Dynamic response of three dimension tunnel on elastic foundation subjected to moving vehicle loads

al energy [9, 11] as Πe = 1 2 ∫ Ae { σif }T e [Dcs] { σif } e dAe − ∫ Ae wp dAe = 1 2 {q}Te [Kp]e {q}e − {q}Te {P}e , (13) with [Kp]e︸ ︷︷ ︸ 12×12 = ∫ Ae [B]T [Dcs] [B] dAe, {P}e︸︷︷︸ 12×1 = ∫ Ae [N]T p dAe, (14) are stiffness matrix and node loading vector of the element, respectively, [N]︸︷︷︸ 1×12 = [ N1 0 0 N2 0 0 N3 0 0 N4 0 0 ] , p is pressure of intensity. Kinetic energy Te of element is determined by [9, 11] Te = 1 2 ∫ Ve ρ {u˙}Te {u˙}e dVe 1 2 {q˙}Te ∫ Ve ρ [N]T [N] dVe  {q˙}e = 12 {q˙}Te [M]e {q˙}e , (15) where ρ-mass density, {q˙}e-velocity vector, and [Mp]e = ∫ Ve ρ [N]T [N] dVe. (16) 2.1.2. Elements for arc of arch Suppose that arc of arch is a shallow cylindrical shell that can be described by 4 nodes flat shell elements with 6 degrees of freedom ui, vi, wi, θxi, θyi, θzi per node and vector of element node displacement { qsh } e = { {qp}Te { q f }T e { qθ }T e }T , (17) where {qp}e︸ ︷︷ ︸ 12×1 = { w1 θx1 θy1 w2 θx2 θy2 . . . w4 θx4 θy4 }T-vector of node dis- placement of bending plate element, { q f } e = { u1 v1 u2 v2 u3 v3 u4 v4 }T-vector of node displacement of tension or compression plate element { qθ } e= { θz1 θz2 θz3 θz4 }T -vector of node twist surrounded the axis z of elements. 110 Nguyen Thai Chung, Do Ngoc Tien Following [9, 12] the matrix of flat shell element stiffness can be derived as [ Ksh ] e︸ ︷︷ ︸ 24×24 =  [Kp]e︸ ︷︷ ︸ 12×12 [0]︸︷︷︸ 12×8 [0]︸︷︷︸ 12×4 [0]︸︷︷︸ 8×12 [ K f ] e︸ ︷︷ ︸ 8×8 [0]︸︷︷︸ 8×4 [0]︸︷︷︸ 4×12 [0]︸︷︷︸ 4×8 [Krz]e︸ ︷︷ ︸ 4×4  , (18) where: [Kp]e-stiffness matrix of bending plate element, [ K f ] e-stiffness matrix of tension or compression plate element [9] and[Krz]e-stiffness matrix of twist plate element. In fact, the components krz(i, j) of matrix [Krz]e are equal to zero (in the calculation these com- ponents are considered to be very small, namely krz(i, j) = 10−3 ×max(k(m,n)), where k(m,n) are components of matrices [Kp]e and [ K f ] e [9, 12]). Similarly, mass matrix of flat shell element [9, 12] is [ Msh ] e︸ ︷︷ ︸ 24×24 =  [Mp]e︸ ︷︷ ︸ 12×12 [0]︸︷︷︸ 12×8 [0]︸︷︷︸ 12×4 [0]︸︷︷︸ 8×12 [ M f ] e︸ ︷︷ ︸ 8×8 [0]︸︷︷︸ 8×4 [0]︸︷︷︸ 4×12 [0]︸︷︷︸ 4×8 [Mrz]e︸ ︷︷ ︸ 4×4  . (19) Load vector, stiffness matrix and mass matrix of element shell in the global coordi- nate system are determined as follow [12]{ qsh }g e = [ Tsh ]T { qsh } e , [ Ksh ]g e = [ Tsh ]T [ Ksh ] e [ Tsh ] , [ Msh ]g e = [ Tsh ]T [ Msh ] e [ Tsh ] , (20) where [ Tsh ] ︸ ︷︷ ︸ 24×24 is transformation coordinate system matrix. 2.1.3. Elements for foundation layers For foundation layers, using the hexagonal 8-node element with 3 degrees of free- dom of each node one can obtain the following relationship {ε}e = [B] {q}e (21) for strain vector {ε}e at a point of element and node displacement {q}e [9, 12]. In the above equation the notations are introduced {ε}e = { εx εy εz γxy γyz γzx }T , [B] = [∂] [N] = [[B1] [B2] [B3] ... [B8]] , Dynamic response of three dimension tunnel on elastic foundation subjected to moving vehicle loads 111 [N] is mode shape function matrix of element. Therefore, the stiffness matrix of element is [12] [K]e = ∫ Ve [B]T [D] [B] dVe, (22) with [D] is element material matrix. The mass load vector is determined by [12] {P}e = ∫ Ve [N]T {g} dV = ∫ Ve [N]T { gx gy gz }T dV, (23) 2.2. Modeling of vehicle movement on pavement plate Let’s consider a four wheel vehicle modeled by 4-degree-of-freedom system which moves on the pavement plate with the trajectory x = x(t), y = y(t) and velocity~v = ~v (t) (see Fig. 3). The mass of vehicle body m is derived as absolute solid body and pavement plate is springs with stiffness k f 1, k f 2, kr1, kr2 and damping elements c f , cr, respectively (Fig. 4b, c). The inertia moment of vehicle body with center-of-mass G is J. The distances from G to the front axle and rear axle are l f and lr, respectively. The position of vehicle body is determined by parameters: vertical displacement u of center-of-mass G, rotation displacement in plane xz, vertical displacement z f of front wheels, vertical displacement zr of rear wheels. The considered system is 4-degree-of-freedom system [13]. Assumes that vibration amplitude is small, vehicle body is in initial horizontal direction. 7 fz fc fm u rc rz rm  PL x O z y kr1 kr1 kf1 kf2 l lr f kr2 Plate Car body Moving trajectory Wp z y x1e 2e Fr Ff a, Real model b, FEM model Fig 3. Plate subjected to 4 degree of freedom vehicle load model At a time, vehicle body is subjected to gravity force P = mg, the exiting forces Fr, Ff, and inertia force mu, J (Fig.4a). G J rF mu mg fF u  lr l f a, vehicle body b, wheel system, front suspension c, wheel system, rear suspension Fig. 4. Applied forces of vehicle Equilibrium equation system of vehicle body is r f r r f f mu + F + F + mg = 0, J - F l + F l = 0, (24) where u is vertical acceleration,  is angular acceleration in the plane xz of vehicle body. The equilibrium equations for wheels and suspension are             r1 1r 2r r1 r 2r r 2r r1 1r 2r r2 2r r 2r r2 2r 2r r k z z F m z c z u k z z k z u 0, c u z k u z F ,                         r r r r l l l l (25)             f1 1f 2f f1 f 2f f 2f f1 1f 2f f 2 2f f 2f f 2 2f 2f f k z z F , m z c z u k z z k z u 0, c u z k u z F .                              