**Table 1.**

*Calculation conditions.*

bathymetry in 1920 (**Figure A1**). During the first period, the parallel contours in 1899 simply advanced by 42 m until 1920, so that a new coordinate was taken for the shoreline to be shifted by 42 m seaward. During the second period, a V-shape shoreline recession began around the river mouth because of the decrease in *Q*in from 4.7 105 m3 /year before 1920 to 1.5 105 m3 /year. However, the contour lines far

addition, *θ*<sup>1</sup> and *θ*<sup>2</sup> are approximately given by 7.5° and 2.5°, respectively, from the geographical map in 1899, as shown in **Figure 10**. Thus, after the trial-and-error calculation of the shoreline changes, while satisfying the relation of *θ*1/*θ*<sup>2</sup> = 3, we obtained *θ*<sup>1</sup> = 12° and *θ*<sup>2</sup> = 4° for the best fit results. Finally, a linear distribution shown in **Figure 11(a)** was assumed with angles of 12° and 4° immediately west and east of the Hino River mouth, respectively. **Figure 11(b)** shows the distribution of longshore sand transport at the initial stage. For the wave condition, the breaker height was determined as *H*<sup>b</sup> = 1.1 m on the basis of the energy mean significant wave height measured between 1995 and 2008 at Hiezu wave observatory.

*Wave direction and distribution of longshore sand transport used for calculation. (a) Wave direction.*

*Sedimentary Processes - Examples from Asia,Turkey and Nigeria*

The initial seabed slope was assumed to be 1/6 between *z* = +3 and 2 m, and 1/30

1/30 and 1/6, on the basis of the measured longitudinal profile. As for the sand back pass on the coast, sand was extracted from the foreshore with an elevation between 0 and + 3 m at *x* = 13 km, and the same amount of sand was supplied from the foreshore

**Figure 12** shows the bathymetric changes from the first to the fourth periods together with an additional expression of bathymetric changes relative to the

(2) of fine and coarse sand were, respectively, assumed to be

between *z* = 2 and 8 m. The number of grain sizes (*N*) was set to 2 with characteristic grain sizes of *d*(1) = 0.3 mm for fine sand and *d*(2) = 0.5 mm for coarse sand. The initial contents *μ*<sup>1</sup> and *μ*<sup>2</sup> for fine and coarse sand were, respectively, assumed to be 0.0 and 1.0 in the cell between *z* = +3 and 1 m, 0.5 and 0.5 in the cell at *z* = 2 m, and 1.0 and 0.0 in the cell between *z* = 3 and 8 m. The equilibrium

at *x* = 8 km. **Table 1** summarizes the other calculation conditions.

slopes tan*β*<sup>c</sup>

**74**

**Figure 11.**

*(b) Longshore sand transport.*

(1) and tan*β*<sup>c</sup>

**5.2 Results of numerical simulation**

period, however, the contour lines continued to advance far from the river mouth. During the fourth period, a seawall was constructed west of the river mouth blocking westward longshore sand transport partially, so that the contour lines

*A Long-Term Prediction of Beach Changes around River Delta using Contour-Line-Change Model*

The shoreline changes in the entire period relative to that in 1920 can be drawn, as shown in **Figure 13**. The shoreline advanced by 42 m between 1899 and 1920 because of the accretion of the entire river delta. After 1920, however, the shoreline receded around the river delta owing to the decrease in sand supply, whereas the

**Figure 14** shows the measured and predicted shoreline changes with reference to the shoreline in 1899 and 1947. Regarding the shoreline changes until 1947, the

/year.

receded west of the seawall, even if *<sup>Q</sup>*in was maintained at 6 104 m3

*Measured and predicted shoreline changes between 1899 and 1947 and between 1947 and 1967.*

shoreline continued to advance far from the river mouth.

*DOI: http://dx.doi.org/10.5772/intechopen.85207*

**Figure 13.**

**Figure 14.**

**77**

*(a) 1899–1947. (b) 1947–1967.*

*Shoreline changes with reference to that in 1920.*

**Figure 12.**

*Bathymetric changes from the first to fourth periods. (a) First period (1899–1920). (b) Second period (1920–1947). (c) Third period (1947–1962). (d) Fourth period (1962–1967).*

from the river mouth continued to advance because of the successive supply of sand to both sides of the river mouth. During the third period, the shoreline markedly receded around the river mouth because of the further decrease in *<sup>Q</sup>*in from 1.5 105 to 6 104 m3 /year owing to the stoppage of mining of iron sand. Even during this

*A Long-Term Prediction of Beach Changes around River Delta using Contour-Line-Change Model DOI: http://dx.doi.org/10.5772/intechopen.85207*

period, however, the contour lines continued to advance far from the river mouth. During the fourth period, a seawall was constructed west of the river mouth blocking westward longshore sand transport partially, so that the contour lines receded west of the seawall, even if *<sup>Q</sup>*in was maintained at 6 104 m3 /year.

The shoreline changes in the entire period relative to that in 1920 can be drawn, as shown in **Figure 13**. The shoreline advanced by 42 m between 1899 and 1920 because of the accretion of the entire river delta. After 1920, however, the shoreline receded around the river delta owing to the decrease in sand supply, whereas the shoreline continued to advance far from the river mouth.

