(1)
Tang
Shifang1
and Li Bei2
1 Shanghai Municipal Government International Shipping Center, Construction Administration
Port Planning Department, 220 Si Chuan Road(Central), Shanghai, 200002 China
Tel: +86 21 63292992, Fax: +86 21 63292992, Email:sifant @ citiz.net
2 Tianjin Research Institute of Water Transport Enginnering, Tanggu,Tianjin, 300456 China
Tel: +86 22 25707168-382, Fax: +86 22 25795125, E-mail: li3-pei2 @ sina.com
Abstract: A method of numerical and physical model complementing each other was applied in this paper, in which the formulae of the resistance coefficient for the single pile and group pile have been obtained through a series of experiments of physical models, then putting it in the studies of numerical model. It overcomes the shortcoming that used to be very difficult to consider the resistance of pile foundation when previewing the scheme of wharf engineering by the numerical simulation model in the past. It makes the obtained velocity and direction of flow in the frontage of the piled wharf to more tally with actual situation, and has important reference value for forecasting the strength of sedimentation, the putting forward of the measure for reducing sedimentation as well as the berthing of ships, etc.
Keywords: tide flow, single pile, and pile group, sedimentation
Numerical models and physical models are the most commonly used simulation tools in engineering application at present. Each model has its own simulation method and characteristics. As a research tool and method, each has its own independent scientific system and has been developed rapidly. Both of these two methods have certain limitation, shortcoming and advantage. Fortunately, their shortcomings and advantages can supplement each other, that is to say, some shortcomings of the numerical simulation can be overcome in the phyisical model; whereas some shortages of the physical model can be supplemented and improved in the numerical simulation. In order to solve the problem of the resistance of water flow caused by the hydraulic structures, such as the piled wharf, etc., the physical and numerical model are combined together in this paper. A series of tests on single pile, single inclined pile, and using flume models carried out pile group transverse array and pile group longitudinal array of three kinds of section. The obtained resistance coefficient was put into the numerical model and was applied in the first phase of the engineering of Yangshan Port of Shanghai International Marine Center. After considering this characteristic, the result of the simulating calculation by this numerical model shows that it can truly reflect the characteristic of motion of the water flow in the frontage of the wharf after the engineering project is completed, providing reliable scientific basis for analyzing and calculating the sedimentation and for the research of the measure to reduce siltation.
In the water flow when the water encountering barriers such as pile foundation, etc. roundabout flow resistance is produced; this value may be shown as follows:
(1)
Where is the resistance coefficient; is the area of the projection of the pile perpendicular to the direction of water flow; is the velocity of water flow before having been influenced by the piles; is the unit weight of water.
Obviously, the resistance coefficient is related to the shape of object, the velocity of water flow, the depth of water, the roughness of the surface of the piles, and riverbed, the Reynolds number and Froude number of the water flow. How to determine the resistance coefficient of single pile and pile group under the action of tidal flow is a very complicated problem, which any theories can not solve at present. It can only be determined through flume tests.
In order to get the preliminary resistance coefficient from the flume in the shortest possible time for the numerical model to use, the experimental condition was determined according to the site of tests, the capacity of water supply of the circulating system, using the flume whose dimensions are 13 meters long, 0.8 meter wide, 0.6 meter deep, the bottom slope i=0 and which was made up of reinforced concrete prefabricated slabs joined together and then plaster it with cement, one side of the flume wall was inlaid with glass for observing the water flow.
In order to get rid of the influence of the side wall on the tested pile, there should be enough distance or space between the side wall and the tested pile. According to the calculation of the velocity around a cylinder in the unlimited flow field, outside the cylinder at a distance as far as five times the diameter of the cylinder, the change of velocity is about 1% of that when there is no cylinder; it can be held that at this spot the flow is not influenced by the cylinder. According to this analysis, and take into account the influence of the roughness of the side wall, under the condition that the width of flume is 80cm, if the model pile s radius is 2.5cm, the influence of the side wall on the flow around the tested pile is enough to get rid, because the ratio of the width of flume and the radius of pile reaches 80/5=16.
The tests are divided into 4 large groups:
(1) Single vertical pile test
(2) Single inclined pile test
(3) Group pile transverse array test
(4) Group pile longitudinal array test
The hydraulic characteristics of each group test are:
Water depth h = 18 ~ 45cm
Velocity v = 20 ~ 90cm/sec.
