**5. Numerical simulation**

#### **5.1 Calculation conditions**

Topographic changes around the artificial reefs built on Kimigahama Beach under the combined actions of waves and wind were calculated using a model in which the

*Numerical Simulation on Sand Accumulation behind Artificial Reefs and Enhancement… DOI: http://dx.doi.org/10.5772/intechopen.107014*


#### **Table 1.**

*Calculation conditions.*

BG model was combined with a cellular automaton method for predicting the amount of windblown sand. **Table 1** shows the calculation conditions. The grain size of the seabed material was set to be 0.2 mm from the grain size measured on the backshore along transect No. 4. In the bathymetric chart in **Figure 4**, no topographic changes can be seen offshore of the opening of the artificial reefs, so the depth of closure due to waves was set to 5.0 m. The equilibrium slope was assumed to be 1/10 from the foreshore slope along transect No. 4, as shown in **Figure 5**. The berm height was given by the height of the break in the slope of 2 m. Since the predominant wave direction is E, as shown in **Figure 3**, wave direction was set to be E. The coefficients *b*<sup>1</sup> and *b*<sup>2</sup> and the mass of moving sand *<sup>q</sup>* were assumed to be *<sup>b</sup>*<sup>1</sup> = 10, *<sup>b</sup>*<sup>2</sup> = 0.5, and *<sup>q</sup>* = 2.5 <sup>10</sup><sup>6</sup> m3 /m<sup>2</sup> /step on the basis of the rate of windblown sand of 2.5 m<sup>3</sup> /m/yr measured along transect No. 4. In the numerical simulation, the topographic changes were predicted in Cases 1 and 2 without/with windblown sand, respectively.

### **5.2 Results of numerical simulation**

The initial topography for the calculation was assumed to have a foreshore slope of 1/10 and a 1/50 slope in the offshore zone deeper than 1 m. Then, waves were incident in this assumed initial topography for a sufficiently long time (10 years) to obtain the beach topography before the installation of the artificial reefs. By this calculation, we carried out the matching of beach topography to the given wave conditions. **Figure 17**

**Figure 17.** *Beach topography adjusted to the given wave conditions.*

shows the result. Then, two artificial reefs and a seawall with a height of 6 m were installed along the shoreline. **Figure 18** is thus the obtained initial topography. Since the seabed with a depth equal to or larger than 2 m is covered with exposed rocks, solid bed was assumed in these areas.

**Figure 19** shows the results of the calculation in Case 1, that is, under waves without the wind effect, after the installation of the artificial reefs. The shoreline advanced owing to the alongshore sand transport toward the lee of the two artificial reefs with an increase in the beach width. Moreover, two salients with a berm height of +2 m were formed behind the artificial reefs.

Then, the calculation in Case 2, that is, with the wind effect, was carried out, given the same topography as that in Case 1. The beach topography and topographic changes relative to the initial topography in Case 2 are shown in **Figure 20**. It is seen that the

**Figure 18.** *Initial topography.*

*Numerical Simulation on Sand Accumulation behind Artificial Reefs and Enhancement… DOI: http://dx.doi.org/10.5772/intechopen.107014*

**Figure 19.** *Predicted topography only under wave action.*

beach width increased behind the artificial reefs, and sand was transported by wind from the foreshore to inland causing the deposition of sand in front of the seawall. Furthermore, part of the windblown sand was transported into the hinterland over the seawall.

**Figure 21** shows for comparison of the beach profiles in Cases 1 and 2 along the transect across *X* = 920 m, as shown by dotted lines in **Figures 19** and **20**. In Case 1, only a flat, plane beach with an elevation of +2 m was formed. In Case 2, however, sand was transported landward by wind, forming a steep slope of 1/7.5 in front of the seawall up to the crown height of +6.0 m of the seawall, whereas the shoreline has retreated because part of the beach sand was transported landward by wind. This result well explains the formation of a 1/5 slope (**Figures 5d** and **9**) from the shoreline to the top of the seawall, which was observed in the field. It is concluded that installing a wave-dissipating structure, such as an artificial reef, on a coast composed of fine and medium-size sand induces the concentrated deposition of sand in the lee of the structure and the decrease in sand volume and the shoreline recession in the entire area.

#### **5.3 Prediction of beach changes**

In Case 3, topographic changes were predicted under the condition that beach nourishment was carried out using sand of the same grain size as that at the present coast at a location where the beach width decreased after the construction of the artificial reefs. **Figure 22a** and **b** show the initial topography in Case 3 and the change in beach elevation under the condition with/without beach nourishment using sand with a volume of 17,000 m<sup>3</sup> behind the openings of the two artificial reefs.

**Figure 23a** and **b** show the results of the prediction and the topographic changes relative to the initial topography in Case 3. In this case, alongshore sand transport continues to occur from the nearby beach to the lee of the artificial reefs, and the salients also continued to develop in the lee of the artificial reefs. Therefore, part of beach nourishment sand was transported over the seawall to the hinterland owing to

#### **Figure 20.**

*Beach topography and topographic changes in Case 2 with wind action. (a) Predicted topography. (b) Topographic changes relative to initial topography.*

**Figure 21.** *Longitudinal profiles along transect across X = 920 m in Cases 1 and 2.*

*Numerical Simulation on Sand Accumulation behind Artificial Reefs and Enhancement… DOI: http://dx.doi.org/10.5772/intechopen.107014*

**Figure 22.**

*Beach topography and topographic changes in Case 3 with beach nourishment. (a) Initial topography. (b) Change in beach elevation relative to initial topography.*

the wind effect. Because part of beach nourishment sand was transported away to the hinterland, the effect of beach nourishment is minimal in increasing the beach width.

In Case 4, the artificial reefs were removed to investigate their adverse effects using the bathymetry shown in **Figure 22a** as the initial bathymetry. **Figure 24a** and **b** show the results of the calculation in Case 4 when artificial reefs were removed, and the change in topography relative to the initial topography. Owing to the removal of artificial reefs, salients that formed in the lee of the artificial reefs disappeared, and nourishment sand was transported to the entire pocket beach, resulting in the sand deposition in the entire area except behind the artificial reefs. Furthermore, since the sand deposition was no longer concentrated behind the artificial reefs owing to the removal of artificial reefs, the amount of sand blown over the seawall to the hinterland has greatly decreased.

**Figure 23.**

*Predicted topography and topographic changes in Case 3 with beach nourishment. (a) Predicted topography in Case 3. (b) Topographic changes in Case 3 relative to initial topography.*