**Figure 14** shows the measured and predicted shoreline changes with reference to the shoreline in 1899 and 1947. Regarding the shoreline changes until 1947, the

**Figure 13.** *Shoreline changes with reference to that in 1920.*

#### **Figure 14.**

*Measured and predicted shoreline changes between 1899 and 1947 and between 1947 and 1967. (a) 1899–1947. (b) 1947–1967.*

from the river mouth continued to advance because of the successive supply of sand to both sides of the river mouth. During the third period, the shoreline markedly receded around the river mouth because of the further decrease in *<sup>Q</sup>*in from 1.5 105

*Bathymetric changes from the first to fourth periods. (a) First period (1899–1920). (b) Second period*

*(1920–1947). (c) Third period (1947–1962). (d) Fourth period (1962–1967).*

*Sedimentary Processes - Examples from Asia,Turkey and Nigeria*

/year owing to the stoppage of mining of iron sand. Even during this

to 6 104 m3

**76**

**Figure 12.**

overall shoreline changes were reproduced well, except for the river mouth area where the shoreline change was underestimated. Regarding the shoreline changes until 1967, the shoreline changes in the overall area including the shoreline recession west of the seawall constructed immediately west of the river mouth were well reproduced. The predicted and measured shoreline changes are in good agreement.

calculation, the changes in contour lines between +3 and 8 m were calculated, assuming the same seabed slopes of 1/6 between *z* = +3 and 2 m, and 1/30 between *z* = 2 and 8 m. The number of grain sizes (*N*), the grain sizes of fine and coarse sand, the initial contents of each grain size of *μ*<sup>1</sup> and *μ*2, the equilibrium slope corresponding to each grain size, and the wave conditions are the same as those in the reproduction calculation. The longshore distribution of the initial breaker angle was given by subtracting the inclination angle of the shoreline reproduced in 1947 from the initial breaker angle in 1899. The change in wave field by the construction of structures was calculated using the angular spreading method for irregular waves. The wave transmission coefficient of detached break-

*A Long-Term Prediction of Beach Changes around River Delta using Contour-Line-Change Model*

waters was set to *K*<sup>t</sup> = 0.2 as shown in **Table 2**, except for the detached

**6.2 Results of the reproduction calculations**

*DOI: http://dx.doi.org/10.5772/intechopen.85207*

because of the decreased *<sup>Q</sup>*in of 6 <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup>

decreased from 6 104 to 4.7 <sup>10</sup><sup>4</sup> m3

whereas the contour lines advanced west of *x* = 5 km.

decrease in the westward longshore sand transport.

many coastal structures, erosion is severe downcoast.

sand was excavated at a rate of 3 <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup>

In the fourth period, although *<sup>Q</sup>*in was the same (4.7 <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup>

*<sup>x</sup>* = 0 and 1.5 km, although *<sup>Q</sup>*in was the same (6 <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup>

artificial reefs.

at 4.7 <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup>

became straight.

**79**

*6.2.1 Change in contour lines*

breakwaters with *K*<sup>t</sup> = 0.4 placed between *x* = 1.4 and 0.5 km, and *K*<sup>t</sup> = 0.8 for

**Figure 15** shows the calculation results between the first and fifth periods together with an additional expression of bathymetric changes relative to the bathymetry in 1947 (**Figure A2**). In the first period (**Figure 15(a)**), erosion concentrated around the Hino River mouth with gradual accretion west of *x* = 4 km

out using the expanded coordinates set on the shoreline in 1947, the triangular shoreline recession area shown in **Figure 15(a)** corresponds to the recession of the protruded shoreline of a river delta. The shoreline receded around the river mouth,

In the second period (**Figure 15(b)**), the seawall had been constructed between

period. Owing to the construction of the seawall, westward longshore sand transport was partially blocked at the protruded seawall, resulting in erosion immediately west of the structure with the accretion upcoast. In the third period, *Q*in

DBs and Kaike fishing port breakwaters (**Figure 15(c)**). Soon after the construction of DBs, cuspate forelands were formed behind the DBs. Simultaneously, severe erosion occurred downcoast of Kaike fishing port located at *x* = 3 km because of the

the third period, new DBs were constructed between *x* = 3.5 and 2.5 km, and between 3.5 and 7 km, and further seawall was constructed between *x* = 5 and 0 km, and between *x* = 3.5 and 13 km, as shown in **Figure 15(d)**. At this stage, land reclamation was carried out at the west end at the shoreline, and the shoreline length was decreased by 4 km, resulting in the advance of all the contour lines. Although the shoreline east of the structures was stabilized by the construction of

In the fifth period between 1995 and 2010 (**Figure 15(e)**), *Q*in was kept constant

amount was supplied at *x* = 8 km. In addition to this, an L-shaped groin was constructed at *x* = 7 km, and an artificial reef and DBs were constructed between *x* = 5 and 0 km. The effect of blocking longshore sand transport by the land reclamation reached upcoast, and the contour lines between *x* = 13 and 7 km

/year, the same as that in the fourth period. For the sand back pass,

/year. Since the calculation was carried

/year together with the construction of 12

/year at *x* = 13 km, and the same

/year) as that in the first

/year) as that in
