FLOW OUT LIMIT OF BACK-FILLING SAND BEHIND REVETMENT UNDER CYCLIC LOADING OF WATER PRESSURE

Shiro. Maeno¹ and Yuji Tsubota²

 ¹Dept. of Environmental and Civil Engineering, Okayama University, Okayama, Japan

 ²Civil Engineering Dept., The Chugoku Electric Power Co. Inc., Hiroshima, Japan

Tel : +81-86-251-8151, Fax: +81-86-251-8257, E-mail : maeno@cc.okayama-u.ac.jp

Abstract: Many hydraulic structures collapse due to flow out of the back-filling sand behind a revetment under attack of flood and stormy waves. This type of destruction caused by the cavity behind the revetment is closely related to the cyclic loading of water pressure acting on the sand surface around the structure. In this study, we investigated the basic characteristics on the flow out of back-filling sand under the cyclic loading of water pressure by using two experimental apparatuses. It is shown that the cyclic seepage force which occurs around the revetment plays an important role to the flow out of back-filling sand. Furthermore, an analysis of the sand bed stability potential against the flow out of back-filling sand is presented, in which almost the experimental cases tested in this study are verified.

Keywords: liquefaction, water pressure variation, pore pressure, seepage force, revetment, back-filling sand, stability potential analysis

1    INTRODUCTION

The collapse of coastal structures under stormy waves is closely related to the dynamic behavior of sand bed around these structures under the cyclic loading of water pressure.  From this point of view, authors have investigated the dynamic behavior of highly saturated sand bed under the cyclic loading of water pressure (Nago and Maeno, 1984, 1987). These studies revealed that the pore water pressure in the sand bed varies with time and the effective stress of the sand bed decreases cyclically and also the cyclic liquefaction occurs under certain condition. As shown in Fig. 1, the positive water pressure acts on the sand surface under the wave crest, whereas the negative water pressure acts under the wave trough.  When the wave trough comes just front of the revetment, upper part of the sand bed in an oblique line liquefies (Maeno et al. 1999). Liquefaction and the decrease in the effective stress of the sand bed may cause the flow out of back-filling sand behind the revetment. In this study, the flow out mechanism of the sand bed is investigated by experimentally and theoretically. Furthermore, an analysis of the sand bed stability potential against the flow out of back-filling sand is proposed and its applicability is investigated.

2    EXPERIMENTAL PROCEDURE

For the experiment two experimental apparatuses as shown in Fig. 2 and Fig. 3 were used. The apparatus (A) can generate a water table type cyclic loading of water pressure, that is the cyclic pressure on the sand surface is uniformly distributed at a certain time. On the other hand, the apparatus (B) can generate a real wave type water pressure. Maximum wave amplitude for the apparatus (B) is not so large.  Whereas, the apparatus (A) can generate a larger amplitude than the apparatus (B).  Highly saturated standard sand (Toyoura standard sand d₅₀≒0.25 mm) were used for the bed materials.  Four cases of experiments were carried out under the condition shown in Table 1. That is, Case 1 is the fundamental experiment.  In Case 2 and Case 3, the effect of amplitude and Permeability are examined.  In Case 4, dynamic behavior of the sand bed under a real wave motion were investigated. In these experiments, the colored sand is arranged around the revetment to visualize the movement of sand. The colored sand is made by burning the standard sand. It’s permeability and specific weight are similar to the standard sand. Pore water pressures were measured at the measuring points shown in Fig. 2 and Fig. 3.

    Table 1    Experimental conditions

3    THEORETICAL PROCEDURE

Basic equations to calculated the pore water pressure around revetment are shown in Eq.(1) (Biot, 1941; Verruijt, 1969, Nago and Maeno, 1984). FEM method was used in the calculation.

                 (1)

Here, b : Compressibility of water, r : density of water, g : gravity acceleration, , : porosities of the water and the air, P : absolute pressure，h : incremental pore pressure, ux uz : incremental displacement in x, z direction, k : permeability coefficient, G : shear modulus, n : poisson ratio.  Numerical conditions are as follows. 

G : 3.5×10７(N/m2), b : 4.2×10-10 (m2/N), k : 0.012(cm/s) and 0.142(cm/s),

 : 0.003,  : 0.40, n : 0.45

Photo 1 shows the flow out of back-filling sand around the revetment for Case 1 after the 2000 minutes loading of water pressure.  As shown in this photo, when the back-filling sand flows out under the toe of the revetment, the sand surrounded by the dotted line moves first.  Triggered by this movement of sand, the back-filling sand behind the revetment flows out gradually.  Considering the experimental results, Eq. (2) is used to investigate the stability potential of the sand bed against the flow out of back-filling sand (see Fig. 4).

               (2)

Here, F is the non-dimensional dynamic resultant force. : dynamic seapage force, : submerged weight of sand, : submerged weight of sand at initial state, : reduction ratio for static shear stress, : static shear stress. In this paper,  and was used in the calculation.  Considering the experimental results, 5cm was adopted for the length of A’-A. In this equation, if the value of F becomes less than zero, the sand in front of the revetment moves upward and the flow out of backfilling sand occurs.

