2.2.2 Land subsidence model

minimizing the land subsidence effect on flood hazard while, at the same time, satisfying the water demand. After obtaining the optimal pumping strategy, the corresponding land subsidence amounts are obtained to define the land topography in Year 2021. Under a different topography, the corresponding flood hazard indicators and inundation damage are obtained for assessing the effect of GWM.

The well-known SOBEK Suite [14], developed by the Deltares Research Institute

The major inputs to the SOBEK 1D/2D simulation for this study are as follows:

1. Rainfall hyetograph: 24-hour design rainfall with six design frequencies (i.e., 2-, 5-, 10-, 25-, 50-, and 100-year) was used. Their corresponding rainfall amounts were 158, 227, 275, 337, 384, and 432 mm, respectively. All six design storm events follow the same dimensionless rainfall pattern as shown in Figure 2 [15]. For simplicity, no spatial variation of rainfall in the study area was

connected to the Taiwan Strait, the boundary condition at the downstream end sections was assigned with a wave form shown as the dash line in Figure 2.

3.Channel profile and DEM: the cross-sectional profile along the drainage lines and DEM within the study area were surveyed in 2012. By considering the trade-off between the accuracy and computational efficiency of hydrodynamic simulation, the grid for the 2D overland flow simulation was set to 120 m. To simulate flood hazard with the projected land subsidence in 2021, the ground

Dimensionless 24-hr design rainfall hyetograph and the downstream tide level for boundary condition [15].

2. Downstream boundary: since major drainage lines in the study area are

in the Netherlands, was used in the study to model flood inundation and the associated hazard. Specifically, the hydrodynamic module, which contains 1D-flow and 2D-overland flow submodules, was used to simulate surface water flow in the study area for determining the levee freeboard and inundation depth under the

2.2 Inundation and land subsidence models

Recent Advances in Flood Risk Management

2.2.1 Inundation model

considered.

Figure 2.

22

selected design rainfall events.

In this study, land subsidence is assumed to be caused by groundwater pumping. An uncoupled model consisting of a layered 3D groundwater solver and a 1D consolidation model was used to simulate land subsidence [17]. The layered 3D groundwater solver is first used to simulate depth-averaged groundwater flow and pore pressure head change due to groundwater extraction in every layer at each time step. The vertical soil displacement during each time step is then calculated by the 1D consolidation equation. The simulation model assumes (1) isotropic soil medium, (2) linear elasticity relationship between average effective stress and average displacement following Hooke's law, and (3) vertical displacements only. These assumptions, however, ignore the presence of the preconsolidation head, which implies that a decrease in pore pressure head due to groundwater extraction will always cause normal consolidation and is unable to consider overconsolidation and rebound (i.e., elastic range). This renders overestimation of land subsidence.

To simultaneously consider the inelastic/elastic behavior of land subsidence, Chang et al. [12] modified the 1D consolidation equation according to Leake [18] as

$$\Delta \mathbf{s}\_{l,k,t} = \begin{cases} \alpha \mathbf{C}\_{\varepsilon} \left( \Delta \mathbf{h}\_{l,k,t-1}^{p} - \Delta \mathbf{h}\_{l,k,t-1} \right) + \mathbf{C}\_{\varepsilon} \left( \Delta \mathbf{h}\_{l,k,t} - \Delta \mathbf{h}\_{l,k,t-1}^{p} \right), \Delta \mathbf{h}\_{l,k,t} > \Delta \mathbf{h}\_{l,k,t-1}^{p} \\\\ \alpha \mathbf{C}\_{\varepsilon} \left( \Delta \mathbf{h}\_{l,k,t} - \Delta \mathbf{h}\_{l,k,t-1}^{p} \right), \Delta \mathbf{h}\_{l,k,t} \le \Delta \mathbf{h}\_{l,k,t-1}^{p} \end{cases} \tag{1}$$

$$
\Delta \mathbf{h}\_{\mathbf{l}, \mathbf{k}, \mathbf{t}}^{\mathbf{p}} = \mathbf{M} \mathbf{a} \mathbf{x} \left[ \Delta \mathbf{h}\_{\mathbf{l}, \mathbf{k}, \mathbf{t}}, \Delta \mathbf{h}\_{\mathbf{l}, \mathbf{k}, \mathbf{t}-\mathbf{1}}^{\mathbf{p}} \right] \tag{2}
$$

where Δsl,k,t = land subsidence within layer-l at control point-k during the t-th time period; Δhl,k,t = drawdowns of layer-l at control point-k at the end of the t-th time period; α (< <1) = ratio of elastic to inelastic compaction per unit increase in drawdown; Cc = ρwgB/(2 μ + λ) with ρ<sup>w</sup> = density of water, g = gravitation