f f f f l l l l (26) where 2r is static deformation of spring with stiffness kr2 and 2f is static deformation of spring with stiffness kf2. Combining (24), (25) and (26) leads to the differential equations for vibration of the systems (4- degree of freedom vehicle) (a) Real model 7 Tải trọng tác dụng Quỹ đạo chuyển động fz fc fm u rc rz rm  PL PW x O z y kr1 kr1 kf1 kf2 l lr f kr2 Tấm z y x1e 2e Fr Ff a) Real model b) FEM model Fig 3. Plate subjected to 4 degree of freedom vehicle load model At a time, vehicle body is subjected to gravity force P = mg, the exiting forces Fr, Ff, and inertia force mu, J (Fig.4a). G J rF mu mg fF u  lr l f a, vehicle body b, wheel system, front susp nsion c, wheel system, rear suspension Fig. 4. Applied forces of vehicle Equilibrium equation system of vehicle body is r f r r f f mu + F + F + mg = 0, J - F l + F l = 0, (24) where is vertical acceleration,  is angular acceleration in the plane xz of vehicle body. The equilibrium equations for wheels and suspension are             r1 1r 2r r1 r 2r r 2r r1 1r 2r r2 2r r 2r r2 2r 2r r k z z F m z c z u k z z k z u 0, c u z k u z F ,                         r r r r l l l l (25)             f1 1f 2f f1 f 2f f 2f f1 1f 2f f 2 2f f 2f f 2 2f 2f f k z z F , m z c z u k z z k z u 0, c u z k u z F .                              f f f f l l l l (26) where 2r is static deformation of spring with stiffness kr2 and 2f is static deformation of spring with stiffness kf2. Combining (24), (25) and (26) leads to the differential equations for vibration of the systems (4- degree of freedom vehicle) (b) FEM model Fig. 3. Plate subjected o 4-degree-of-freedom vehicle load model At a time, the vehicle body is subjected to gravity force P = mg, exiting forces Fr, Ff , and inertia forces mu¨, J ϕ¨ (Fig. 4a). The equilibrium equation system of vehicle body is written as follows mu¨ + Fr + Ff + mg = 0, J ϕ¨− Frlr + Ff l f = 0. (24) 112 Nguyen Thai Chung, Do Ngoc Tien 7 Tải trọng tác dụng Quỹ đạo chuyển động fz fc fm u rc rz rm  PL PW x O z y kr1 kr1 kf1 kf2 l lr f kr2 Tấm z y x1e 2e Fr Ff a) Real model b) FEM model Fig 3. Plate subjected to 4 degree of freedom vehicle load model At a time, vehicle body is subjected to gravity force P = mg, the exiting forces Fr, Ff, and inertia force mu, J (Fig.4a). G J rF mu mg fF u  lr l f a, vehicle body b, wheel system, front suspension c, wheel system, rear suspension Fig. 4. Applied forces of vehicle Equilibrium equation system of vehicle body is r f r r f f mu + F + F + mg = 0, J - F l + F l = 0, (24) where u is vertical acceleration,  is angular acceleration in the plane xz of vehicle body. The equilibrium equations for wheels and suspension are             r1 1r 2r r1 r 2r r 2r r1 1r 2r r2 2r r 2r r2 2r 2r r k z z F m z c z u k z z k z u 0, c u z k u z F ,                         r r r r l l l l (25)             f1 1f 2f f1 f 2f f 2f f1 1f 2f f 2 2f f 2f f 2 2f 2f f k z z F , m z c z u k z z k z u 0, c u z k u z F .                              f f f f l l l l (26) where 2r is static deformation of spring with stiffness kr2 and 2f is static deformation of spring with stiffness kf2. Combining (24), (25) and (26) leads to the differential equations for vibration of the systems (4- degree of freedom vehicle) (a) Vehicle body 7 Tải trọng tác dụng Quỹ đạo chuyển động fz fc fm u rc rz rm  PL PW x O z y kr1 kr1 kf1 kf2 l lr f kr2 Tấm z y x1e 2e Fr Ff a) Real mod l b) FEM model Fig 3. Plate subjected to 4 degree of freedom vehicle load model At a time, vehicle body is subjected to gravity force P = mg, the exiting forces Fr, Ff, and inertia force mu, J (Fig.4a). G J rF mu mg fF u  lr l f a, vehicle body , wheel system, front suspension c, wheel system, rear suspension Fig. 4. Applied forces of vehicle Equilibrium equation system of vehicle body is r f r r f f mu + F + F + mg = 0, J - F l + F l = 0, (24) where u is vertical acceleration,  is angular acceleration in the plane xz of vehicle body. The equilibrium equ tions for wheels and suspension are             r1 1r 2r r1 r 2r r 2 r1 1r 2r r2 2r r 2r r2 2r 2r r k z z F m z c z u k z z k z u 0, c u z k u z F ,                         r r r r l l l l (25)             f1 1f 2f f1 f 2f f 2f f1 1f 2f f 2 2f f 2f f 2 2f 2f f k z z F , m z c z u k z z k z u 0, c u z k u z F .                              f f f f l l l l (26) where 2r is static deformation of spring with stiffness kr2 and 2f is static deformation of spring with stiffness kf2. Combining (24), (25) and (26) leads to the differential equations for vibration of the systems (4- degree of freedom vehicle) (b) Wheel system, front suspension 7 Tải trọng tác dụng Quỹ đạo chuyển động fz fc f u rc rz rm  PL PW x O z y kr1 kr1 kf1 kf2 l lr f kr2 Tấm z y x1e 2e Fr Ff a) Real model b) FEM model Fig 3. P ate subjected to 4 degree of freedom vehicle load model At a time, vehicle body is subjected to gravity force P = mg, the exiting forces Fr, Ff, and inertia force mu, J (Fig.4a). G J rF mu mg fF u  lr l f a, vehicle body b, wheel system, front suspension c, wheel syste , rear suspension Fig. 4. Applied forces o vehicle Equilibrium equation system of vehicle body is r f r r f f mu + F + F + mg = 0, J - F l + F l = 0, (24) where u is vertical acceleration,  is angular acceleration in the plane xz of vehicle body. The equilibrium equations for wheels and suspension are             r1 1r 2r r1 r 2r r 2r r1 1r 2r r2 2r r 2r r2 2r 2r r k z z F m z c z u k z z k z u 0, c u z k u z F ,                         r r r r l l l l (25)             f1 1f 2f f1 f 2f f 2f f1 1f 2f f 2 2f f 2f f 2 2f 2f f k z z F , m z c z u k z z k z u 0, c u z k u z F .                              