## 3 Effects of Rainfall and Groundwater on the Strain  
The data detected by strainmeters in Taiwan contain some response strains regarding natural environmental factors such as air pressure, tide, and especially hydrology. In a subtropical environment with an annual rainfall of 2500 mm on average such as in Taiwan, the hydrology generally has a strong effect on the observed strain. The effects of continuous heavy rainfall on the observed strain can be divided into two parts: (1) A large volume of rainwater falls in a short period of time, causing an increase of the external pressure on the rocks due to the extra loading of the rainwater. The rainwater that cannot infiltrate into the ground becomes land-surface runoff and rapidly merges into creeks. This will respond rapidly in hours since rainfall began, which is called the rainfall quick response (RQR); and (2) water slowly sinks into the strata to complement the groundwater level, which will last for several days to a few weeks due to the low permeability of the strata. This is called rainfall slow response (RSR) or base flow. Strainmeter is designed to record the deformation behavior of the rock under stress. However, because the steel cylindrical strainmeter does not allow fluid flow into or out of the cylinder, the response of strainmeter is the same as the strain in the rock only when the rock remains undrained [42]. Checks the strain data during heavy rain, it shows a compressional strain within a short time after the loading of heavy rain, then gradually expands as groundwater pressure increasing with time (Figure 3). This is different from the change of groundwater pressure under stress. When the rock is subjected to external stress in instant, the water in the rock cannot be drained immediately because of the low permeability of the rock, which can be considered as the undrained condition. In the undrained case, when the whole rock is compressed, the water pressure inside the rock will increase and the extra pore pressure will squeeze the strainmeter inwards. Both the instrument strain and rock strain show compression during this period. Next, the process of rainwater permeating into strata is continuous and slow, extra pore pressure can be balanced as water flowing. In this drained condition, the strainmeter showed expansion as groundwater pressure rose. However, these changes only reflect the balance of internal stress in the strata, there is no actual change in the far-field strain. Considering that the observed strain is closely related to the groundwater changes, a widely used recursive digital filter technique in hydrology was adopted in this study to separate quick and slow rainfall responses. The basic equation for recursive digital filter simply expressed as the following [43]:  
\[F_{i}=\lambda F_{i-1}+\frac{1+\lambda}{2}(H_{i}-H_{i-1}) \tag{10}\]  
where \(F_{i}\) and \(F_{i-1}\) are the filtered responses and \(H_{i}\) and \(H_{i-1}\) are the strain at the \(i\)th and \((i-1)\)th sampling instants, respectively; \(\lambda\) is the filter parameter. Under the condition of 1800 sps (seconds per sample) preset in this study, we gave \(\lambda=0.996\) into the Equation (10) to create a high-pass filter that can effectively filter out the low-frequency signals with a period of around five days. The high-frequency signals can then be separated from the observed strain to identify the rainfall quick responses (RQRs). We could obtain the strain corresponding to the rainfall load from the observed strain. Furthermore, we need to acquire the rainfall impact function \(R_{i}(t)\), which describes the whole responding process of each single unit of rainfall falling on the ground before flowing out of the effective area around the station. \(R_{s}(\tau)\) is the rainfall record in half an hour in  
Figure 3: The diagram shows the relation between the strainmeter strain and groundwater pressure induced by rainfall. Data from the DARB station located in Southern Taiwan (location shown in Figure 1). this study. Set \(\tau\) as the unspecified time change.