The Reynolds number Re = (1.0 0.4)×104
The Froude number of water flow Fr = 0.01 ~ 0.36
3 kinds of pile s cross sections are used in the test, circular(cylinder), square and square rotated 45°(Simply called right angle rhombus in the following). In order to make the pile’s area projecting perpendicularly to the direction of the flow keeps same, the diameter of the cylinder, the length of the side of the square pile, and the length of the diagonal line of the right angle rhombus, all is 5cm.
The piles used in this test having 3 kinds of
cross sections, as above mentioned, circular, square
and right angle rhombus. The location of each single pile in the flume is shown
in Fig. 1.
It was observed that when the water flows past through the single pile, the water flow is separated and vortex is formed behind the pile, resistance increases. This phenomenon is most obvious in the square pile, it is the weakest in the right angle rhombus and it is the second weakest in circular pile.
Fig. 1 The sketch of the planar arrangement of the single pile
Following is the test situations in 3 different cross section of pile.
(1) Circular single pile test
The test can only be done within the range of Re = 11.7 ~ 4.0×104 due to the limitation of equipment. Within this range it is found that the resistance coefficient does not have close relation with Re and Fr, but it varies with the water depth. Their relations are as shown in Fig. 2.
ξ
h/d
Fig. 2 The relation curves of ~ h/d for single vertical cylinder
(2) Square single pile test
Each side of the square pile is 5cm long, its area of projection facing the water flow is the same as that of a circular one. It is known according to the test that within the range of test the resistance coefficient does not have obvious relationship with Re and Fr, but it varies with the water depth. The relationship is shown in Fig. 3.
ξ
h/d
Fig. 3 The relation curve of square single vertical pile ~ h/d
(3) Square right angle rhombus single pile test
It can be found from the test that within the range of this test, the resistance coefficient does not have important relationship with Re and Fr, but it also varies with the water depth. For the comparison, drawn the tested resistance coefficients of cylinder, square and right angle rhombus pile in Fig. 4.
From Fig. 4 it is found that the resistance coefficient of square pile is the largest, that of right angle rhombus pile is smallest, and that of cylinder is between them.
Fig. 4 The curves of resistance coefficient ~ h/d of right angle rhombus, square and cylinder single pile
Due to the limit of time the content of this test is only the cylinder inclined in the current downstream and upstream. Judged from the result of observation, when the cylinder inclines in the current downstream, its resistance coefficient is a little less than that of the relevant vertical single pile; whereas the resistance coefficient is a little larger than that of the vertical single pile when the cylinder inclines in the current upstream. So in the alternating tidal flow, if taking the average value within a tidal period, the resistance coefficient of the single inclined pile may be considered as the same as that of single vertical one.
The aim of this test is to understand the influence of the transverse interval of piles on the resistance coefficient. On the cross section of the flume there are several kinds of arrangements of pile array (Fig. 5).
Fig. 5 The sketch of the transverse arrangement of pile array
Fig. 6 The relation curve of ~ B/d
In this test only one test condition was conducted with water depth of h = 24cm and flow rate Q = 100L/sec.
Through the test it is found that when the number of piles in the flume increase (from two to four), the hydraulic characteristics near the section where the piles were set will be changed due to the reducing of flow section. The water level in front of this section is raised, the current velocity is reduced a little, the water level behind this section is somewhat lowered and larger vortex appears. The water current in the vicinity of this section varies greatly, local hydraulic gradient increases, current velocity is increased and the resistance coefficient also increases.
According to the test it was come to know that there exists a certain relationship between the resistance coefficient and the relative interval between the piles B/d (B is the interval between piles, d is the diameter of the piles). This relationship is shown in Fig. 6.
From the above results it can be found that the resistance coefficient increases with the reduction of the space between piles. The following expression can show how the resistance coefficient of the pile group is influenced by transverse interval.
Here KB is the transverse influence factor of pile group and 0 is the resistance coefficient when there is single pile. According to the tests, the relationship between KB and B/d can be obtained as shown in Fig. 7.
Fig. 7 Transverse influence factor of pile group KB~B/d
When the pile groups are arranged longitudinally, the resistance coefficient will be reduced due to their flow shielding action, and the mutual influence of fore and back piles. So the flow shielding tests of back and fore piles along the longitudinal direction with different spaces were carried out. The type of the cross section of the piles are of three kinds: circular, square and right angle rhombus, the test conditions are respectively as follows.
