Abstract:
The present invention provides a new method for designing a multi layered pipe highly resilient to longitudinal bending, wherein the layer pipe includes an inner pipe, an outer pipe, and a separating layer. According to one embodiment the method includes the following of: determining the preferred ratio between inner and outer pipe radiuses, evaluating the external pressure developed by the surrounding soil in accordance with simplified linear model, calculating preferred stiffness and elastic for the separating material according to evaluated external pressure soil properties and determining the preferred composition of separating material according to calculated radiuses and calculated stiffness and elastic.

Description:
FIELD OF INVENTION 
       [0001]    The invention relates to co-centric multilayer pipes comprising one or more inner pipes surrounded by a middle layer of a softer material, and an outer pipe enclosing said middle layer. 
       BACKGROUND OF INVENTION 
       [0002]    Pipelines are important lifelines of modern civilization, allowing the continuous supply of water, gas and oil. The failure of a pipeline due to ground displacements may cause economical and environmental damages. These displacements may result due to variety of reasons: heave, earthquake, landslides, seasonal water content changes, near by construction, water leaks, liquefactions etc. 
         [0003]    Ground displacements might occur for various reasons. Local ground displacements occur due to ground liquefactions or landslides. When saturated sand is subjected to ground vibrations, it tends to compact and decrease in volume; if drainage is unable to occur, the tendency to decrease in volume results in an increase in pore water pressure, and if the pore water pressure builds up to the point of which it is equal to the overburden pressure, the effective stress becomes zero, the sand loses its strength completely, and it develops a liquefied state. One approach for reducing the risk associated with liquefactions or landslides events is by rerouting of pipelines around the problem during early repairs. Another approach aimed for reducing said risks is by increasing the seismic performance by soil improvement. Such related methods includes the densification of otherwise loose soil, the drainage and dissipation of excess pore water pressure, the confinement and limit lateral flow of the soil, and the physical or chemical modification of the soil to increase its strength. 
         [0004]    Another type of ground displacement is the faulting. Seismic activity occurring at the boundaries of two or more tectonic plates resulting from their general motion may cause stress to accumulate on faults and lead to rapid energy release and earthquakes. One approach, aimed for reducing such mitigating fault rapture risks, is by orienting pipelines in a specific direction relative to the fault. Pipeline is then placed at the position relative to the fault direction such that its movement would result in minimum straining of the pipe. 
         [0005]    Another approach for reducing said risks concentrates on the pipe itself, rather than on modification of the soil around it or the direction of its loading. Such methods use high strength and high ductility materials in conjunction with flexible joints. An isolated multi-layered pipe can serve as a good example. 
         [0006]    A good example for an isolated pipe is the co-extruded multilayer plastic pipe. It is an isolated pipe comprising one thin-walled inner pipe and an outer pipe and between them middle layer of a softer material than the inner pipe. It can be used, for example, as underground drain pipes, pressure pipes and cable ducts. These types of pipes are more complicated to manufacture than conventional single-layer pipes, but may have better mechanical properties. U.S. Pat. No. 6,176,269, incorporated by reference herein, describes such pipes. 
         [0007]    One known problem with isolated pipes is their limited longitudinal flexure capacity. Ground displacements may cause extreme pressure on certain areas along these pipes, thereby risking the inner pipe continuity. There is a demand for isolated pipes with a proper longitudinal flexibility to be able to safely keep continuity of inner pipe under such external stress. 
       SUMMARY OF INVENTION 
       [0008]    The object of the present invention is to provide a co-extruded multi-layer pipe reducing the longitudinal flexure (longitudinal bending) risk to pipeline due to ground displacement, thereby supplying a more efficient protection to the inner pipe than in prior art solutions. The present invention does not deal with any axial or cross sectional mechanical properties of the pipe. 
         [0009]    A further object of the present invention is to provide a co-extruded multilayer pipe which has better mechanical properties, than those of the corresponding known pipes. 
         [0010]    According to the invention, the essential part that carries the fluids (e.g. gas, oil, water) is the inner pipe hence its integrity is of importance. This part is protected by softer outer layers, i.e. layers which are more easily deformed, whereby the adhesive forces between the interfaces of all the layers are as small as possible and adjustable. The inner pipe thus remains circular and undamaged even if the outer pipe becomes oval as a result of compression or even breaks as a result of longitudinal pressure. The outer pipe exists to allow sufficient support for the soil under static conditions, and its integrity in the event of an earthquake is not important (i.e. cracks may develop in it). In essence, the outer pipe should have sufficient cross sectionals stiffness to prevent soil collapse, but no special requirement for longitudinal bending or axial stiffness. The separating material properties are function of the ratio of diameters of inner and outer pipe, and the properties of the soil surrounding the pipe. 
         [0011]    According to one embodiment, the separating layer may be composed of inhomogeneous or anisotropic matter or contain multiple zones, relatively small that are filled with void. The nature of the separating material should be instantiated by the mechanical demands of the location, such as the soil type and geological conditions. 
     
