L i (i = 2, …, N).
In turn, the relation (20) allows at i=N to come to expression (22) On the other hand, based on (15) we have: ) Where will get: Thus, substituting (24) into formula (20) allows to calculate all unknown values Full radial tension on the outer L i-1 and L i the internal contours of the i -layer are defined by the formulas: The ability to determine the stresses in the layers of the underground constructions allow to verify the strength of concrete layer and the bearing capacity of underground construction in General formula [3]: where Finally the formulas (27) taking The carrying capacity is estimated by the ratio: where N − is the calculated normal force is determined from the first expression (28); NS − ultimate bearing capacity of the radial cross section of the lining defined by the ratio 0 2 1; eccentricity of application of longitudinal force.

The calculation algorithm
Thus, the stress-strain state of layered underground structures, constructed in a technologically heterogeneous array, based on the study of the equilibrium state of a single deformable "multi-layered liningarray" represents the following sequence of operations: 1.The initial data are given by: N * − the number of layers, modeling of technologically heterogeneous array of species; N -total number of layers modeling the system "multi-layered lining-rock mass" as a whole; R i (i = 1,…, N) are the radii of the layers of the lining (m); Е and also given the designation The algorithm is the basis of a computer program of calculating multilayered tunnel lining circular cross-section, constructed in a technologically heterogeneous array.

Conclusion
The obtained formulas for determination of normal tangential and radial stresses in the underlying layers of technologically heterogeneous array and the tunnel lining, the simulated multi-layered concentric ring, allow us to estimate the carrying capacity used underground structures.Given the calculation algorithm implemented in computer programs, allowing to produce multiple calculations for practical design.

Fig. 1 .
Fig. 1.A design scheme for a multilayer lining of a tunnel, constructed in a technologically heterogeneous array ., charge amount and initial stress.In the expression (2) symbol  marked all components of stresses, as a function of 

3 .
characteristics of rock mass in its natural state -the deformation modulus (MPa) and Poisson's ratio respectively; Е i ,  I (i = 2,…, N) be the modulus of deformation (MPa) and the Poisson's ratios of the material layers, modeling of technologically heterogeneous array of species (i = 2, 3,…, N * ) and the lining (i = N * +1, N * +2,…, N);  − averaged value of the specific weight of rocks in the array (MN/m 3 ); H -depth of tunnel (m); l 0 -is the lag of construction of the lining from the bottom of the tunnel (m). 2. Is determined by the value of the If you change the index i = 1, ..., N are auxiliary quantities: с 1 =0 and modifying the index i in the range i = 1, …, N−1