Square pile, depth of water h/d = 3.6 ~ 8.4 (h = 0.18 ~ 0.42m), rate of flow Q = 60 ~ 125L/sec;
Circular pile, depth of water h/d = 8.4 (h = 0.42m), rate of flow Q = 80 ~ 125L/sec
Square rhombus pile, depth of water h/d = 4.8 (h = 0.24m), rate of flow Q = 80 ~ 125L/sec
Through the tests it can be found that due to the flow shielding action of the piles the pulsation in the vortex region between two piles is weakened, water level is raised, current velocity is reduced, the average resistance coefficient of the two piles is reduced. With the increase of the space between the fore and back two piles, the resistance coefficient gradually increases. Using KL as a reduction factor to show the degree of weakening of the resistance coefficient of a pile by the fore and back piles, then the resistance coefficient of the pile may be shown as follows:
Here, 0 is the resistance coefficient of a single pile when there are no fore and back piles shielding the flow;KL is the average reduction factor due to flow shielding action by the fore and back piles.
The reduction factor obtained from the test is shown in Fig. 8. L in this figure is the space between the fore and back piles.From the above it can be know that the flow shielding influence of square pile is great, the degree of reduction is stronger than that of circular and
Fig. 8 Longitudinal reduction factor of pile group KL~L/d
right angle rhombus piles, therefore the reduction factor of square pile is less than that of circular and right angle rhombus piles, and the reduction factor of circular and right angle rhombus piles near the same basically, only that of right angle rhombus is a little smaller.
Summing up the above tests the following can be found.
When the current passes through the pile group, the roundabout flow resistance of a pile may be calculated by the following equation:
where, the resistance coefficient may be determined according to the shape of cross section and arrangement of the pile as follows:
(2)
where nL is the number of piles within the unit length along the direction of flow(longitudinal);nB is the number of piles within unit length perpendicular to the direction of flow (transverse);KLis the longitudinal reduction factor of pile group (See Fig. 8); KB is the transverse influencing factor of pile group (See Fig. 7); 0 is the resistance coefficient of single pile, which can be found in Fig. 2, Fig. 3 or Fig. 4 according to pile s cross sections.
Equation(2) may be written as follows:
(3)
where N is the total number of group piles per unit area.
In the basic equation of tidal motion, in order
to calculate the resistance of pile foundation this resistance item is add
to the dynamic equation. The general expression is
, or written into the simplified expressing
V2, where
is called the resistance coefficient of pile foundation in
the latter part of this paper, the expression of
is shown as follows.
(4)
Piled wharf is a kind of permeable structure. When the flows pass through the pile foundation, on one hand the velocity is reduced due to the influence of the resistance of pile foundation; and on the other hand the velocity increases because the existence of piles makes the flow section become smaller; in addition, the existence of piles makes vortex formed in the current. Therefore the current in the pile foundation area is quite complicated, it may cause great influence on the movement of silt in the flow. In general situation, the serious siltation will happen inside the piled wharf.
Due to the fact that the flow and silt inside the pile foundation vary greatly, this can also influence the flow field and the movement of silt in front of the wharf. Therefore, in the numerical simulation of tidal flow in the pile foundation wharf it is quite necessary to take the influence of pile foundation into account.
In the past numerical simulation of tide flow, the piled wharf was simplified into a gravity wharf and the wall of wharf was simplified into a fixed boundary, because the influence of pile foundation was not known well enough and also because lack of the experience of how to take into account the influence of pile foundation. This kind of treatment does not affect the whole fluid greatly, but it will cause distortion to the local flow field of the frontage of the wharf, whereas the flow fields in this areas are the important basic data for analyzing and calculating the siltation and the ships berthing on and leaving off the wharf. Therefore for simulating local flow field in the frontage of pile foundation in the engineering scheme it is quite necessary to consider the influence of pile foundation.
Two aspects should be considered, the increase of resistance and the reduction of the flow section, therefore in the numerical simulation of tidal flow the resistance coefficient and the water depth should be revise.
(1) The resistance coefficient of pile foundation
According to the test results in the previous section, in the region of pile foundation, an item pile of resistance coefficient of pile foundation should be added, it can be determined from the formula (3).
(2) The revision of the water depth
In the region of pile foundation, the water depth may be revised according to the following equation.
