Fundamentals The explosion process in a natural gas pipe is a flow process of shock waves with high temperature and pressure in restricted space. To simplify the calculation, the following assumptions were made: 1 Gravity effect and delivery pressure of pipe are not considered 2 The pipe is ideal elastic-plastic, regardless of the joint between pipe sections 3 The soil and pavements are uniformly continuous and isotropic 4 The pavement surface is a free surface, and the other directions of soil and pavement extend indefinitely 5 The contact surface between the pipe and the soil is smooth, and the soil is closely connected with the pavement 6 The initial ambient temperature is the normal temperature, and explosive is the only heat source in the model 7 The intermediate process of chemical reactions in the gas explosion is not considered 8 The release center of the explosive energy is at the origin of the coordinates The destructive effects of a natural gas explosion on the environments are caused by energy exchange.

Equivalent of Gas Leakage 2. Model of Gas Leakage There are two types of gas pipe leakage: orifice leakage and fracture leakage, and the possibility of orifice leakage is greater than that of fracture leakage [ 8 ]. Calculation for TNT Equivalent The destructive effect of vapor cloud explosion is usually determined by the energy it releases. Numerical Scheme In this study, a numerical model was firstly established based on the pipe explosion experiment, and the PE pipe material model and modeling method used in this study were verified.

Figure 1. Figure 2. Table 1. Table 2. Table 3. Table 4. Figure 3. Figure 4. Stress distribution of PE pipe in the verification model. Table 5. Figure 5. Grid independence and time independence verification diagram. Grid number Fracture width m 0. Table 6. Variation of fracture width with grid number and time step. Figure 6. Propagation process of explosive shock waves. Figure 7. Figure 8. Figure 9. Figure Total energy curves of pavements under different TNT equivalents.

Dynamic response curves of pavements under different TNT equivalents. Displacement and strain distribution of pavements. The maximum pressure and effective stress of pipes under different buried depths. Relationship between buried depth and deformation of pavement. References A. Liu, J. Huang, Z. Li et al. Zhao, L. Xihong, and L.

Ebrahimi-Moghadam, M. Farzaneh-Gord, A. Arabkoohsar, and A. Moloudi and J. Cheng, M. Wu, L. Zhao, and M. View at: Google Scholar L.

Xinhong, C. Guoming, Z. Renren, Z. Hongwei, and F. Mirzaei, M. Najafi, and H. Zheng, B. Zhang, and P. Xu, A. Yao, H. Jiang, Y. Li, and X. Li and B. View at: Google Scholar X. Liu, H. Zhang, M. Xia et al. Cui, S. Shao, and X. Zhang, L. Zhang, and Z. View at: Google Scholar M. Mokhtari and A. Wang, C. Liao, J. Wang, and D.

Bang, H. Park, J. Kim, S. Al-Deyab, A. Yarin, and S. Carbone, E. Pastor, R. Bubbico, and J. Zhian, L. Zhigang, C. Shengguo, Z. Yansong, and Z. Ye, G. Wang, Z. Jia, and C. Cirimello, J. Otegui, and L. Wang, T. Shi, Y. He, M. Li, R. Si, K. Gao, X. Qin, and L. Nie, X. He, R. Zhang, W. Chen, and J. Guo, C. Liu, D.

Wen, A. Yao, and T. View at: Google Scholar Y. Du, F. Zhou, L. Ma, J. Zheng, C. Xu, and G. Russo and F. Wang, X. Qian, M. It is described by a power function 21 , and is presented in Fig. Fracture surface — straight front of the notch. Fracture surface — slant front of the notch. A comparison of the two R-curves shows that the decline of the R-curve obtained with the curved CT specimens is less than the decline of the R-curve obtained with plane, i.

The higher decline of the R-curve with the straightened CT specimens is most probably connected with work hardening of a semiproduct during straightening. In the mathematical description of the R-curve of the curved CT specimens, not only the exponent but also the constant is less than for the standard R-curve.

This means that the standard R-curve is situated above the R-curve of the curved CT specimens. However, the lower position of the R- curve for the curved CT specimens does not mean significantly lower magnitudes of the fracture toughness characteristics.