Table 2. Relationship between the Nikuradse roughness coefficient kn and land use [15]. acceleration, B = layer thickness, and μ, λ = Lame constants; and Δh p l,k,t = difference between initial head and preconsolidation head at the end of the t-th time period. The positive value of Δh p l,k,t denotes that the initial head is higher than the preconsolidation head. The total land subsidence amount at the control point-k can be determined by

$$
\Delta \sigma(k) = \sum\_{l=1}^{NL} \sum\_{t=1}^{NT} \Delta \sigma\_{l,k,t} \tag{3}
$$

Minimize max ½ � Δs kð Þ uc kuc ¼ 1, …, NUC (4)

Q j ð Þ ; t ≥ QDð Þt t ¼ 1, …, NT (6)

<sup>Q</sup>Lð Þ <sup>j</sup>; <sup>t</sup> <sup>≤</sup> Q j ð Þ ; <sup>t</sup> <sup>≤</sup> <sup>Q</sup>Uð Þ <sup>j</sup>; <sup>t</sup> (7)

ð Þ kc kc ¼ 1, …, NC (5)

∗

in which kuc = the kuc-th control point outside the near-shore low-lying area;

NP = number of pumping wells; Q j ð Þ ; t = pumping rate at the j-th well during the tth time period; QDð Þt = groundwater demand during the t-th time period; and <sup>Q</sup><sup>L</sup>ð Þ <sup>j</sup>; <sup>t</sup> ,Q<sup>U</sup>ð Þ <sup>j</sup>; <sup>t</sup> = minimum and maximum allowable pumping rates, respectively,

The objective function Eq. (4) is to minimize the maximum land subsidence among all control points outside the near-shore low-lying area. The consideration of Eq. (4) can optimally reduce the magnitude and spatial variation of land subsidence outside the near-shore low-lying area. On the other hand, for any control point within the near-shore low-lying area, constraint Eq. (5) that directly limits the land subsidence can be imposed to prevent flood hazard from worsening due to the

To demonstrate the positive contribution of GWM to flood hazard reduction in land subsidence prone areas, the optimal groundwater pumping model developed

The study area chosen has a catchment area of 267 km<sup>2</sup> located in the northwest part of Yunlin County, Taiwan (see Figure 3). The northern boundary of the study area is defined by the Zhuoshui River, the longest river in Taiwan, and the western boundary is adjacent to the Taiwan Strait. The study area covers nine townships and has four drainage systems consisting of Shihtsoliao, Yutsailiao, Makungtso, and Chiuhuwei. The mean annual rainfall in the study area is about 1200 mm of which about 80% of rainfall occurs between May and September due to monsoons and typhoons (see Table 3). Despite the fact that the mean annual rainfall in the study area is less than half of the average value in Taiwan (i.e., 2500 mm), the study area is still highly susceptible to flood hazard due to its low lying and flat terrain. Figure 4 is the topographic map of the study area, which shows its ground elevation ranging from �1.0 to 28 m with reference to the mean sea level. The eastto-west average land surface gradient is less than 1/1000 indicating that the surface runoff produced by heavy rainfall can be easily trapped in the study area. Furthermore, ground elevation in the downstream part of the study area is lower than the average spring high tide of 2.1 m. This implies that flood water in the drainage channels from a rainstorm event may not be effectively drained into the Taiwan

by Chang et al. [13] is applied here to a selected study area in Taiwan.

kc = the kc-th control point within the near-shore low-lying area; NUC and NC = number of control points outside and inside the near-shore low-lying area, respectively; Δs(•), Δs\*(•) = cumulated and the maximum allowable land subsidence, respectively, at control points at the end of the management period;

Subject to Δs kð Þ<sup>c</sup> ≤Δs

Flood Damage Reduction in Land Subsidence Areas by Groundwater Management

∑ NP j¼1

DOI: http://dx.doi.org/10.5772/intechopen.80665

at the j-th well during the t-th time period.

reduced levee freeboard.

3. Model application

3.1 Description of the study area

Strait due to the backwater effect.

