Stable Coastline between Two Groins Equation

In this research an equation of static equilibrium geometry shoreline on coastal segment between two groins with quadratic polynomial equations is developed. Equation coefficients were formulated based on the characteristic of stable coastline geometry of the previous study and conservation law of mass, where volume of erosion and sedimentation are identical. The equation is capable of predicting erosion and accretion for coastline between two groin. Furthermore, with the predicted erosion and sedimentation, the groins gap and the length of groin can be planned using maximum permitted erosion criteria.


I. INTRODUCTION
Groin is a type of massive construction as coastal protection against erosion. This construction is constructed perpendicular to the coast to withstand littoral drift. At the coastal segment located between two groins ( Fig.1.), erosion and sedimentation will still occur until the formation of a stable coast, i.e. a condition where net sediment transportation is zero. There are two conditions of stability, i.e. dynamic equilibrium and static equilibrium. At static equilibrium condition, there is no sediment transportation parallel with the coast or resultant of the long shore drift is zero. For a quite long time span, this static equilibrium condition exists if the evolution observed is the result of dominant wave. At static equilibrium condition, even sediment transportation still happened, the coastline will not change due to balance of sediment transportation..

Fig.1 Evolution of Shoreline At The coast Between Two Groins
The aim of this research is to obtain coastline equation between two groins at static equilibrium condition. The equation is obtained by studying the shape of stable coastal geometry from previous researches, such as Haligan   1 , half-heart bay, Silverster   2 , crenulate shaped bays, Silverster and Hso   3 , Hsu and Evans   4 and some other researchers . The prediction of erosion and sedimentation at coastal segment between two groins can be done using GENESIS software or similar model. However, the analysis requires a long time. If the equation of stable coastline between two groins is obtained, the calculation can be done more practical with shorter time. Then, using the equation, the planning of the length of groin and the distance between groin can be done using the permitted erosion criteria.

II.
STABLE COASTAL GEOMETRY In this section the characteristic of stable coastal geometry will be studied. Based on the geometry characteristic, the approximation equation for stable coastal geometry between two groins will be formulated. It has been recognized that in the nature there is stable coastal geometry in static equilibrium condition which many researches have studied to this form of stable coast. There are varieties of terminologies for the form of stable coast, i.e. Haligan    The stable shoreline consists of two parts (Fig.2), i.e. curve part, which is shaped by diffracted wave, and the straight part which is shaped by incident wave and is parallel to it. It is known that littoral drift that is parallel to the coast is a sine function of the angle between the wave and the shoreline. Therefore, the tangent of this linear part must be parallel with the wave crestline where littoral drift is minimal or zero.
b. Logarithmic spiral model Yasso   5 also discovered that stable coastal geometry has similar shape like the one in parabolic theory. However, he used the logarithmic spiral model equation for the stable coastal geometry, i.e.  is a logarithmic parameter. One thing that should be taken into account is that either parabolic model or logarithmic spiral model is equation in the diffracted wave area. Therefore, it can be stated that the curve shape of the stable coast is the result of diffracted wave. c. Shoreline Change Model Some of the above theories on stable coastal geometry are stable coastal geometry between two headlands, whereas on stable coastal geometry between two groins, no research has been done, where at the down drift groin, coastal geometry is shaped by diffracted wave. Changes in coastline around the groin can be modeled with shoreline change model. The first shoreline change model was developed by Pelnard-Considere      It should be noticed that at the longshore equation of the transport sediment, the volume of transport sediment longshore is determined by the angle of the incoming wave, and the higher the angle of the incoming wave the higher the velocity of the secondary longshore current and the bigger the littoral drift will be. Therefore, this secondary longshore current is a protector for part of the beach around down drift groin against erosion. The longer the groin, the larger the shadow zone area will be, and the bigger the secondary longshore current, the smaller the erosion or even the presence of sedimentation.

III. STATIC EQUILIB RIUM SHORELINE EQUATION BETWEEN TWO GROINS
The result of the study on section II. is that stable coastal geometry, between two headlands and also between two groins, consists of two parts, i.e. curve part and linear part. The curve part is formed by diffracted wave, whereas the linear part is formed by incident wave, where the linear part is perpendicular to wave direction or parallel with coastline.

International Journal of Advanced Engineering Research and Science (IJAERS)
[ sedimentation could occur at the downstream groin, where the higher the angle of the incoming wave, the larger the sedimentation will be (2). From the result of the study on part II, a hypothesis line for the static equilibrium shoreline geometry between two groins is made as presented in Fig.7, where there is linear part (straight line) and curve line. This is in accordance with parabolic theory. The straight part (BD line) is perpendicular to incident wave, which is the requirement for stable coastal line so that there will be no littoral drift, whereas the curve part is formed by diffracted wave.

V. APPLICATION FOR THE GROIN PLANNING
The aim of shore protection using groin is to prevent erosion at coastal segment between two groins, where the actual erosion is still happening. Therefore, as the parameter for the planning of groin is the permitted maximu m of the erosion. Erosion can be limited by arranging the distance between groin and the length of groin so that the erosion that happens does not exceed the permitted erosion. For example, with the calculation on table (2) with the permitted erosion of 5 m, for angle of incoming wave of 25 o , then distance between groin that can be used is 100 m, with the length of groin 40m, and with this length the sand bypassing at the updrift groin will not happen since the sedimentation is only 14.0 m.

VI.
CONCLUSION At the method that is developed, there are the effects of the length of groin and the distance between groin s on erosion as well as sedimentation. In addition, this method can also represent the effect of secondary longshore current from Van Rijn   11 , so it can be said that this method can predict erosion and sedimentation at the coastal segment between two groins and the geometry static equilibrium condition of its shoreline. The method that is developed in this research can also be used to conduct initial estimation on the length of groin and the distance between groins, for preliminary study at a planning of coastal protection using groin. For further development, a research should be done by comparing the equation with the result of physical model.