     
       BRIEF DESCRIPTION OF DRAWINGS 
         [0012]      FIG. 1  is a longitudinal sectional view of a multilayer plastic pipe of the invention comprising one inner pipe 
           [0013]      FIG. 2  is a longitudinal sectional scheme of a mechanical equivalent system. 
       
    
    
     DETAILED DESCRIPTION 
       [0014]      FIG. 1  illustrates the pipe principle components. The pipe comprises an inner pipe ( 1 ), an outer pipe ( 2 ), and a separating layer ( 3 ) of relatively softer matter. According to the present invention the separating layer can be composed any of inhomogeneous or anisotropic matter. For example, separating layer may consist of small void volumes ( 4 ). 
         [0015]    Choosing the proper combination of materials composing the separating layer could be a complicated task. The separating layer must be able to support the longitudinal pressure developed along the pipe, in order to protect its continuity. The magnitude of the pressure is constituted by the nature of the soil and its potential displacements. The separating layer should be able to absorb part of this pressure and allow flexible movements of both inner and outer layers. The materials composing this layer must have the proper physical stiffness and elastic properties, enabling said functionality. These properties can be defined by the Young&#39;s modulus. Young&#39;s modulus is the measure of stiffness for a given material measured in N/m 2 . It can be defined as the ration of stress to corresponding strain. This rate can be experimentally determined from the gradient of a stress-strain curve created during tensile tests conducted on a sample of said material. 
         [0016]    The pressure magnitude developed on the outer pipe due to ground displacements can be estimated using a simplyfing model describing a system of springs. With this model, the complex soil pressure is reffered to as an equivalent discrete set of springs, connecting between the outer pipe, inner pipe and external static points. A known and relativly simple solution for the linear force generated by a spring enables the development of a set of equations solving the original, more complex problem. Furthemore, external soil pressure is also reflected by the separating layer. A model of equivalent springs can be used to evaluate the pressure magnitude derived from the more complex system, thereby enabling to obtain the proper Young&#39;s modulus needed for the seperating layer, for a given external pressure. 
         [0017]    The external pressure developed by the surrounding soil can be estimated using simplifying linear models. One commmon model is using the linear subgrade coefficient, where an ampirical evaluation of the soil propery is obtained. A coefficient of subgrade reaction is determined by the measuring of the California Bearing Ratio (CBR) test, which is a simple penetration test for evaluation of the mechanical strength of road subgrades. Another common model is using the linear Young&#39;s module evaluation, previously discussed. 
         [0018]      FIG. 2  illustrates the mechanical properties of the pipe wherein the bending forces developed by the separating material are equivalent to said system of springs ( 5 ) connected between inner ( 1 ) and outer ( 2 ) pipes and the bending forces developed by the soil on the outer pipe ( 2 ) are equivalent to a system of springs ( 6 ) connected between the outer pipe and static points. 
         [0019]    The separating material properties are instantiated by the ratio of diameters of both inner and outer pipe, and the properties of the soil surrounding the pipe. A condition is set on the representative Young&#39;s modulus, E Y   R  for the separating material which may be calculated as: 
         [0000]    
       
