ANALYSIS OF FORCES ACTING UPON THE UNCONVENTIONAL TYPE OF PARAPET SLAB ON THE TOP OF BULKHEAD

Zhong Husui and Guo Da

The College of Harbour, Waterway and Coastal Engineering,

 Hohai University, Nanjing, 210098

Abstract: For the unconventional type of parapet slab structures configured by the boundary conditions of practical project, the usual methods to calculate the wave forces acting on the parapet are not still suitable in analyzing the force effects. In this paper by means of profile model test in wave channel, the wave forces exerted on the parapet structure with low elevation and long slab are measured. Moreover the characters of forces on such structure are also well summarized.

Keywords:  wave pressure, uplift force, parapet slab, overtopping discharge, rear parapet

1    INTRODUCTION

The top elevation of a bulkhead project located in Zhe Jiang province was strictly limited in raising at will, in order to match the existing road elevation fixed by the municipal planning. At the same time it’s also not the desire to lower the bottom elevation of the parapet for the sake of heightening its weight and stability, because the core of bulkhead was already completed beforehand by means of explosive rock filling and any digging up of it should be avoided as possible. But the extreme high tide level with return period of 50 years which has an important bearing on the safety of the bulkhead are relatively high and the design wave height with accumulated frequency of 1% are also relatively large. In this condition how to ensure the safety of the parapet becomes a difficult and crucial problem in the design process.The restrain to both upper and lower elevation of parapet slab makes it the only choice to search the space for slab along the horizontal direction rearward. From the view point of usage there will be a sightseeing platform behind the front line of bulkhead within 23m on which overtoppings are permitted, so it’s possible to deal with the rear area as part of parapet slab rather than ordinary road work. Under these something special boundary conditions a special form of parapet slab with lower elevation and longer dimension along the direction of wave spreading has put forward out, see Fig.1.

As for the uplift forces exerted on the bottom surface of a conventional parapet on the top of bulkhead, it can be calculated and determined using the methods provided by the Code of Hydrology for Sea Harbour, issued by Chinese Ministry of Communication ^[1]. The calculation methods assume that the distribution of uplift force on bottom surface were in triangular form, i.e. the pressure on front toe of slab equals to the average wave pressure acting on the screen wall surface, and that on the rear end of slab approaches to zero. As calculated results the above uplift force should yet be reduced by 30%.If the elevations of slab bottom keep enough height from the design water level and the length of slab along wave spreading direction are in same order of magnitude with the height of screen wall, the above assumption may be reasonable.But in our case with lower elevation and longer slab of parapet, the current code doesn’t meet the need of design. To search the basis for design of new alternatives, the wave model tests were conducted in an irregular wave channel. Besides the important data such as stability and overtopping discharge etc. have been collected in both regular and irregular wave condition, the pressure distributions both on top and bottom of the new type of slab have also been determined and compared with that of conventional parapet structures.

2    TYPES OF PARAPET SECTION AND THE BOUNDARY CONDITIONS IN TEST

There are two types of unconventional parapet slab, i.e. thick and thin slab and defined as alternative Ⅰand Ⅱ respectively. These two alternatives are same in their dimension and top elevation, the only difference lies in that the slab thickness of alternative Ⅰis 1.5m and alternative Ⅱ 0.8m. Fig. 1 shows the alternative Ⅱ. The whole parapet slab can be separated into two parts of front and rear. The bottom surface of the former is equipped with two sills one after another and the seaward section from front sill has a bottom elevation of 2.80m. On the surface of the rear part of slab, there exists a rear wave screen. The two parts of slab are same in top elevation of 4.50m. The front face of parapet is an 1:1 slope, that is consistent with the gradient of armor surface. The armor units are hallow squares with four legs above -1.0m, but are dolos at the foot of slope.

To measure the pressure distribution along the parapet slab, two rows of total 17 transducers were set longitudinally upward (at top plane) and downward (at bottom plane) respectively. Those downward were for the measurement of uplift forces and the pressure directions towards the transducer surface (i.e. upward) were defined as positive. The transducers at top plane with identical position were for the measurement of forces caused by overtopping discharge and the pressure directions were also defined as positive as towards the transducer surface, see Fig. 2.

The design water level are extreme high water level of 3.01m with return period of 50 years and design high water level of 2.05m, to which wave height H_1% of 4.15m and 3.75m correspond respectively. Pressure measurements have been conducted under regular wave action with wave flatness of 20、14 and 11 at each water level to determine the effects of wave flatness on the pressures. These wave flatnesses correspond to wave periods of 11.4s、8.10s and 6.57s at extreme HWL, but 11.4s、7.90s and 6.40s at design HWL.