For example, the J m value is lower by 1. In absolute units, the difference is 2. There is a significant difference in J in , namely R-curve for curved CT specimens.

The test CT specimens were manufactured from a real pipe section cut out from a DN gas pipeline 4. Before the CT specimens were manufactured, the pipe section was press straightened. Owing to the small thickness of the specimens a low constraint , the fracture toughness values cannot be qualified to represent the real fracture toughness values.

However, they can be used as a comparative measure of fracture toughness, thus enabling quantification of the effect of stress corrosion cracks on the apparent fracture toughness. A constant force F of 3 kN was applied to the specimens. The corresponding level of the nominal stress tension and bending at the fatigue crack tip exceeded the yield stress R p0. In total, three groups of CT specimens were prepared. The first group A was the reference group; the specimens from this group contained only the fatigue crack.

The second group of CT specimens B contained specimens that were left freely in air at the indoor temperature for two weeks after being removed from the SC crack generator, and were then subjected to fracture toughness tests.

The specimens from the third group C were tested immediately after they had been removed from the SC crack generator the time difference between testing the first specimen and the last specimen being approximately 20 minutes. The results confirmed that the fracture resistance of a component given by the apparent fracture toughness depends not only on the material of the component and on the crack tip constraint the thickness of the wall of the component but also on the origin of the crack fatigue, stress corrosion , and thus on the corresponding crack growth mechanism.

In contradiction with the opinion that low-C steels are not susceptible to stress corrosion cracking our results showed that under conditions specified in NACE Standard TM, stress corrosion cracks can also be generated from fatigue cracks in low-C steels such as CSN The results for all three groups of specimens are summarized in Fig.

A bar chart of the J integral values for specimens of groups A, B and C. As this figure shows, the stress corrosion fracture toughness characteristics for the low-C steel CSN were lower than the fatigue fracture toughness characteristics by a factor ranging between 4.

It follows from here that in evaluating the reliability of gas pipelines it is always necessary to examine the character of the cracks in the pipe wall, and in the case of stress corrosion cracks to take into account that the fracture toughness can be drastically lower than the values determined on specimens with cracks of fatigue origin.

An experimental verification of the fracture conditions of gas pipelines can be made most accurately on a test pipe body cut out of the gas pipeline to be examined. When deciding on the length of the test pipe body, we should bear in mind that the working length of the body characterized by the absence of stress effects from welded-on bottoms will be shorter by 2 x 2.

It is usually sufficient for the distance between the welds of dished bottoms to be at least 3. This length permits a number of starting cuts to be placed axially along the length of the body.

The cuts are made to initiate crack growth when the body is subsequently pressurized by a fluctuating pressure. The cuts can be made in several ways, one of which uses a thin grinding wheel. The smallest real functional thickness of such a wheel is about 1. Depending on the type of pipes of which gas pipelines are built seamless, spirally welded, longitudinally welded , the starting cuts can be provided in the base material, in the transition region or in the weld metal, their orientation being axial, circumferential or along the spiral weld.

It is appropriate to relate the surface length of the cuts to the wall thickness of the pipe body. Testing the body for the danger posed by so-called long cracks should be carried out with crack lengths not exceeding twenty times the wall thickness of the pipe body.

The situation with the depth of the starting cuts is different. The depth of an initiated fatigue crack must be at least 0. Substitution of a notch with a crack by the equivalent crack. As described in paragraph 3. These check slits functioned as a safety measure to prevent cracks that developed at the working slits from penetrating through the pipe wall.

For illustration, a DN test pipe body with a working length of 3. The check slits are denoted in Fig. The material of the test pipe body is a thermo-mechanically treated steel X70 according to API specification.

It is provided with starting cuts oriented either axially or in the direction of the strip axis i. We are particularly interested in axial longitudinal slits situated aside welds, because these are sites where axial cracks will be formed in the basic material of the pipe.