         
           
             
               E 
               Y 
               R 
             
             = 
             
               
                 
                   ∫ 
                   V 
                 
                  
                 
                   
                     E 
                     Y 
                   
                    
                   
                      
                     v 
                   
                 
               
               = 
               
                 
                   ∫ 
                   0 
                   
                     2 
                      
                     π 
                   
                 
                  
                 
                   
                      
                     θ 
                   
                    
                   
                     
                       ∫ 
                       
                         r 
                         i 
                       
                       
                         r 
                         o 
                       
                     
                      
                     
                       r 
                        
                       
                          
                         r 
                       
                        
                       
                         
                           ∫ 
                           0 
                           
                             L 
                             p 
                           
                         
                          
                         
                           
                              
                             x 
                           
                           · 
                           
                             E 
                             Y 
                           
                         
                       
                     
                   
                 
               
             
           
         
       
     
         [0000]    where E Y  is the distribution of Young&#39;s modulus (Young&#39;s modulus per volume unit) of the different materials composing the separating materials (e.g. if voids are involved than EY takes the value of zero for them), r i  and r o  are the radiuses of the inner and outer pipe respectively, and L p  is any section of the pipeline with minimum length of two meters. The demand for a maximum value of E Y   R  is a function of the surrounding soil properties and the ratio of inner to outer pipe radiuses. The following example demonstrates the calculation of the equivalent Young&#39;s modulus for two different materials: 
         [0020]    In our example, the radius of the inner pipe is 5 cm and the outer radius is 10 cm. The separating layer composed of two different materials: The first one has the Young&#39;s modulus value of E Y =3000 kN/m 2  per volume unit (Polystyrene) and it fills part of the volume: from r=5 cm to r=6 cm. The second material has the Young&#39;s modulus value of E Y =2000 kN/m 2  per volume unit (Polyethylene terephthalate) and it fills part of the volume: from r−6 cm to r−10 cm. The total Young&#39;s modulus for the entire separating material should than be: 
         [0000]    
       
         
           
             
               E 
               Y 
               R 
             
             = 
             
               
                 
                   ∫ 
                   V 
                 
                  
                 
                   
                     E 
                     Y 
                   
                    
                   
                      
                     v 
                   
                 
               
               = 
               
                 
                   
                     10 
                     3 
                   
                   · 
                   
                     ( 
                     
                       
                         
                           ∫ 
                           0 
                           
                             2 
                              
                             π 
                           
                         
                          
                         
                           
                              
                             θ 
                           
                            
                           
                             
                               ∫ 
                               0.05 
                               0.06 
                             
                              
                             
                               r 
                                
                               
                                  
                                 r 
                               
                                
                               
                                 
                                   ∫ 
                                   0 
                                   2 
                                 
                                  
                                 
                                   
                                      
                                     x 
                                   
                                   · 
                                   3 
                                 
                               
                             
                           
                         
                       
                       + 
                       
                         
                           ∫ 
                           0 
                           
                             2 
                              
                             π 
                           
                         
                          
                         
                           
                              
                             θ 
                           
                            
                           
                             
                               ∫ 
                               0.06 
                               0.1 
                             
                              
                             
                               r 
                                
                               
                                  
                                 r 
                               
                                
                               
                                 
                                   ∫ 
                                   0 
                                   2 
                                 
                                  
                                 
                                   
                                      
                                     x 
                                   
                                   · 
                                   2 
                                 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                 
                 ≈ 
                 
                   100 
                    
                   
                     [ 
                     
                       k 
                        
                       
                           
                       
                        
                       
                         N 
                         / 
                         
                           m 
                           2 
                         
                       
                     
                     ] 
                   
                 
               
             
           
         
       