3    ANALYSIS OF PRESSURE ON THE PARAPET SLAB

The measured pressures for two alternatives at the extreme HWL of 3.01m are listed in Tab.1 taking wave period of 11.4s for example. The non-synchronic pressures in the table indicate the average peak values taken from the pressure-time processes of relevant transducers, so that the diagram plotted by connecting these pressures represent the envelope of average pressure peak values. The synchronic pressures mean that integrating the pressures of all transducers at every synchronic instant in a test run, during which over 2000 sampling data recorded for each transducer, calculating the average and maximum peak values from time process of integrated results, the pressures which are corresponding to maximum peak value are exactly the synchronic pressures showed in the Tab.1. The above mentioned average and maximum peak values are average and maximum net uplift forces respectively and listed in Tab.2. And Fig. 3 shows the distribution of synchronic pressures.From Tab.1 and 2 as well Fig.3 it can be seen that because the elevation of slab bottom closes to SWL and the length of slab greater obviously than conventional one, the exerted forces on the slab demonstrate following characters:

(1) The uplift pressure on the rear end of slab are still not going to reach zero even if the length of slab reaches 1/4 of wave length. The rubble within the core under armor layer keep certain porosity, which allow the pressures produced by wave motion to spread along the wave direction in a long distance. Therefore the uplift pressures on slab bottom near SWL damp out slowly, the stronger the porosity of core is, the slower it damps out. Tab.1 shows that for alternative Ⅰ the non-synchronic uplift pressure on the bottom 20m apart from the front line is 16.12 kpa and is 59% of the uplift pressure on the front end; the synchronic uplift pressure on the rear end may reach 50% of front end, and in Fig. 3 the distribution of pressure appears nearly rectangular instead of triangular.

(2) The distance between the elevation of slab bottom and SWL has greatly affected on the uplift pressures. At the same extreme HWL of 3.01m, because of the bottom elevation of alternative Ⅱ has been increased by 0.17 times of wave height, the non-synchronic uplift pressure at rear end has been 63% reduced compared with alternative Ⅰin same position. As a result this uplift pressure reaches only 5.94kpa, equals to 25% of the pressure at front end. The synchronic uplift pressure at rare end has also been 57% reduced compared with alternative I.

Not only the uplift pressure at rear end decreases rapidly by the raise of bottom elevation, but also the total uplift force on the bottom be reduced correspondingly. At extreme HWL the net uplift force on the front part of alternative Ⅰ is 21.92t/m, because of the bottom elevation of alternative Ⅱ 0.17H increased, the net uplift force reduce to 13.52 t/m, which is 38% less than alternativeⅠ.As for the net uplift force on rear part of slab, 77% of it has already eliminated.

(3) The damping rate of uplift pressure is related to wave flatness L/H. Tab.1 is an example in wave period T=11.4s that means L/H=20. As wave flatness is smaller or wave form reveals steeper, the uplift pressure on bottom at rear end would damp slowly. For example of the wave with L/H=11, the pressure at rear end of alternative Ⅰ is 15.50kpa, which is 72% of the pressure of 21.48kpa at front end; but for alternativeⅡ the pressure at rear end is 50% of that one at front end. These percentages are all higher than the percentage of 59% and 25% respectively in case of L/H=20. Of cause this is only true as dealing with the ratio of change of uplift pressure. So as to the total uplift forces the one induced by wave with larger wave flatness would be generally greater than the one with smaller wave flatness, as shown in Tab. 2.

(4) Because of the lower elevation of slab, the downward exerted forces of the overtopping discharge on the top of structure have played an important role, see the column of “downward pressure on top surface” in Tab.1. At extreme HWL, the ratio of downward force on front part of alternative Ⅱ to the synchronic uplift force is 30% in average; but on rear part the ratio reaches more than 0.5. So that if comparing the net uplift force which take the force caused by overtopping discharge into account with those which put the overtopping discharge out of account, the ratio would be 0.84—0.86 for alternative Ⅰ and 0.60—0.80 for alternative Ⅱ. This shows that the overtopping discharge makes net uplift force cutting down obviously. But in view of the unstability of the effect of overtopping, it should be handled with great care whether take these forces into account in designing.