f f f f l l l l (26) where 2r is static deformation of spring with stiffness kr2 and 2f is static deformation of spring with stiffness kf2. Combining (24), (25) and (26) leads to the differential equations for vibration of the systems (4- degree of freedom vehicle) (c) Wheel sy tem, rear suspension Fig. 4. Applied forces of vehicle where u¨ is vertical ac eler i n, ϕ¨ is angul r acceleration in th plane xz of vehicle body. The equilibrium equations for wheels and suspension are kr1 (z1r − z2r) = Fr1, mr z¨2r + cr (z˙2r − u˙ + ϕ˙lr)− kr1 (z1r − z2r) + kr2 (z2r − u + ϕlr) = 0, cr (u˙− z˙2r − ϕ˙lr) + kr2 (u− z2r − ϕlr − δ2r) = Fr. (25) k f 1 ( z1 f − z2 f ) = Ff 1, m f z¨2 f + c f ( z˙2 f − u˙ + ϕ˙l f )− k f 1 (z1 f − z2 f )+ k f 2 (z2 f − u + ϕl f ) = 0, c f ( u˙− z˙2 f + ϕ˙l f ) + k f 2 ( u− z2 f + ϕl f − δ2 f ) = Ff . (26) where δ2r is static deformation of spring with stiffness kr2 and δ2 f is static deformation of spring with stiffness k f 2. Combining (24), (25) and (26) leads to the differential equations for vibration of the systems (4-degree-of-free om vehicle) mu¨+cr(u˙− z˙2r − ϕ˙lr)+c f ( u˙− z˙2 f + ϕ˙l f ) +kr2(u− z2r − ϕlr)+k f 2 ( u− z2 f + ϕl f ) =0, J ϕ¨−lrcr(u˙−z˙2r− ϕ˙lr)+l f c f ( u˙−z˙2 f+ ϕ˙l f )−lrkr2(u−z2r−ϕlr)+l f k f 2(u−z2 f+ϕl f )=0, mr z¨2r − cr (u˙− z˙2r − ϕ˙lr) + kr1 (z2r − z1r)− kr2 (u− z2r − ϕlr) = 0, m f z¨2 f − c f ( u˙− z˙2 f + ϕ˙l f ) + k f 1 ( z2 f − z1 f )− k f 2 (u− z2 f + ϕl f ) = 0, (27) where z1r, z1 f are vertical displacements of pavement plate at position of contact with the wheels and z2r, z2 f are displacements of mass mr and m f , respectively. Let (ξ1, η1) and (ξ2, η2) be coordinates of the contact points where loads Fr1 and Fr2 are applied to elements e1 and e2 of pavement plate. The global coordinate systems of the plate elements are (x1 = x01 + ξ1, y1 = y01 + η1) and (x2 = x02 + ξ2, y2 = y02 + η2). Using the representation (9) for flexural displacement we obtain z1r = [Ne1 (ξ1, η1)] {qe1} = [N (ξ1, η1)] [G]−1 {qe1} , z1 f = [Ne2 (ξ2, η2)] {qe2} = [N (ξ2, η2)] [G]−1 {qe2} , (28) Dynamic response of three dimension tunnel on elastic foundation subjected to moving vehicle loads 113 where [G]︸︷︷︸ 12×12 is matrix of geometrical properties for the elements [9]. Substituting (28) into (27), leads to the equation [Mv] {q¨v}+ [Cv] {q˙v}+ [Kv] {qv} = {Fv} , (29) where vectors of acceleration, velocity and displacement {q¨v} , {q˙v} , {qv}; matrices of mass, damping and stiffness [Mv], [Cv], [Kv] and load vector {Fv} are determined, re- spectively, as {qv} = {u ϕ z2r z2 f}T , [Mv] =  m 0 0 0 0 J 0 0 0 0 mr 0 0 0 0 m f  , (30) [Cv] =  cr + c f l f c f − lrcr −cr −c f l f c f − lrcr l2r cr + l2f c f lrcr −l f c f −cr lrcr cr 0 −c f −l f c f 0 c f  , {Fv} =  0 0 k1r [N (ξ1, η1)] [G] −1 {qe1} k1 f [N (ξ2, η2)] [G] −1 {qe2}  , (31) [Kv] =  kr2 + k f 2 l f k f 2 − lrkr2 −kr2 −k f 2 l f k f 2 − lrkr2 l2r kr2 + l2f k f 2 lrkr2 −l f k f 2 −kr2 lrkr2 kr1 + kr2 0 −k f 2 −l f k f 2 0 k f 1 + k f 2  . (32) Assuming that the plate element e1 is subjected to moving load Fr1 and element e2 subjected to moving load Ff 1, the forces can be rewritten as Fr1 = kr1 (z1r − z2r) = mr z¨2r − cr (u˙− z˙2r − ϕ˙lr)− kr2 (u− z2r − ϕlr) , Ff 1 = k f 1 ( z1 f − z2 f ) = m f z¨2 f − c f ( u˙− z˙2 f + ϕ˙l f )− k f 2 (u− z2 f + ϕl f ) . (33) By using Delta-Dirac function δ(·) [9, 11, 14] the concentrated loads (33) can be represented as the distribution force pi(ξ,η,t) as follows pr1 (ξ, η, t) = Fr1 · δ (ξ − ξ1) · δ (η − η1) , p f 1 (ξ, η, t) = Ff 1 · δ (ξ − ξ2) · δ (η − η2) . (34) Therefore, the node load vector of element becomes [9] {Fe1} = [N (ξ1, η1)]T Fr1, {Fe2} = [N (ξ2, η2)]T Ff 1. (35) Substituting (33) into (35), leads to{ Fe1 } = [ M1r ] {q¨v}+ [C1r] {q˙v}+ [K1r] {qv} ,{ Fe2 } = [ M1 f ] {q¨v}+ [C1 f ] {q˙v}+ [K1 f ] {qv} , (36) 114 Nguyen Thai Chung, Do Ngoc Tien where[ M1r ] = [ 0 0 [N (ξ1, η1)] T mr 0 ] , [ M1 f ] = [ 0 0 0 [N (ξ2, η2)] T m f ] ,[ C1r ] = [ − [N (ξ1, η1)]T cr [N (ξ1, η1)]T crlr [N (ξ1, η1)]T cr 0 ] ,[ C1 f ] = [ − [N (ξ2, η2)]T c f − [N (ξ2, η2)]T c f l f 0 [N (ξ2, η2)]T c f ] ,[ K1r ] = [ − [N (ξ1, η1)]T kr2 [N (ξ1, η1)]T kr2lr [N (ξ1, η1)]T kr2 0 ] ,[ K1 f ] = [ − [N (ξ2, η2)]T k f 2 − [N (ξ2, η2)]T k f 2l f 0 [N (ξ2, η2)]T k f 2 ] . So, the equations of motion for elements e1 and e2 get to be [Me1 ] {q¨e1}+ [Ce1 ] {q˙e1}+ [Ke1 ] {qe1} = {Fe1} , (37) [Me2 ] {q¨e2}+ [Ce2 ] {q˙e2}+ [Ke2 ] {qe2} = {Fe2} , (38) with [Mei ] , [Cei ] , [Kei ], (i = 1, 2) are matrices of mass, damping and stiffness, respectively. Introducing the node displacement vector {qe}v = { {qe1}T {qe2}T {qv}T }T , (39) composed off those of the plate elements e1, e2 and body car and combining Eqs. (36) (37), (38) with (29) allow the equations of motion for vehicle system and pavement elements to be written in the matrix form [Me]v {q¨e}v + [Ce]v {q˙e}v + [Ke]v {qe}v = {Fe}v , (40) with [Me]v = [Me1] [0] − [M1r][0] [Me2] − [M1 f ] [0] [0] [Mv]  = [Met ] + [Mep]v , [Ke]v = [Ke1] [0] − [K1r][0] [Ke2] − [K1 f ] [0] [0] [Kv]  = [Ket ] + [Kep]v , [Ce]v = [Ce1] [0] − [C1r][0] [Ce2] − [C1 f ] [0] [0] [Cv]  = [Cet ] + [Cep]v , {Fe}v =  {0}{0}{Fv}  . Assembling all elements matrices and nodal force vectors the governing equations of motions of the total system can be derived as [M] {q¨}+ [C] {q˙}+ [K] {q} = {F} , (41) with [M] =∑ e [Met ] +∑ e [ Mep ] v , [K] =∑ e [Ket ] +∑ e [ Kep ] v , [C] =∑ e [Cet ] +∑ e [ Cep ] v , {F} =∑ e {Fe}v, Dynamic response of three dimension tunnel on elastic foundation subjected to moving vehicle loads 115 This is a linear differential equation system with time dependence coefficient that can be solved by using direct integration Newmark’s method. A Matlab program named by 3D Structures Moving 2014 was conducted to solve equation (41). 3. NUMERICAL ANALYSIS 3.1. Validation of computer program To validate the present approach, consider a tunnel with square box cross section area Htun ×Wtun = 4 m×4 m, thickness of wall ttun = 0, 5 m, length Ltun = 10 m in the homogeneous foundation, depth from center of tunnel section to freely surface of foundation is htun = 4 m, subjected by concentric loading at the center point of pave- ment, load law P(t) = P0 sin 2pi f t, with P0 = 50000 N, f = 10 Hz. Tunnel is made by concrete with elastic modulus Etun = 0.34 × 107 N/cm2, Poisson ratio νtun = 0.3, mass density ρtun = 2.5 × 10−3 kg/cm3; characteristic of foundation: elastic modulus E f = 0.2 × 106 N/cm2, Poisson ratio ν f = 0.35, mass density ρ f = 1.8 × 10−3 kg/cm3. The considered region dimensions: Hs ×Ws × Ls = 20 m×40 m×10 m. The results are obtained by using 3D Structures Moving 2014 and Ansys 13.0 programs. The first three of fundamental frequency and displacement amplitude at loaded point for two methods are shown in Tab. 1. Table 1. Comparison between present results with Ansys software results Fundamental frequency Maximum displacement Characteristics f1[Hz] f2[Hz] f3[Hz] Wmax[cm] Method Ansys 13.0 36.21 98.36 142.84 0.268 Present 36.54 98.69 143.18 0.271 Different (%) 0.91 0.34 0.25 1.12 This comparison shows that the good agreements are obtained, the difference is very small (≤ 0.25% for fundamental frequency and 1.12% - for displacement). 