4    RESULTS AND DISCUSSIONS

Characteristic of pore water pressure

Fig. 5 and Fig. 6 show the pore water pressure variation around the revetment for Case 1 and Case 4 respectively. From these figures, pore pressure on the sand surface propagates around the revetment with the attenuation in amplitude and the phase lag. The characteristics of the pore water pressure variation for the water table type loading (Case 1) is similar to that for the real wave type loading (Case 4). Numerical results show in good agreement with experimental results. This means that the theoretical treatment used in this study is appropriate to express the dynamic behavior of sand bed around the revetment under the cyclic loading of water pressure.

Fig. 7 and Fig. 8 show the numerically obtained seepage force distribution and equipotential line in the sand bed for Case 1 and Case 4 respectively. These figures show the state of wave trough. Space of equipotential line becomes narrower and the seepage force becomes larger around the vicinity of revetment. Direction of the seepage force is similar to the movement of sand around revetment as shown in Photo 1. The seepage force for Case 4 is smaller than that for Case 1 because the amplitude of the cyclic loading of water pressure for Case 4 is smaller than that for Case 1. 

Applicability of stability potential analysis

Fig. 9 shows the volume of sand which flows out from the back-filling side of the revetment.  The volume was calculated by integrating the difference in the height of the sand surface from that of the initial state. As shown in this figure, the flowing out rate of the back-filling sand is higher in the early stage of the experiment and it decreases gradually with time. The flowing out volume of the sand increases with the increase of the amplitude of the cyclic water pressure loading on the sand surface (see Case 1, 2, and 4). The sand did not move for Case 4 in which the real wave was loaded as a type of water loading. This is considered that the amplitude for Case 4 is too small to trigger the movement of sand around the revetment.

Permeability of the sand bed have a considerable effect to reduce the amount of the flowing out of the sand (see Case 1, 3). The main reason of this is that the higher permeable sand improves the propagation characteristics of the pore water pressure. In the experiment, both the attenuation and the phase lag of the pore water pressure for Case 3 become smaller than those for Case 1. This improvement of the pore water pressure distribution leads the stability of the sand bed (Maeno et al., 1999).

Fig. 10 shows the variation of non-dimensional resultant dynamic force by using Eq. (2). Numerically obtained pore water pressure variation was used to calculate this resultant force. Continuous loading of the resultant dynamic force can induce a step wise flow out of back-filling sand behind the revetment if an instability conditions is fulfilled. It is considered that if the value of resultant force becomes less than zero, the sand bed is not stable against the flow out of back-filling sand. Judging from this figure, Case 1 is the most critical case against the movement of sand around the revetment. Case 2 is the secondly dangerous case. Case 3 and 4 are considered to be stable. Comparing with the experimental results, the formula used for assessing the stability of the sand bed is effective to evaluate the flow out of back-filling sand except for Case 3.

5    CONCLUSIONS

In this study, the basic characteristics on the flow out of back-filling sand under the cyclic loading of water pressure was investigated experimentally and theoretically. It is shown that the cyclic seepage force which occurs around the revetment plays an important role to the flow out of back-filling sand. Furthermore, it is clarified that the presented analysis of the sand bed stability potential is useful to predict the stable limit against the movement of sand around the revetment.

Acknowledgement

This study was partially supported by the Grant-in-Aid for Scientific Research ((C), (2), No.11650529) of Japanese Society for the Promotion of Science.

References

Biot, M. A. (1941): General theory of three dimensional consolidation, Journal of Applied Physics, Vol. 12, pp. 155-164.

Maeno, S. and Nago, H. (1988) : Settlement of a concrete block into a sand bed under water pressure variation, Proceedings of the International Symposium on Modeling Soil-Water-Structure Interactions, pp. 67-76.

Maeno, S. and Kotani, U., Tsubota, U and Nago, H. (1999) : Dynamic behavior of sand bed around coastal revetment under wave motion,

Maeno, S., Magda, W. and Nago, H. : Floatation of buried pipeline under cyclic loading of water pressure, Proc. 9th ISOPE, Vol.2, pp.217-225,1999.

Nago, H. (1981): Liquefaction of highly saturated sand layer under oscillating water pressure, Memoirs of the School of Engineering, Okayama Univ., Vol. 16, No. 1, pp. 91-104.

Nago, H. and Maeno, S. (1984) : Pore water pressure in sand bed under oscillating water pressure, Memoirs of the School of Engineering, Okayama Univ., Vol. 19, No. 1 pp. 13-32.

Nago, H. and Maeno, S. (1987) : Pore pressure and effective stress in a highly saturated sand bed under water pressure variation on its surface, Natural Disaster Science, Vol. 9, No. 1, pp. 23-35.

Verruijt, A. (1969): Elastic Storage of Aquifers, Flow Through Porous Media, Ed. DeWiest, R. J. M., Academic Press, New York, pp. 337-344.

Photo 1    Flow out of sand around revetment

Fig. 4     Component of forces

Fig. 5    Pore water pressure variation (Case 1)

Fig. 6    Pore water pressure variation (Case 4)

Fig. 7    Seepage force distribution (Case 1)

Fig. 8    Seepage force distribution (Case 4)

Fig. 9    Volume of flow out sand (Case 4)

Fig. 10    Resultant force F (Case 4)