（5）
Where h pile is the reduced water depth in the region of pile foundation; d is the diameter of the pile; B is the space between piles; h is the depth of natural water; h is the reduction factor coefficient of the water depth, it is the function of d/B, the value is between 1.3—4.0.
The planning region of Shanghai Yangshan Port is located in the sea area of Da Yangshan and Xiao Yangshan island to the north of Hangzhou Bay. The depth of burying of bedrock in the port region varies greatly, so the structure of the port may have different types. In the section where bedrock is deeply buried under the earth high piled beam and slab structure might be adopted; in the section where the bedrock is not deeply buried under the earth or is exposed, gravity structure might be adopted. Therefore when carrying out two-dimension tidal flow numerical simulation in this region, in the section of the high piled beam and slab wharf the influence of pile foundation should be considered; while in the section of gravity wharf fixed boundary can be accepted.
According to the feature that there is a lot of islands in the sea area to be calculated there be the coastline is tortuous, the arbitrary triangle grid was used in this model. The advantages of this grid lies in the fact that within the calculation range it can accurately simulate the change of arbitrary winding of the island coastline and can reach the precision that other grid can t accomplish when dealing with the complicated boundary.
For calculating the flow resistance in whole calculation area, fc=g/c2 can be used approximately, where fc is the resistance coefficient, c is Chezy coefficient, c=H1/6 1/n, n is Manning resistance coefficient, which is decided to be 0.010 ~ 0.025 after many groups of debugging calculation. In the numerical model, n also includes the influence of other factors on the water flow, besides the bed roughness. So n is no longer the original meaning of the roughness factor, it can be as a integrated influence coefficient.
In the area of the piled wharf the influence of the pile foundation on the flow should also be taken into account. According to the features of the tidal flow in this sea area and the arrangement of pile foundation in the harbor, using of the test results, the additional resistance coefficient of the pile group was obtained to be 0.018 ~ 0.02. In addition, the area of pile foundation water depth was also revised by equation (5).
After testing and verifying, a series of calculation of the tidal flow in this sea area for different engineering scheme has been carried out. Fig. 9 is the sketch map of the calculated flow pattern in tide flood after the engineering project. In this simulation the influence of the pile foundation in the area of the piled wharf has been considered. From these maps it can be found that the result of calculation basically accords with the features of the tidal flow and tide in this area.
Fig. 9 Sketch map of calculated flow pattern in tide flood after the engineening project
The influence of pile foundation on the flow is in two aspects, one is the influence of resistance, the resistance coefficient of the pile foundation can be obtained through flume experiments; the other is the influence of the flow section, which can be determined through analysis. The flow suffers from the action of resistance of pile group of wharf, thus changing the velocity. Moreover, it is relevant closely to the siltation analysis that whether or not correct the numerical simulation of tidal flow in the frontage of the wharf is. At present it is difficult to determine resistance coefficient theoretically, it can only be determined by mean of physical model. In this paper the test results of physical simulation were applied to the calculation of numerical simulation, the two different hydrodynamic study methods supplementing each other. Thus, the difficult problem of selecting resistance coefficient of pile group in numerical simulation was solved.
In the tidal flow numerical simulation in the area of piled wharf considering the influence of pile foundation is of greater importance to such engineering area as the first phase engineering of Yangshan harbor area where the water is deep and the flow is rapid. Besides providing the data for the analysis of resedimentation, it is also of great importance to the berthing of ships. In the past the piled wharf and the gravity wharf generally used to be regard as the same solid boundary in the numerical simulation of the harbor engineering scheme, thus making the circumfluent effect around the side wall flow happens in the frontage of wharf. The calculated results is somewhat different from the actual situation (the authors have made some reproduction comparisons in this respect).
This study combines flume model test with numerical simulation so that they can supplement each other. Its research result is of universal significance; it may serve as a reference for selecting resistance coefficients for different hydraulic structures, single piles and group piles with different cross sections in numerical simulation.
References
[1] Prant, An Introduction to Fluid Mechanics, translated by Guo Yonghai.
[2] S. F. Hoerner, Fluid-Dynamics, Drag.
[3] A Collection of Formulae of Hydraulics, Revised Edition by JSCE, 1971.
[4] The Study on Erosion in the Circumference of Bridge Pier, The Publishing House of French National Hydraulic Engineering Institute.