3.2. Numerical results A concrete double tunnel with symmetric cross section, as shown in Fig. 5 is con- sidered. The tunnel is subjected to moving load of 4-wheel vehicle which moves in lon- gitudinal direction of the left tunnel with velocity v = 60 km/h. Length of tunnel L = 20 m; wall thickness t1 = t2 = W2 −W1 = 5.95 m – 4.45 m = 1.5 m; wall height H3 = 3.6 m; pavement thickness H1 = 0.4 m; tunnel width 2W1 = 9.5 m, radius of arch R1 = 6.5 m, R2 = 8.5 m, respectively. Dimension of cross section of hollow box (serape 2 single tunnels) ELH × ELW = 3 m×1.5 m. Elastic modulus of concrete Ec = 3.4×1010 N/m2; Poisson ratio νc = 0.3; mass density ρc = 2500 kg/m3. Accuracy of iteration εd = 0.5%, considered re- gion dimensions H ×W × L = 20 m × 70 m × 20 m. Three foundation layers 1, 2, 3 with properties are presented in Tab. 2. Vehicle body mass m = 7000 kg, m f = 600 kg, mr = 900 kg, inertia moment of ve- hicle body about the center-of-mass J = 30000 kgm2, distances from front wheel and 116 Nguyen Thai Chung, Do Ngoc Tien Table 2. Foundation properties Layer Depth (m) E f (N/cm2) ν f ρ f (kg/m3) 1 1.4 0.20×106 0.28 1.70×103 2 4.2 0.44×106 0.25 1.90×103 3 18.6 0.90×106 0.25 2.15×103 rear wheel are l f = 3.2 m, lr = 1.8 m, respectively, elastic spring stiffness are k f 1 = 3000000 N/m, k f 2 = 450000 N/m, kr1 = 4000000 N/m, kr2 = 700000 N/m, damping co- efficients c f = cr = 500 Ns/m. Considered points are A(−6.7, 10, 10.8) , the middle of pavement and in the foundation surface. The system model and FEM configuration are shown in Figs. 5-6. 11 Remark: Clearly, this comparison once again shows that the good agreements are obtained, the difference is very small (≤ 0,25% for fundamental frequency and 1,12% - for forced vibration). 3.2. Numerical results A concrete double tunnel with symmetric cross section, as shown in Fig 5 is considered. The tunnel is subjected to moving load of 4-wheel vehicle which moves in longitudinal direction of the left tunnel with velocity v = 60km/h. Length of tunnel L = 20m; wall thickness t1 = t2 = W2 – W1 = 5,95m – 4,45m = 1,5m; wall height H3 = 3,6m; pavement thickness H1 = 0,4m; tunnel width 2W1 = 9.5m, radius of arch R1 = 6.5m, R2 = 8.5m, respectively. Dimension of cross section of hollow box (serape 2 single tunnels) ELH×ELW = 3m×1.5m. Elastic modulus of concrete Ec = 3.4×10 10 N/m2; Poisson ratio c = 0.3; mass density c = 2500kg/m 3 . Accuracy of iteration d = 0.5%, considered region dimensions H×W×L = 20m×70m×20m. Three foundation layers 1, 2, 3 with properties are presented in Table 2. Table 2. Foundation properties Layer Depth (m) Ef(N/cm 2 ) f f(kg/m 3 ) 1 1,4 0,20106 0, 8 1,70103 2 4,2 0,44106 0, 1,90103 3 18,6 0,90106 0,25 2,15103 V hicle body mass m = 7000kg, mf = 600kg, mr = 900kg, inertia moment of vehicle body about the center-of-mass J = 30000kgm 2 , distances from front wheel and rear wheel are lf = 3.2m, lr = 1.8m, respectively, elastic spring stiffness are kf1 = 3000000N/m, kf2 = 450000N/m, kr1 = 4000000N/m, kr2 = 700000N/m, damping coefficients cf = cr = 500Ns/m. Considered points are A(-6.7,10,10.8) , the middle of pavement and in the foundation surface. The system model and FEM configuration are shown in Figs.5-6. H 2 H 3 W2 W1 H1 R1R2 ELW ELHH 4H 5 W3 1 2 3 L B LB y x z L/2 L/2 Fig. 5. Problem model Fig. 5. Model of double tunnel 12 z y x Fig. 6. Configuration of FEM. Displacement and acceleration response results of considered points are shown in Fig.7 and Fig.8. Fig.7. Vertical displacement response at A Fig.8. Vertical acceleration response at A 3.2.1. Effect of speed of load Displacement responses at the point A are shown in Fig.9 with the speed of vehicle various from 50km/h to 100km/h, variation of maximum displacement at point B are presented in Fig.10. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -0.045 -0.04 -0.035 -0.03 -0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 Time t[s] V e rt ic a l d is p la c e m e n t [c m ] 60km/h 60km/h 70km/h 80km/h 90km/h 100km/h Fig. 9.Vertical displacement response at point A Fig.10. Variation of maximum displacement at point B Fig. 6. Configuration of FEM Fig. 7 shown the relationship of displacement amplitude at point A (z-dir.) and frequency. And we have 4 first natural frequency are f1 = 19.82, f2 = 20.89, f3 = 21.93, f4 = 22.16 (Hz). Displacement and acceleration response results of considered points are shown in Figs. 8-9. Dynamic response of three dimension tunnel on elastic foundation subjected to moving vehicle loads 117 12 Fig.7 shown the relationship of displacement amplitude at point A (z-dir.) and frequency. 10 12 14 16 18 20 22 24 26 28 30 0 0.2 0.4 0.6 0.8 1 1.2 1.4 x 10 -4 Frequency f[Hz] D is p . a m p li tu d e z -d ir .[ m ] Fig.7. Vertical displacement amplitude – frequency And we have 4 first natural frequency are f1=19.82, f2=20.89, f3=21.93, f4=22.16 (Hz). Displacement and acceleration response results of considered points are shown in Fig.8 and Fig.9. Fig.8. Vertical displacement response at A Fig.9. Vertical acceleration response at A 3.2.1. Effect of speed of load Displacement responses at the point A are shown in Fig.10 with the speed of vehicle various from 50km/h to 100km/h, variation of maximum displacement at point B are presented in Fig.11. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -0.045 -0.04 -0.035 -0.03 -0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 Time t[s] V e rt ic a l d is p la c e m e n t [c m ] 60km/h 60km/h 70km/h 80km/h 90km/h 100km/h Fig.10.Vertical displacement response at point A Fig.11. Variation of maximum displacement at point B Fig. 7. Vertical displacement amplitudefrequency 12 z y x Fig. 6. Configuration of FEM. Displacement and acceleration response results of considered points are shown in Fig.7 and Fig.8. Fig.7. Vertical displacement response at A Fig.8. Vertical acceleration response at A 3.2.1. Effect of speed of load Displacement responses at the point A are shown in Fig.9 with the speed of vehicle various from 50km/h to 100km/h, variation of maximum displacement at point B are presented in Fig.10. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -0.045 -0.04 -0.035 -0.03 -0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 Time t[s] V er tic al d is pl ac em en t [ cm ] 60km/h 60km/h 70km/h 80km/h 90km/h 100km/h Fig. 9.Vertical displacement response at point A Fig.10. Variation of maximum displacement at point B Fig. 8. Vertical displacement response at A 12 z y x Fig. 6. Configurati n of FEM. Displac ment and acceleration respons results of considered points are shown in Fig.7 and Fig.8. Fig.7. Vertical displac ment response at A Fig.8. Vertic l acceleration response at A 3.2.1. Effect of speed f load Displac ment responses at the point A are show in Fig.9 wi the speed of vehicle various from 50km/h to 100km/h, variati n of maxi um displac ment at point B are presented in Fig.10. 0.2 0.4 0.6 0.8 1.2 1.4 1.6 1.8 2 -0.045 - .04 -0.035 -0.03 -0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 Time t[s] V er tic al d is pl ac em en t [ cm ] 60km/h 60km/h 70km/h 80km/h 90km/h 100km/h Fig. 9.Vertical displac ment response at point A Fig 10. Variati n of maxi um displac ment at point B Fig. 9. Vertical acceleration response at A 3.2.1. Effect of speed of load Displacement responses at the point A are shown in Fig. 10 with the speed of ve- hicle various from 50 km/h to 100 km/h, variation of maximum displacement at point B are presented in Fig. 11. 12 z y x Fig. 6. Configuration of FEM. Displacement and acceleration response results of considered points are shown in Fig.7 and Fig.8. Fig.7. Vertical displacement response at A Fig.8. Vertical acceleration response at A 3.2.1. Effect of speed of load Displacement responses at the point A are shown in Fig.9 with the speed of vehicle various from 50km/h to 100km/h, variation of maximum displacement at point B are presented in Fig.10. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -0.045 -0.04 -0.035 -0.03 -0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 Time t[s] V er tic al d is pl ac em en t [ cm ] 60km/h 60km/h 70km/h 80km/h 90km/h 100km/h Fig. 9.Vertical displacement response at point A Fig.10. Variation of maximum displacement at point B Fig. 10. Vertical displacement response at point A 12 z y x Fig. 6. Configuration of FEM. Displacement and acceleration response results of considered points are shown in Fig.7 and Fig.8. Fig.7 Vertical displacement response at A Fig.8. Vertical acceleration response at A 3.2.1. Effect of speed of load Displ cement responses at the point A are shown in Fig.9 with the speed of vehicle various from 50km/h to 100km/h, variation of maximum displacement at point B are presented in Fig.10. 0 .2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -0.045 -0.04 -0.035 -0.03 -0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 Time t[s] V er tic al d is pl ac em en t [ cm ] 60k /h 60k /h 70k /h 80k /h 90k /h 100k / Fig. 9.Vertical displacement response at point ig.10. ariation of axi u displacement at point B Fig. 11. Variation of maximum displacement at point B 118 Nguyen Thai Chung, Do Ngoc Tien 3.2.2. Effect of foundation surrounding tunnel In this section, elastic modulus E3 of third foundation layer (the foundation sur- rounds tunnel) varies from 0.2×106 N/cm2 to 2.0×106 N/cm2. Obtained dynamic re- sponses are shown in Figs. 12-13. 13 3.2.2. Effect of foundation surrounding tunnel In this section, elastic modulus E3 of third foundation layer (the foundation surrounds tunnel) varies from 0,2106N/cm2 to2,0106N/cm2. Obtained dynamic responses are shown in Figs.12-13. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 -7 -6 -5 -4 -3 -2 -1 0 1 2 x 10 -4 Time [s] V er ti ca l d is p la ce m en t [m ] 0.2e6 0.5e6 0.7e6 0.9e6 1.2e6 1.4e6 1.7e6 2.0e6 Fig.12.Vertical displacement response at point A Fig.13.Maximum displacement at point B 3.2.3. Effect of tunnel type Consider two tunnel types: box – arch section (Type 1) and box section (Type 2) with the same pavement, depth of wall and total section area. Dynamic responses of point A are as Figs. 14-15. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 x 10 -4 Time [s] V er ti ca l d is p la ce m en t [m ] Type 1 Type 2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 x 10 6 Time [s] S tr es s [N /m 2 ] Xicma x -Type 1 Xicma x -Type 2 Xicma y -Type 1 Xicma y -Type 2 Fig.14.Vertical displacement responses Fig.15. Stress responses Remark: The result shows that displacement, acceleration and stress of arc of arch tunnel are smaller than those of flat roof tunnel, and therefore load-carrying capacity of arc of arch tunnel is larger than one of flat roof tunnel. 4. EXPERIMENTAL VALIDATION 4.1. Experimental model and equipment 4.1.1. Tunnel Double tunnel, N o 05-TEDI-003-HĐ at Km7+358 Lang - Hoa Lac expressway, Hanoi, cross section is rectangular box, made by reinforced concrete. Fig. 12. Vertical displacement response at point A 13 3.2.2. Effect of fo ti s rr i t l In thi section, elasti l 3 f t ir f ti l r (the foundation surrounds tun el) varies fro 0,2106 /c 2 t , 6 / 2. t i i res onses are shown in Figs.12-13. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 -7 -6 -5 -4 -3 -2 -1 0 1 2 x 10 -4 Ti e [s] V er ti ca l d is p la ce m en t [m ] . . . . 1.7e6 2.0e6 Fig.12.Vertical dis la t r s s t i t i . . i u displacement at point B 3.2.3. Effect of tu el type Consider t o tunnel types: box – arch section ( ype 1) and box section (Type 2) with the same pavement, depth of all and total section area. yna ic responses of point are as Figs. 14-15. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 x 10 -4 Time [s] V er ti ca l d is p la ce m en t [m ] Type 1 Type 2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 x 10 6 Time [s] S tr es s [N /m 2 ] Xicma x -Type 1 Xicma x -Type 2 Xicma y -Type 1 Xicma y -Type 2 Fig.14.Vertical displacement responses Fig.15. Stress responses Remark: The result shows that displacement, acceleration and stress of arc of arch tunnel are smaller than those of flat roof tunnel, and therefore load-carrying capacity of arc of arch tunnel is larger than one of flat roof tunnel. 4. EXPERIMENTAL VALIDATION 4.1. Experimental model and equipment 4.1.1. Tunnel Double tunnel, N o 05-TEDI-003-HĐ at Km7+358 Lang - Hoa Lac expressway, Hanoi, cross section is rectangular box, made by reinforced concrete. Fig. 13. Maximum displacement at point B 3.2 3. Effect of tunnel type Consider two tunnel types: box-arch section (Type 1) and box section (Type 2) with the same pavement, depth of wall and total section area. Dynamic responses of point A are shown in Figs. 14-15. The result shows that the displacement, acceleration and stress of arc of arch tunnel are smaller than those of flat roof tunnel, and therefore load-carrying capacity of arc of arch tunnel is larger than one of flat roof tunnel. 13 3.2.2. Effect of foundation surrounding tunnel In this section, elastic modulus E3 of third foundation layer (the foundation surrounds tunnel) varies from 0,2106N/cm2 to2,0106N/cm2. Obtained dynamic responses are shown in Figs.12-13. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 -7 -6 -5 -4 -3 - -1 0 1 2 x 10 -4 Time [s] V e rt ic a l d is p la c e m e n t [m ] 0.2e6 0.5e6 0.7e6 0.9e6 1.2e6 1.4e6 1.7e6 2.0e6 Fig.12.Vertical displacement response at point A Fig.13.Maximum displacement at point B 3.2.3. Ef ect of tunnel type Consider two tunnel types: box – arch section (Type 1) and box section (Type 2) with the same pavement, depth of wall and total section area. Dynamic responses of point A are as Figs. 14-15. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 x 10 -4 Time [s] V er ti ca l d is p la ce m en t [m ] Type 1 Type 2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 x 10 6 Time [s] S tr e s s [ N /m 2 ] Xicma x -Type 1 Xicma x -Type 2 Xicma y -Type 1 Xicma y -Type 2 Fig.14.Vertical displacement responses Fig.15. Stress responses Remark: The result shows that displacement, acceleration and stress of arc of arch tunnel are smaller than those of flat roof tunnel, and therefore load-carrying capacity of arc of arch tunnel is larger than one of flat roof tunnel. 4. EXPERIMENTAL VALIDATION 4.1. Experimental model and equipment 4.1.1. Tunnel Double tunnel, N o 05-TEDI-003-HĐ at Km7+358 Lang - Hoa Lac expressway, Hanoi, cross section is rectangular box, made by reinforced concrete. Fig. 14. Vertical displacement responses 13 3.2.2. Effect of foundation surrounding tunnel In this section, elastic modulus E3 of third foundation layer (the foundation surrounds tunnel) varies from 0,2106N/cm2 to2,0106N/cm2. Obtained dynamic responses are shown in Figs.12-13. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 -7 -6 -5 -4 -3 -2 -1 0 1 2 x 10 -4 Time [s] V e rt ic a l d is p la c e m e n t [m ] 0.2e6 0.5e6 0.7e6 0.9e6 1.2e6 1.4e6 1.7e6 2.0e6 i . . ert cal i lace e t res se at point Fig.13. axi u displaceme t at point B . . . f t f t l t i r t t l t s: arch section ( ype 1) and box section (Type 2) with the same t, t f ll t t l secti n area. yna ic responses of point A are as Figs. 14- 5. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 - - . - - . - - . . x 10 -4 Ti e [s] V er ti ca l d is p la ce m en t [m ] Type 1 Type 2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 x 10 6 Time [s] S tr es s [N /m 2 ] Xicma x -Type 1 Xicma x -Type 2 Xicma y -Type 1 Xicma y -Type 2 i . . rti l is l e t responses Fig.15. Stres responses : r s lt s s t at isplace ent, acceleration and stress of arc of arch tun el are s aller t a t se f flat r f t nel, and therefore load-carrying capacity of arc of arch tunnel is larger than one of flat roof tunnel. . I I I 4.1. xperi ental odel and equip ent 4.1.1. Tunnel Double tunnel, N o 05-TEDI-003-HĐ at K 7+358 Lang - Hoa Lac expressway, Hanoi, cross section is rectangular box, made by reinforced concrete. Fig. 15. Stress responses Dynamic response of three dimension tunnel on elastic foundation subjected to moving vehicle loads 119 4. EXPERIMENTAL VALIDATION 4.1. Experimental model and equipment 4.1.1. Tunnel The experiment was carried out for the double tunnel, N◦ 05-TEDI-003-H at Km7 +358 Lang-Hoa Lac expressway, Hanoi. Its cross section is rectangular box, made by reinforced concrete, (see Fig. 16). 14 a) Experimental tunnel b) Cross section dimension Fig. 15.Configuration of experimental tunnel 4.1.2. Loading generation Loading equipment is passenger cars four wheels, conversion parameters: m = 6600kg, mf = 320kg, mr = 410kg, J = 21000kgm 2 , lf = 3,2m, lr = 1,8m, kf1 = 2400000N/m, kr1 = 3600000N/m, kf2 = 390000N/m, kr2 = 540000N/m, cf = cr = 460Ns/m. 4.1.3. Acceleration sensor, resistors plate: Acceleration sensors ARF-10A are placed on the right of pavement plate to determine vertical acceleration and at the longitudinal tunnel position; resistor plate is attached 1m from acceleration sensor position in longitudinal tunnel to determined relative deformation. Accelerometer specifications are: mass: 2g, sensitivity: 0,5mV/(m/s 2 ), the frequency ranges: 1 to 12000 (10%)Hz, peak acceleration: 10m/s2, accuracy: ≤ 0.05%. In the experimental procedure, resistors plate is attached on the pavement and is deformed according to the deformation of pavement. 