     
         [0021]    Inner and outer pipe radiuses are commonly determined by the physical requirements of the problem. Inner pipe radius, for example, can be determined by the minimum fluid capacity planned to flow through it. In such cases, the separating layer&#39;s materials properties are instantiated by the total Young&#39;s modulus calculation previously discussed. Nevertheless, there might be different scenarios, when the separating layer&#39;s materials are given, and the pipe radiuses needed to be obtained. In such cases, the calculation previously discussed, should also be used, with the relevant adjustments. If, for example, the Young&#39;s modulus is given with the value of E Y =2000 kN/m 2  (Polyethylene terephthalate) per volume unit, and the total Young&#39;s modulus E Y   R =100 kN/m 2 , then the general formula would be: 
         [0000]    
       
         
           
             
               E 
               Y 
               R 
             
             = 
             
               
                 
                   ∫ 
                   V 
                 
                  
                 
                   
                     E 
                     Y 
                   
                    
                   
                      
                     v 
                   
                 
               
               = 
               
                 
                   
                     
                       10 
                       3 
                     
                     · 
                     
                       ( 
                     
                   
                    
                   
                     
                       ∫ 
                       0 
                       
                         2 
                          
                         π 
                       
                     
                      
                     
                       
                          
                         θ 
                       
                        
                       
                         
                           ∫ 
                           ri 
                           ro 
                         
                          
                         
                           r 
                            
                           
                              
                             r 
                           
                            
                           
                             
                               ∫ 
                               0 
                               2 
                             
                              
                             
                               
                                  
                                 x 
                               
                               · 
                               2 
                             
                           
                         
                       
                     
                   
                 
                 = 
                 
                   100 
                    
                   
                     [ 
                     
                       k 
                        
                       
                           
                       
                        
                       
                         N 
                         / 
                         
                           m 
                           2 
                         
                       
                     
                     ] 
                   
                 
               
             
           
         
       
     
         [0000]    and the radiuses would be: 
         [0000]    
       
         
           
             
               
                 r 
                 o 
                 2 
               
               - 
               
                 r 
                 i 
                 2 
               
             
             = 
             
               
                 25 
                 
                   1000 
                    
                   π 
                 
               
               ≈ 
               
                 
                   8 
                   1000 
                 
                  
                 
                   m 
                   2 
                 
               
             
           
         
       
     
         [0022]    A mathematical model analyzing the physical configuration presented in  FIG. 2  can be obtained. A linear elastic solution for the response of an isolated pipeline due to surface fault is given in the following Tables (1, 2), wherein the properties and configuration of the separating materials should be such that it obtains a representative value smaller than the one stated in said tables. 
         [0023]    Figures in table 1 relates to the subgrade coefficient evaluation attributed to the soil, where each item in the table relates to the subgrade modulus and the ratio of inner and outer pipes radiuses. The subgrade modulus can be calculated using the relation K=kB, where k is the coefficient of subgrade reaction, measured in kN/m 2  (kN represents the magnitude of force given in kilo Newtons) and B=2 ro (where ro is the radius of outer pipe given in meters). If, for example, the soil&#39;s subgrade coefficient measured to be 10,000 kN/m 2  , the outer pipe radius is 10 cm (10 −1  meter ) and the inner pipe radius is 5 cm, then, K=10000 2·10 −1 =2000 kN/m 2  and the proper item value in table 1 for these values is equal to 299 kN M 2 . It means that the Young&#39;s modulus, E Y   R  for the separating material must me less than (or equal to) 299 kN/m 2 . 
         [0024]    Figures in table 2 relates to the Young&#39;s modulus evaluation attributed to the soil, where each item in the table relates to both soil&#39;s Young&#39;s modulus and the ratio of inner and outer pipes radiuses. If, for example, the soil&#39;s Young&#39;s modulus equivalent value measured to be 10,000 kN/m 2 , the outer pipe radius is 10 cm (10 −1  meter) and the inner pipe radius is 5 cm, then the proper item value in table 2 for these values is equal to 449 kN/M 2  . It means that the Young&#39;s modulus, E Y   R  for the separating material must be less than (or equal to) 449 kN/m 2 . 
         [0025]    If the soil behaves nonlinear, an equivalent linear stiffness for displacement of 3 cm should be considered. It means that the parameters representing soil properties must be evaluated accordingly. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Subgrade modulus of the soil K[kN/m2] 
               