(5) In front of parapet structure the wave screen has been canceled and as substitution a rear wave screen be built about 20m behind the front line. In case of lower structure elevation, the wave screen on front line has no distinct function for diminishing the overtopping discharge, on the contrary enhanced the horizontal wave force.The upper elevation and geometric form of alternative Ⅰ and Ⅱ are same, at the extreme HWL of 3.01m, the wave pressures on front side in horizontal direction equal to 18—25kpa, which are equivalent to 0.44—0.61γH, and the pressures on rear wave screen are 14—27kpa ,equivalent to 0.34—0.66γH. Comparing with the parapet structure with 1m high front wave screen but identical top elevation of slab (see Fig. 1) and in same wave condition, the horizontal pressures with wave screen may reach 44.9kpa, equivalent to 1.1—1.2γH. That means the structures like alternative Ⅰor Ⅱ could not only reduce 40%—50% of horizontal forces in front, but also produce evident phase shift with the forces on rear wave screen.

(6) The parapet structure with conventional front wave screen would sustain greater uplift pressure than those alternatives in this paper in same condition. As L/H=20 and at two different water levels of 3.01m and 2.05m respectively, the average uplift pressures on bottom of parapet slab with front wave screen are 41.42kpa and 21.86kpa, equivalent to 1.02γH and 0.60γH respectively. But for alternative Ⅰ the uplift pressures in same condition are 27.21kpa (0.67γH) and 21.66kpa(0.59γH), for alternative Ⅱ the pressures are even smaller and only reach 25.08kpa (0.62γH) and 12.53kpa(0.34γH) respectively. This is owing to the cancellation of front wave screen, so that the pattern of wave motion in front of structure have been changed from strong reflection and turbulence as well splashing severely to a relatively smooth going overtopping. The reduction of horizontal wave pressure means the reduction of corresponding uplift pressure, which is identical with the approach of calculation for parapet in general ^[1]. It should be noticed that if the slab stretches longer and above the SWL with certain distance, the assumptions of uplift pressure distribution being in triangular form and at the rear end of slab the pressure approaching to zero might over estimate the total force, because the uplift pressure might be already decreased to zero before it transmitted to the rear end along the slab bottom.

It should be pointed out that, the problem of parapet structures in this project are extremely large overtopping discharge. Comparing with the parapet with 1m high front wave screen and in same top elevation of slab, the overtopping discharges induced by irregular wave test are shown in Tab 3. In the table the row “with 1m wave screen” indicates the measured overtopping discharge over the top of screen near front line, and the row with “alternative ⅠorⅡ” means the measured overtopping discharge over the top of rear screen about 20m apart from the front line.

4   CONCLUSIONS

(1) In case of the core materials with certain permeability, for the parapet slab whose elevation is set lower and whose bottom surface lies close to SWL, i.e. the distance between them is less than 0.2H (H notes wave height), then on the rear end of slab bottom the uplift pressures would not approach to zero even if the length of slab reaches 1/4 wave length. But if the distance between bottom surface and SWL is larger than 0.4H, the assumption of uplift pressure distribution in triangular form approaches the reality.

(2) The above distance has great influences to the uplift pressure on slab bottom. The enlargement of the distance leads the ratio of pressures on rear and front end to a rapid reduction, and also to a rapid reduction of the uplift force upon whole bottom plane.

(3) As the top elevation of slab set lower, there exist two effects: the advantageous effect of the downward forces induced by overtopping discharge to eliminate the net uplift forces; and the unfavorable effect of enhanced overtopping discharge on the inner region behind wave screen.

(4) The rear setting of wave screen could evidently diminish the horizontal wave force acting on the whole parapet structure.

References

[1]   The First Design Institute of Navigation Engineering, Ministry of Communications, Code of Hydrology for Sea Harbour, JTJ213—98, People’s Communication Press, 1998.

[2]   Yen Kai editor in chief, Coastal Engineering in China, Ocean Press, 1992.

[3]   Zhong H.S. and Guo D., The Characters of Wave Forces on Rear Wave Screen, Proceeding of 8th National Symposium of Coastal Engineering and 97’ Symposium of Harbour and Coastal Engineering on Both Strait Sides, Ocean Press,1997.

[4]   Sun J.S., Li Z.X. and Huang Y.L., The Experimental Research of Break Water Sections in Bayuquan Port, 1983.

Table 1  The pressures on bottom and top of the slab(Water level 3.01m, T=11.4s, H_1%=4.15m) (Unit: kpa )

Note:  The pressures in the table are positive as pointing to the acting surface; negative as pointing away from the surface.

Table 2  The uplift forces as results of synchronic pressures integral (Water level: 3.01m)   (Unit: t/m )

Note: The direction of uplift forces in above table are all pointed to the bottom surface

Table 3  The overtopping discharge for different type of parapets

                                                   Unit: m³/s.m

Fig. 1  Section of unconventional parapet slab and the parapet structure with wave screen for comparison

Fig. 2  Arrangement of pressure measuring positions (unit: centimeter)

Fig.3  The distribution of synchronic pressures and net uplift forces on both front and rare part of slab