4.1.3. Dynamic measurement system: a) Experimental equipment preparation b) Acceleration and deformation sensor disposition Fig.16. Experimental preparation (a) rimental tunnel 14 a) Experimental tunnel b os section dimension Fig. 15.Configuration of experimental tunnel 4.1.2. Loading generation Loading equipment is passenger cars four wheels, conversion parameters: m = 6600kg, mf = 320kg, mr = 410kg, J = 21000kgm 2 , lf = 3,2m, lr = 1,8m, kf1 = 2400000N/m, kr1 = 360000 N/m, kf2 = 390000N/m, kr2 = 540000N/m, cf = cr = 460Ns/m. 4.1.3. Acceleration sensor, resistors plate: Acceleration sensors ARF-10A are placed on the right of pavement plate to determine v rtic l accelerati n and at he longitudinal tunnel position; resistor plate is attached 1m from acceleration sensor position in longitudinal tunnel to determined relative deformation. Accelerometer specifications are: mass: 2g, sensitivity: 0,5mV/(m/s 2 ), the frequency ranges: 1 to 12000 (10%)Hz, peak acceleration: 10m/s2, accuracy: ≤ 0.05%. In the experimental procedure, resistors plate is attached on the pavement nd is deformed according to the deformation of pavement. 4.1.3. Dynamic measurement system: a) Experimental equipment preparation b) Acceleration and deformation sensor disposition Fig.16. Experimental preparation (b) Cross ection dimensio Fig. 16. Configuration of experimental tunnel 4.1.2. Loading generation Loading is excited by passenger cars of four wheels and conversion parameters: m = 6600 kg, m f = 320 kg, mr = 410 kg, J = 21000 kgm2, l f = 3.2 m, lr = 1, 8 m, k f 1 = 2400000 N/m, kr1 = 3600000 N/m, k f 2 = 390000 N/m, kr2 = 540000 N/m, c f = cr = 460 Ns/m. 4.1.3. Acceleration sensor, resistors plate Acceleration sensors ARF-10A are placed on the right of pavement plate to deter- mine vertical acceleration and at the longitudinal tunnel position; resistor plates are at- tached 1m from acc leration sens r position in longitudinal tunnel to determined relative deformation. Accelerometer specifications are: mass: 2 g, sensitivity: 0.5 V/(m/s2), the frequency ranges: 1 to 12000 (±10%) Hz, peak acceleration: 10 m/s2, accuracy: ≤ 0.05% (see Figs. 17-18). 4.1.4. Dynamic measurement system Dynamic measurement system SDA-810C (Japan), made in 2010, with: 8 chan- nels, linear frequency response: 10 kHz, electronic source: DC10.5-30V 1.4A; AC170-250V 50/60 Hz 25VA, accuracy: 0.0025%, resolution ADC: 16 bit, sampling rate: 19.2 kHz. This equipment gathers in-situ data that are stored into a computer. Consider thre ve ocity l vels of vehicle 30 km/h, 40 km/h, 50 km/h, urcharge 15 times for each velocity level (n = 15). 120 Nguyen Thai Chung, Do Ngoc Tien 14 a) Experimental tunnel b) Cross section dimension Fig. 15.Configuration of experimental tunnel 4.1.2. Loading generation Loading equipment is passenger cars four wheels, conversion parameters: m = 6600kg, mf = 320kg, mr = 410kg, J = 21000kgm 2 , lf = 3,2m, lr = 1,8m, kf1 = 2400000N/m, kr1 = 3600000N/m, kf2 = 390000N/m, kr2 = 540000N/m, cf = cr = 460Ns/m. 4.1.3. Acceleration sensor, resistors plate: Acceleration sensors ARF-10A are placed on the right of pavement plate to determine vertical acceleration and at the longitudinal tunnel position; resistor plate is attached 1m from acceleration sensor position in longitudinal tunnel to determined relative deformation. Accelerometer specifications are: mass: 2g, sensitivity: 0,5mV/(m/s 2 ), the frequency ranges: 1 to 12000 (10%)Hz, peak acceleration: 10m/s2, accuracy: ≤ 0.05%. In the experimental procedure, resistors plate is attached on the pavement and is deformed according to the deformation of pavement. 4.1.3. Dynamic measurement system: a) Experimental equipment preparation b) Acceleration and deformation sensor disposition Fig.16. Experimental preparation (a) Experimental equipment preparation a) Experimental tunnel b) Cross section dime sion Fig. 15.Configurati n of experimental tunnel . . . oading generation ading equipment is passenger cars four wheels, conversion parameters: m = 6600kg, mf = , r = 410kg, J = 21 0kgm 2 , lf = 3,2m, lr = 1,8m, kf1 = 24 000N/m, kr1 = 3600000N/m, f 0000N/m, kr2 = 54 0N/m, cf = cr = 460Ns/m. . . cceleration sensor, re istors plate: celeration sensors ARF-10A are placed on the right of pavement plate to determine ti al acceleration and a the longitudinal tunnel position; resistor plate is attached 1m from l ration sensor pos tion in longitudinal tunnel to determined relativ deformation. lero eter specifications are: mass: 2g, sensitivity: 0,5mV (m/s 2 ), the frequency ranges: 1 to (10 )Hz, peak a c leration: 10m/s2, accuracy: ≤ 0.05%. the experimental procedure, resistors plate is ttached on the paveme t an is deformed r ing to the deformation of pavement. . . ynamic measurement system: xperimental equipment prep ration b) Acceleratio and deformatio sensor disposition Fig.16. Experimental reparation (b) Acceleration and deformation sensor disposition Fig. 17. Experimental preparation 15 a) Vehicle b) Result on the screen (01 time) Fig.17. Experimental procedure Dynamic measurement system SDA-810C (Japan), made in 2010, with: 8 channels, linear frequency response: 10kHz, electronic source: DC10.5-30V 1.4A; AC170-250V 50/60Hz 25VA, accuracy: 0,0025%, resolution ADC: 16 bit, sampling rate: 19,2kHz. This equipment gathers in-situ data that are stored into a computer. Consider three velocity level of vehicle 30km/h, 40km/h, 50km/h, surcharge 15 times for each velocity level (n = 15). 4.2. Experimental results The comparison of results between theoretical calculation by 3D_Structures_Moving_2014 program and experimental method (with three velocity levels) is presented in Fig. 18 and table 3. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 Time t[s] A c c e le ra ti o n a z [m /s 2 ] Experimental Theoretical Fig. 18. Vertical acceleration responses of considered point (V = 50km/h) Table 3. Maximum acceleration of considered point Car velocity V[km/h] 30,0 40,0 50,0 Acceleration az[m/s 2 ] 3D_Structures_Moving_2014 (Theoretical) 0,1947 0,2328 0,2616 Experimental 0,1746 0,2063 0,2971 Different [%] 11,51 12,85 13,55 (a) Vehicle 15 a) Vehicle b) Result on the screen (01 time) Fig.17. Experimental procedure Dynamic measurement system SDA-810C (Japan), made in 2010, with: 8 channels, linear frequency response: 10kHz, electronic source: DC10.5-30V 1.4A; AC170-250V 50/60Hz 25VA, accuracy: 0,0025%, resolution ADC: 16 bit, sampling rate: 19,2kHz. This equipment gathers in-situ data that are stored into a computer. Consider three velocity level of vehicle 30km/h, 40km/h, 50km/h, surcharge 15 times for each velocity level (n = 15). 4.2. Experimental results The comparison of results between theoretical calculation by 3D_Structures_Moving_2014 program and experimental method (with three velocity levels) is presented in Fig. 18 and table 3. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 Time t[s] A c c e le ra ti o n a z [m /s 2 ] Experimental Theoretical Fig. 18. Vertical acceleration responses of considered point (V = 50km/h) Table 3. Maxi um acceleration of considered point Car velocity V[km/h] 30,0 40,0 50,0 Acceleration az[m/s 2 ] 3D_Structures_Moving_2014 (Theoretical) 0,1947 0,2 28 0,2616 Experimental 0,1746 0,2063 0,2971 Different [%] 11,51 12,85 13,55 (b) Result on the screen (01 ti e) Fig. 18. Experimental procedure 4.2. Experimental results The comparison of re ults between theo etical calculation by 3D Structures Mov- ing 2014 program and experimental work (wit three velocity levels) is present d in Fig. 19 and Tab. 3. Table 3. Maximum acceleration of considered point Car velocity V [km/h] 30.0 40.0 50.0 Acceleration 3D Structures Moving 2014 (Theoretical) 0.1947 0.2328 0.2616 az[m/s2] Experimental 0.1746 0.2063 0.2971 Different [%] 11.51 12.85 13.55 It is obtained that the dynamic responses measured at the considered points are more uneven than those by theoretical calculation. The maximum differences of vertical Dynamic response of three dimension tunnel on elastic foundation subjected to moving vehicle loads 121 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 Time t[s] A c c e le ra tio n a z [m /s 2 ] Experimental Theoretical Fig. 19. Vertical acceleration responses at considered point (V = 50 km/h) acceleration with three velocity levels are from 11.51% to 13.55%. This result shows that experimental results agree with calculation results. Therefore, we realize that 3D Structures Moving 2014 calculation program is reliable. 5. CONCLUSION This paper presented an algorithm of element finite method established for dy- namic analysis of tunnel and foundation in space model subjected to moving loads of vehicle. Numerical investigation has been carried out for an example with different pa- rameters and showed effects of parameters of structure and load to the dynamic response of tunnel-foundation system. The established finite element model and the computer program were tested on a real tunnel. The obtained experimental results are acceptably agreed with the numerical ones. REFERENCES [1] S. C. Mo¨ller, P. A. Vermeer, and P. G. Bonnier. A fast 3D tunnel analysis. In Second MIT Con- ference on Computational Fluid and Solid Mechanics, (2010), pp. 1–4. [2] P. G. Bonnier, S. C. Mo¨ller, and P. A. Vermeer. Bending moments and normal forces in tun- nel linings. In 5th European Conference of Numerical Methods in Geotechnical Engineering, Paris, France, (2002), pp. 515–522. [3] H. J. Kim, J. H. Park, and Y. S. Shin. Dynamic analysis of tunnel structures considering soil- structure interaction. Division of Environmental, Civil and Transportation Engineering, Ajou Uni- versity, Journal of the KOSOS, 20, (1), (2006), pp. 101–106. [4] A. Sramoon, P. Mruetusatorn, B. Lekhak, and R. Sittipod. Design of reinforced concrete lin- ings of NN2 headrace tunnel. CEAT Journal, 3, (2009), pp. 29–34. [5] M. F. M. Hussein and H. E. M. Hunt. Dynamic effect of slab discontinuity on underground moving trains. In 11th International Congress on Sound and Vibration, (2004), pp. 3045–3054. [6] C.-X. Shi, Q. Yang, and Z.-Y. Guo. Mechanical analysis on cement concrete pavement in high- way tunnel under moving load. Journal of Highway and Transportation Research and Develop- ment, 10, (2008), pp. 22–25. 122 Nguyen Thai Chung, Do Ngoc Tien [7] Q. Yang, Z.-Y. Guo, and L.-P. Chen. Stress analysis of compound pavement in road tunnel considering level loads. Journal of Highway and Transportation Research and Development, 23, (2006), pp. 16–19. [8] D. Clouteau and G. Degrande. Three-dimensional modelling of free field and structural vibration due to harmonic and transient loading in a tunnel. Katholieke Universiteit Leuven Press, (2003). [9] K. J. Bathe. Finite element procedures. Prentice Hall International, Inc Press, (1996). [10] J. N. Reddy. Mechanics of laminated composite plates and shells: theory and analysis. CRC press, (2004). [11] C. I. Bajer and B. Dyniewicz. Numerical analysis of vibrations of structures under moving inertial load. Springer-Verlag Berlin Heidelberg, (2012). [12] J. A. Hernandes and R. T. Melim. A flat shell composite element including piezoelectric ac- tuators. In Proceedings of 12th, Intrenational Conference on Composite Materials, (2000), pp. 172– 181. [13] C. Ren, C. Zhang, and L. Liu. Variable structure control on active suspension of 4 DOF vehicle model. International Journal of Information Engineering and Electronic Business, 2, (2), (2010), pp. 54–64. [14] L. Fry`ba. Vibration of solids and structures under moving loads. Thomas Telford, (1999).