Efforts were made in the fracture tests to keep the circumferential fracture stress below the yield stress, because the operating stress in gas pipelines is virtually around one half of the yield stress and does not exceed two-thirds of the yield stress even in intrastate high-pressure gas transmission pipelines. Calculations reveal that in order to comply with this, the depth of the axial semi-elliptical cracks should be greater than one half of the wall thickness. Oblique cracks should be even deeper, as the normal stress component opening these cracks is smaller.

If the crack depth is to have a certain magnitude before the fracture test is begun, the depth of the starting slit should be smaller than this magnitude by the fatigue extension of the crack along the perimeter of the slit tip. At the same time, we should bear in mind that the greater the fatigue extension of the crack, the better the agreement with a real crack.

Test pipe body with the starting cuts marked. After the starting slits were made, the test pipes were subjected to water pressure cycling to produce fatigue cracks in the tips of the starting slits.

The cycling was carried out in a pressurizing system, which included a high-pressure water pump, a collecting tank, a regulator designed to control the amount of water that was supplied and, consequently, the rate at which the pressure is increased in the pipe section. This was effected by opening by-pass valves. The period of a cycle was approximately seconds. The cycling continued until a crack initiated in one of the check slits became a through crack.

This moment was easy to detect, because it was accompanied by a water leak. To run a test for a fracture, however, it was necessary to remove the check slit which had penetrated through the wall of the test pipe from the body shell and to repair the shell, e. After removing the check slit with a crack which penetrated through the wall, and repairing the shell of the test pipe, the pipe was loaded by increasing the water pressure to burst.

The test procedure, which was common for all test pipes, will now be briefly described for the DN pipe shown in Fig. The burst of the test pipe at crack B is shown in Figs. A part of the fracture surface is shown in Fig. Burst initiated on slit B with a fatigue crack. Burst initiated on slit B — a detail. Evidently, at the instant of fracture the crack spread not only through the remaining ligament, but also lengthwise.

After removing the part of the pipe shell with crack B, a patch was welded in and the second burst test followed. It should be noted that Table 2 includes the Ramberg-Osgood constants for the circumferential direction of the test pipe, with the crack oriented axially in the pipe. This is because the stress-strain properties perpendicular to the crack plane are crucial in determining the J-integral for an axial crack.

The stress-strain dependence in the circumferential direction should therefore be taken into account where an axial orientation of the crack is concerned. The most important fracture test results from the viewpoint of the fracture conditions are the magnitudes of the fracture pressure, p f , and the fracture depth, a f , for a given crack length 2c. These values are also shown in the last two columns of Table 1. Now let us predict the fracture conditions according to engineering approaches, and compare the prediction results with the real fracture parameter values pressure, crack depth.

The procedure for verifying the engineering methods for the predictions involves determining either the fracture stress for a given fracture crack depth, or the fracture crack depth for a given fracture pressure.

To illustrate this, we select the latter case — i. As is evident from Fig. They are illustrated in Fig. A specific fracture-mechanics-based procedure for assessing the integrity of pressurized thin-walled cylindrical shells made from steels includes a theoretical treatment for cracks in pipes.

On the basis of both experimental work and a fracture-mechanical evaluation of experimental results, an engineering method has been worked out for assessing the geometrical parameters of critical axial crack-like defects in a high-pressure gas pipeline wall for a given internal pressure of a gas.

The method makes use of simple approximate expressions for determining fracture parameters K, J, and it accommodates the crack tip constraint effects by means of the so-called plastic constraint factor on yielding. One is a gas supply. An electric heater will only have two plumbing pipes but it will have an electical conduit or electrical wire feed line.

You might be thinking of a stress fracture; a fracture of a bone caused by repeated rather than sudden mechanical stress. You treat the simple fracture with immobilization, in most of the cases. This is done usually with the help of plaster of Paris and bandage.

It depends on where it is dripping. The spinning cycle of the machine might be causing the pipes to loosen up.

You might want to check out the pipes if they are loose. Log in. Study now. See Answer. Best Answer. Study guides. Q: If gas pipes fracture there might be? Write your answer Related questions. If gas pipes fracture what might there be? What happens if gas pipes fracture?

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