25

where NL, NT = the numbers of layer and time period, respectively. More detailed descriptions on the land subsidence model can be found in the studies of Chang et al. [11, 12].

In the process of developing the groundwater subsidence model for the study area, monitored data on pore pressure head and land subsidence during 2007–2009 were used to calibrate the model parameters such as hydraulic conductivity and soil compaction coefficients. Then, monitored data made in 2010–2011 were used for validation. The validated model was used to predict the cumulative land subsidence in the study area over a 10-year period during 2012–2021. Calibration and validation of pore pressure head and land subsidence in the study area were found quite satisfactory for pore water pressure and less satisfactory for land subsidence [13]. The reason might be because groundwater extraction alone is not the only cause for land subsidence. In addition, the 1D consolidation equation used in the land subsidence model cannot account for the body force and viscoelastic effects, which might have influences on land subsidence in thick aquitards. However, the validation results indicate that the simulation model can reasonably reproduce the general pattern of land subsidence in both time and space.

## 2.3 Optimal groundwater pumping model

Before developing a viable GWM for optimal pumping in the study area, insights were gained by applying the validated simulation model to examine the subsidence behavior under the existing pumping practice. The simulation results indicated that the levee freeboard and maximum inundation depth have a similar tendency in spatial variation affected by land subsidence. Both tend to become worsened in the near-shore low-lying area due to reduced difference between the sea level and levee crown elevation. Thus, continuing land subsidence would worsen the flood hazard in this area, and the results are consistent with those of Ward et al. [4] and Wang et al. [5]. On the other hand, outside the near-shore low-lying area, it was found that the freeboard and maximum inundation depth do not necessarily get worse. This is because the influence of the downstream boundary condition defined by the sea level is minimal. Instead, the relative variation of land subsidence in space becomes the dominant factor affecting the changes in freeboard and maximum inundation depth because it alters the slopes of drainage channels and the land surface.

By incorporating the above insights about land subsidence—flood hazard interrelationship, an effective GWM model can be developed for reducing the undesirable pumping-induced land subsidence and flood hazard in the study area. For the near-shore low-lying area, one could reduce the land subsidence amount because flood hazard is highly related to the magnitude of land subsidence. For the region outside the near-shore low-lying area, one could reduce the relative variation of land subsidence in space to prevent flood hazard from worsening. The optimal groundwater pumping model can be formulated as

Flood Damage Reduction in Land Subsidence Areas by Groundwater Management DOI: http://dx.doi.org/10.5772/intechopen.80665

$$\text{Minimize } \max \left[ \Delta \mathbf{s}(\mathbf{k}\_{\text{uc}}) \right] \mathbf{k}\_{\text{uc}} = \mathbf{1}, \dots, \text{NUC} \tag{4}$$

$$\text{Subject to } \Delta s(k\_c) \le \Delta s^\*(k\_c) \, k\_c = \mathbf{1}, \dots, \text{NC} \tag{5}$$

$$\sum\_{j=1}^{NP} Q(j, t) \ge Q\_D(t) \; t = 1, \dots, NT \tag{6}$$

$$Q^L(j,t) \le Q(j,t) \le Q^U(j,t) \tag{7}$$

in which kuc = the kuc-th control point outside the near-shore low-lying area; kc = the kc-th control point within the near-shore low-lying area; NUC and NC = number of control points outside and inside the near-shore low-lying area, respectively; Δs(•), Δs\*(•) = cumulated and the maximum allowable land subsidence, respectively, at control points at the end of the management period; NP = number of pumping wells; Q j ð Þ ; t = pumping rate at the j-th well during the tth time period; QDð Þt = groundwater demand during the t-th time period; and <sup>Q</sup><sup>L</sup>ð Þ <sup>j</sup>; <sup>t</sup> ,Q<sup>U</sup>ð Þ <sup>j</sup>; <sup>t</sup> = minimum and maximum allowable pumping rates, respectively, at the j-th well during the t-th time period.

The objective function Eq. (4) is to minimize the maximum land subsidence among all control points outside the near-shore low-lying area. The consideration of Eq. (4) can optimally reduce the magnitude and spatial variation of land subsidence outside the near-shore low-lying area. On the other hand, for any control point within the near-shore low-lying area, constraint Eq. (5) that directly limits the land subsidence can be imposed to prevent flood hazard from worsening due to the reduced levee freeboard.
