Study on Force Characteristics of Buried Pipeline Under Impact Load Caused by Bridge Pile Foundation Construction

Transcription

1 American Journal of Mechanics and Alications 018; 6(): 6-67 htt:// doi: /j.ajma ISSN: (Print); ISSN: (Online) Study on Force Characteristics of Buried Pieline Under Imact Load Caused by Bridge Pile Foundation Construction She Yanhua School of Urban Construction, Yangtze University, Jingzhou, China address: To cite this article: She Yanhua. Study on Force Characteristics of Buried Pieline Under Imact Load Caused by Bridge Pile Foundation Construction. American Journal of Mechanics and Alications. Vol. 6, No., 018, doi: /j.ajma eceived: August 8, 018; Acceted: Setember 18, 018; Published: October 18, 018 Abstract: In the ile foundation construction of highway bridge, the imact hammer falls from a certain height, which roduces a great imact when it collides with soil. In order to gain a clear idea of force characteristics of buried ieline under imact load caused by bridge ile foundation construction, the effect of construction imacting load on buried ieline is analyzed theoretically. Firstly, taking advantage of Boussinesq solution and Mindlin solution, the distribution of additional load on the surface of ieline under imact load is analyzed, and the transmission and diffusion of imact force in soil are calculated by elastic half-sace theory. Secondly, the mechanical models of buried ieline under surface imacting and ile hole imacting are established resectively. Combined with Boussinesq equation, Mindlin calculation and infinite beam elastic foundation model, the calculation formula of buried ieline under imact load is obtained. Finally, according to the formula established above, an examle is given to calculate the additional bending moments and axial tension and comression stresses of buried ieline caused by bridge ile foundation construction, so as to estimate the effect of construction imacting load on buried ieline. The research results rovide some guidance for the stress analysis of buried ielines under such construction conditions. Keywords: Buried Pieline, Imacting Load, Pile Foundation Construction, Calculation Formula 1. Introduction In highway construction, scholars ut extra emhasis on the dynamic loads of buried ielines, such as the ramming loads [1], rolling stone imact loads [, 3], traffic loads [4, 5], blasting vibration loads [6, 7], which have been carried out on the effect of buried ielines and many achievements have been made. However, the effect of imact load caused by bridge unching ile construction on adjacent buried ielines is seldom studied, while it is very imortant to understand the influence of this kind of imact load ut on the buried ieline in ractical engineering. Therefore, the force characteristics of buried ieline under imact load caused by bridge ile foundation construction are studied. In the bridge ile foundation unching construction, the hammer will fall from a certain height. When colliding with soil mass, the larger imact is roduced. The influence of imact load on buried ieline is through the transfer of soil around the ie and the interaction between ie and soil, and finally acts on the ieline in the form of soil ressure. In the analysis of mechanical roerties of buried ieline, it is assumed that the ie is an infinitely long structure, only considering the joint action of the imact load and the soil ressure around the ie, and ignoring the influence of internal ressure, construction defects, chemical corrosion, temerature changes and other ancillary structures on the buried ieline.. Surface Additional Load Distribution of Buried Pieline The imact load has a strong instantaneous imacting force on the soil around the ieline, resulting in additional loads on the ieline. In the analysis of the additional load distribution on the ie surface, the elastic half sace theory is used to calculate the imacting force transmission and

2 American Journal of Mechanics and Alications 018; 6(): diffusion in the soil. Assuming that the soil is the uniform linear elastic infinite body, when a vertical concentrated force is acted on the surface of an elastic half sace, the elastic solution of the stress and dislacement caused by any oint in the elastic half sace is made by Boussinesq. As shown in Figure 1, the various stress comonents at any oint in the half sace are as follows[8, 9]: τ xy 3 3P z 3P 3 σz = cos θ 5 π = π (3) ( + ) ( + ) 3P xyz 1 ν xy z = τyx = 5 3 π 3 z (4) 3P yz 3Py τ yz = τzy = cos θ 5 3 π = π (5) 3P xz 3Px τzx = τxz = cos θ 5 3 π = π (6) In the above formula: Distance from ointm to oint O, = x + y + z = r + z = z cosθ, Figure 1. Force schematic diagram of arbitrary oint in the elastic semi-sace. 3P x z 1 ν z z x σx = + π 3 ( + z) + z ( + z) ( ) P y z 1 ν z z y σ y = + π 3 ( + z) + z ( + z) ( ) (1) () r The horizontal distance between the oint M and the oint of concentrated force acting, θ The angle between the line and the axis of the z coordinate, E Elastic modulus of foundation, v Poisson ratio of foundation. When the load of the surface action is distributed load, the Boussinesq solution can be used to calculate the stress and dislacement of the distribution load on the arbitrary oint in the elastic half sace by the integral of the load distribution surface. Assuming a rectangular uniform load on the foundation, the coordinates of the load center are ( x, y, z ) and the border length are resectivelyland b. Figure. Schematic diagram of ie force analysis.