             
          
           
               
                   
                 1000 
                 2000 
                 4000 
                 8000 
                 15000 
                 30000 
                 50000 
                 100000 
                 200000 
               
               
                   
                   
               
             
          
           
               
                 ro/ri 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                   
                 1.2 
                 39 
                 77 
                 155 
                 310 
                 581 
                 1162 
                 1937 
                 3874 
                 7749 
               
               
                   
                 1.4 
                 72 
                 143 
                 287 
                 574 
                 1076 
                 2152 
                 3586 
                 7172 
                 14345 
               
               
                   
                 1.6 
                 101 
                 201 
                 402 
                 805 
                 1509 
                 3017 
                 5029 
                 10058 
                 20116 
               
               
                   
                 1.8 
                 126 
                 253 
                 505 
                 1010 
                 1895 
                 3789 
                 6316 
                 12631 
                 25262 
               
               
                   
                 2 
                 150 
                 299 
                 598 
                 1196 
                 2243 
                 4487 
                 7478 
                 14956 
                 29912 
               
               
                   
                 2.2 
                 171 
                 342 
                 683 
                 1366 
                 2562 
                 5124 
                 8539 
                 17079 
                 34158 
               
               
                   
                 2.4 
                 190 
                 381 
                 761 
                 1523 
                 2855 
                 5710 
                 9516 
                 19032 
                 38065 
               
               
                   
                 2.6 
                 208 
                 417 
                 834 
                 1667 
                 3126 
                 6253 
                 10421 
                 20842 
                 41684 
               
               
                   
                 2.8 
                 225 
                 451 
                 901 
                 1802 
                 3379 
                 6758 
                 11264 
                 22528 
                 45046 
               
               
                   
                 3 
                 241 
                 482 
                 964 
                 1928 
                 3616 
                 7232 
                 12053 
                 24105 
                 48211 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Young&#39;s Modulus of the soil [kN/m2] 
               
             
          
           
               
                   
                 1000 
                 2000 
                 4000 
                 8000 
                 15000 
                 30000 
                 50000 
                 100000 
                 200000 
               
               
                   
                   
               
             
          
           
               
                 ro/ri 
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                   
                 1.2 
                 58 
                 116 
                 232 
                 465 
                 872 
                 1743 
                 2906 
                 5811 
                 11623 
               
               
                   
                 1.4 
                 108 
                 215 
                 430 
                 861 
                 1614 
                 3228 
                 5379 
                 10759 
                 14345 
               
               
                   
                 1.6 
                 151 
                 302 
                 603 
                 1207 
                 2263 
                 4526 
                 7544 
                 15087 
                 30174 
               
               
                   
                 1.8 
                 189 
                 379 
                 758 
                 1516 
                 2842 
                 5684 
                 9473 
                 18947 
                 37893 
               
               
                   
                 2 
                 224 
                 449 
                 897 
                 1795 
                 3365 
                 6730 
                 11217 
                 22434 
                 44868 
               
               
                   
                 2.2 
                 256 
                 512 
                 1025 
                 2049 
                 3843 
                 7685 
                 12809 
                 25618 
                 51237 
               
               
                   
                 2.4 
                 285 
                 571 
                 1142 
                 2284 
                 4282 
                 8565 
                 14274 
                 28549 
                 57097 
               
               
                   
                 2.6 
                 313 
                 625 
                 1251 
                 2501 
                 4690 
                 9379 
                 15632 
                 31263 
                 62527 
               
               
                   
                 2.8 
                 338 
                 676 
                 1352 
                 2703 
                 5069 
                 10138 
                 16896 
                 33792 
                 67584 
               
               
                   
                 3 
                 362 
                 723 
                 1446 
                 2893 
                 5424 
                 10847 
                 18079 
                 36158 
                 72316