3 64 She Yanhua: Study on Force Characteristics of Buried Pieline Under Imact Load Caused by Bridge Pile Foundation Construction As shown in Figure, the direction of the ie length is x axis, the direction of the width is y axis, and the vertical direction is z axis (vertical downward direction is ositive). The left end oint of the ie calculation section is the coordinate origin, and the coordinates of any oint on the ie are ( M,0,0 ). Then according to the above formula and coordinate transformation, the exression of vertical and horizontal additional loads on the surface ieline can be obtained as follows: q z 3z 3 y + 0.5b x + 0.5l π y 0.5b x 0.5l dxdy 5 = (7) q y y + 0.5b x + 0.5l y z z y + z ν 3 π z ( ) y 0.5b x 0.5l z ( ) = + (1 )[ ] dxdz In the formula (7) and (8), = ( x M) + y + z (8) The dislacements and stresses caused by horizontal concentrated forces acting on the interior of a semi-infinite body are roosed by Mindlin. The calculation model is shown in Figure 3. The horizontal stress exression at any oint in the half-sace caused by the force P along the x-axis (arallel to the half-sace surface) is as follows[10]: Px 1 µ (1 µ )(5 4 µ ) 3x 3(3 4 µ ) x 4(1 µ )(1 µ ) σx = ( + 8 π (1 µ ) ( + z + h) (3 + + ) 6 5 h µ z h ( + + ) x z h h x z (3 ) + (3 (3 )( + ) + )) z h (9) In the formula (9), µ Poisson's ratio for soil medium, the meaning of other symbols is shown in Figure 3. Figure 4. Mechanical analysis model of ieline under imact loads. The force of the imact on the ieline can be calculated by the Boussinesq equation as follows[11]: 3. Surface Imact Figure 3. Calculation Model of Mindlin. Under the imact of hammer droing, besides the imact on the surface, the stress on the ieline is also the self weight stress of the uer soil, as shown in Figure 4. P 3F = L πh [1 + ( ) ] H.5 In the formula (10): P The load imacted on the ie, (10) F Imact load on the surface, H Overlying layer thickness above ie, L Horizontal distance between imact load oint and the ieline. The force acted on the ie is: P = f P + P (11) s v In the formula (11): P the earth ressure above buried ieline, v

4 American Journal of Mechanics and Alications 018; 6(): f enetration coefficient associated with the ie buried deth[11], as shown in Table1. Table 1. Penetration coefficient ( f ) versus buried deth. buried deth (m) 0~ ~ ~0.9 >0.9 f Imacting in Pile Hole 4.1. Calculation of Soil Pressure Acting on Buried Pie Punching ile construction has great disturbance to strata. With the excavation of the ile hole, the hammer imacting on the soil causes the extrusion ressure around the ile hole wall. This horizontal extrusion ressure can be regarded as an internal force acting on a semi infinite body arallel to the x axis, and the two dimensional calculation model is shown in Figure 5. 6r E P = (14) 1 + u The P value is relaced into the formula (9), and the calculation arameters in formula (9) are as follows: =, = ( L D / ) + 4H, z = H, 1 L D 1 / 1 x = L D 1 /. Then the maximum horizontal earth ressure σmax acting on buried ielines can be obtained. 4.. Pieline Stress Calculation The soil ressure on the buried ieline caused by the unching construction makes the ie stress reach the maximum at the intersection oint of the x and y axis, and with this oint as the center, the ie stress gradually decreases until zero. The ie is extruded and bent under the action of active ressure and roduces tensile and comressive stresses along the axial direction. To determine the magnitude of this stress, it should first determine the buried ieline stress. Suose that under the action P( y ), the reaction force on the buried ieline is q( y ) and the friction between the uer and lower sides of the ieline is f, as shown in Figure 6. Figure 5. Model of unching construction effect on the ieline. It is assumed that the hammer imacting rocess is the rocess of ushing the soil of the same size into the soil layer without drainage. This causes large stress increment around the ile hole wall and it can be analyzed by the small hole exansion theory. The elastic theory and Mohr-Coulomb failure criterion are used to analyze the following results[1]: P = C (1) x In the formula (1), C u the soil undrained strength. The radius of lastic zone around the ile hole wall caused by hammer imacting is: = r In the formula (13): E soil elastic modulus, µ soil Poisson ratio, u E (1 + µ ) C u (13) r The exansion hole radius, taken by the hammer radius. In order to use the above Mindlin calculation model, P x is converted into an equivalent concentrated force (considering 3 times the radius of lastic range ), there is: Figure 6. Force analysis model of ieline. Because the size of buried ieline in the y axis is much larger than that in the x axis, it can be regarded as an infinite beam. If the deformation of the ieline along the y direction is w( x, y ), then there is: 4 d w( x, y) = D( P( y) f q( y)) (15) 4 dy In the formula (15): E Elasticity modulus of ie material, I The moment of inertia of the ie section, π 4 4 I = ( D d ), 64 D The outer diameter, d inner diameter of the ie. Since the distribution of P( y) is about X axisymmetric, it can be assumed to cosine function. If the force acting on the origin is P 0 andais the length unit, then there is:

5 66 She Yanhua: Study on Force Characteristics of Buried Pieline Under Imact Load Caused by Bridge Pile Foundation Construction 0 P 1 P( y) = sin( md / a)cos( my / a) dm (16) π m 0 The formula (16) is substituted (6) to get the bending moment of any section of the ieline, then ( P0 f ) π m 0 d w( x, y) sin( md / a)cos( my / a) M( y) = = ma dm dy + Ω (17) In the formula(17), Ω dimensionless quantity, determined by different foundation models. ka D For the Winkler foundation, Ω =, a D For the Pasternak foundation, Ω = ( m GP + ka ), For the homogeneous isotroic foundation, 3 Esma D Ω =. (1 ν) For simle calculation, the active ressure acting on the buried ieline is equivalent to the concentrated forceq at the origin of coordinates. Then the bending moment of the buried ieline can be obtained as follows[13]: For the Winkler Foundation: Q f β y M( y) = e (cos β y sin β y) (18) 4β In the above formula, β a comrehensive arameter related to the elastic roerties of ie and foundation, kd β = 4. 4 Then the maximum bending moment of the ie section is M max For the two arameter model, there is: M max * In the formula(0), 3 I(1 ν L = ), D 4 Q f = (19) 4β * ( Q f ) L = (0) 4α * 4 S + r Dk( L ) DGP( L ) α =, S =, r =. For homogeneous isotroic foundation model: M = 0.166( Q f ) D 16(1 ν) max 4 EsD * 0.77 (1) When Mmax is known, the tensile and comressive stresses on buried ieline caused by unching ile construction can be calculated as follows: 5. Examle Analysis Mmax 3DMmax σx = = 4 4 W π( D d ) () Taking the imact drilling construction of bridge ile foundation of ong-wu exressway crossing Shaanxi- Beijing gas ieline located Laiyuan as an examle, the ieline stress is analyzed. The diameter of unching hammer is 1.6m, the diameter of ile hole is m, and the horizontal distance between unching osition and ie center is 6m. The buried ieline is a X60 grade steel ie with the buried deth of 3m, outer diameter of 66cm, wall thickness of 8.7mm, and the modulus of 10GPa. The soil layer around the buried ieline is sandy cobble soil, with deformation modulus of 10MPa and Poisson's ratio of According to the above method, the influence of the construction of the unching ile on the buried ieline is estimated. The additional bending moment and the additional axial tension and ressure stress of the buried ieline caused by unching ile construction are calculated as follows: For the Winkler model: M max = 4.63kN m, σ = 1.6MPa. For the double arameter model: M max = 4.4kN m, σ = 1.55MPa. For the homogeneous and isotroic elastic model: M max = 4.1kN m, σ = 1.47MPa. From the above calculation results, it can be seen that the imact of unching ile construction on ieline is not obvious for the steel buried ieline with large tensile stress. 6. Conclusion In this aer, the effect of imacting load caused by bridge ile foundation construction on buried ieline is analyzed theoretically. The distribution of additional load on the surface of ieline under imact load is exounded. Based on the Boussinesq equation, the stress exression of buried ieline under the imact load of the ground surface is established. Based on the Mindlin calculation model and the model of the infinite beam elastic foundation, the calculation formula of the force of the buried ieline under the imact load of the ile hole is established. And the influence of unching ile construction on buried ieline is analyzed by taking a ractical roject as an examle. The research results can be helful for force theoretical analysis of buried ielines. Acknowledgements This work is financially suorted by National Natural Science Foundation of China ( NSFC, ) & Youth Talent Project of Yangtze University (015cqr06).

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