Effects of flow dimension in faulted or fractured rock on natural reductions of inflow during excavation: a case study of the Horonobe Underground Research Laboratory site, Japan

Major inflows of groundwater can occur during excavation in faulted or fractured rock masses, even if pre-excavation grouting is applied; postexcavation grouting may then be required to reduce these inflows. However, the diffusion equation for fluid pressure suggests that inflows may reduce naturally by 50–90% or more within days or weeks when the dimension of the flow in faults or fractures that feed the inflow (flow dimension) is close to 1, but inflow reduction is minimal when the flow dimension is close to 3. Therefore, if the flow dimension is close to 1, the natural reduction in inflow may obviate countermeasures. Nevertheless, this natural reduction being dependent on flow dimension is seldom considered explicitly when planning excavations or countermeasures. To verify the applicability of the relationship between natural changes of inflow and the flow dimension, this study measured changes in inflow at six locations at the Horonobe site, Japan, where major inflows occurred during excavations of tunnels or shafts in faulted or fractured siliceous rocks. The flow dimension at each location was assessed using pre-excavation packer tests in surface-based boreholes. The results confirm that changes in the inflows during the days and weeks immediately after their commencement depended consistently on the assessed flow dimension. Natural reductions in inflow during excavation are predictable based on the flow dimension, which can be estimated using pre-excavation borehole investigations or from the initial changes in inflow during the first several days. This approach may be helpful for improving the efficiency of excavations.


Introduction
Inflows during excavation of deep faulted or fractured rock masses represent a critical issue in a variety of fields including tunnel construction, mining, and radioactive waste disposal (Coli and Pinzani 2013;Loew et al. 2015;Mas Ivars 2006;Su et al. 2022;Yu et al. 2021). The inflows may need substantial reduction depending on requirements at the site, and countermeasures such as pre-excavation grouting (e.g., Barton and Quadros 2019) should be conducted in advance to reduce the inflows during excavation when preliminary investigations predict them to exceed an acceptable limit. However, unexpected large inflows may occur during excavation, even if pre-excavation grouting is applied (e.g., Ishii and Furusawa 2017). Once the inflows exceed the limit, countermeasures such as postexcavation grouting must be planned and implemented. Nevertheless, postexcavation grouting deep underground is generally harder than preexcavation grouting because of the high water pressure and the difficulty of securing sufficiently thick rock cover (Ehrbar et al. 2013;Japan Atomic Energy Agency 2015).
Although large inflows can substantially affect the schedule and cost of excavation, inflows may naturally decrease with time without postexcavation grouting, depending on the site conditions, possibly obviating the need for countermeasures. An example is a major inflow at the Horonobe Underground Research Laboratory (URL) in Hokkaido, Japan (Fig. 1). During excavation of a clay-rich shear zone, the total inflow at the URL rose to 1,200 m 3 /day, exceeding the limit of 750 m 3 /day (Ishii and Furusawa 2017), but it naturally dropped to 500 m 3 /day within 10 days (Japan Atomic Energy Agency 2015). Such a natural reduction could be helpful when considering countermeasures to sudden major inflows 1 3 during excavation. A major inflow also occurred during the excavation of a permeable fault zone at the Gotthard Base Tunnel in Switzerland, which was postexcavation grouted to reduce the inflow; however, the resultant reduction in inflow was attributed largely to natural causes (Loew et al. 2015).
Following the diffusion equation for fluid pressure, natural reductions in inflow can be related to the flow dimension, although they can also be affected by the far-field boundary conditions (Barker 1988;Doughty 1995). The relationship between the inflow and flow dimensions is as follows: a flow dimension of 3 indicates that the inflow is caused by a pressure pulse propagating three-dimensionally (spherically) far from the inflow location through flow paths that are well connected in three dimensions within faults or fractures (Fig. 2a). However, the flow dimension decreases, with reducing void (flow path) areas within faults or fractures, and a flow dimension of 1 indicates that the inflow is caused by a pressure pulse propagating one-dimensionally far from the inflow location through continuous one-dimensional (1D; channelized) flow path(s) within a single (or several) fault(s) or fracture(s)- Fig. 2b; Figueiredo et al. (2016); Fransson et al. (2010); Lisa et al. (2012); Ohno and Ishii (2022). Simulating changes in inflow with time for a tunnel of radius 4 m and hydraulic diffusivity (K/S s , where K is hydraulic conductivity and S s is specific storage) of 0.01-10 (a typical range inferred for major inflows), the inflow hardly reduces after commencement when the flow dimension is 3, but it reduces to one-third within 10 days of commencement and to one-tenth within 100 days when the flow dimension is 1, as shown in Fig. 3. Thus, even major inflows encountered during excavation could naturally reduce to the point of not requiring additional countermeasures when the flow dimension is close to 1 (Fig. 2b). However, inflows during tunnel excavation are commonly treated assuming a steady flow or a flow dimension of 2 or 3 (e.g., Su et al. 2022;Wu et al. 2021); it is rare that any natural reduction dependent on the flow dimension is explicitly considered in planning excavation or countermeasures to sudden major inflows during excavation.
Although natural reductions in inflow are strongly controlled by the flow dimension as shown in Fig. 3, whether inflows at actual excavation sites change consistently with the flow dimension remains poorly explored. Various factors in the field, including pre-excavation grouting (Brantberger et al. 1998) and degassing caused by depressurizing after excavation (Doughty 1995;Jarsjö and Destouni 2000;Mochizuki et al. 2020), may result in positive skin zones (less-permeable zones) along the tunnel or shaft. This could obscure any direct effect of the relationship in Fig. 3. Other factors could also have an impact, such as excavation processes and far-field boundary conditions, in Relationships between reduction in relative inflow and flow dimension, n, calculated using Eqs. (4)-(6) in section 'Basis of the relationship between inflow and flow dimension' under conditions of constant-head withdrawal tests for n = 1, 2, and 3 and hydraulic diffusivity, K/S s = 0.01 and 10. a A linear-linear plot diagram. b A log-log plot diagram 1 3 addition to difficulties in measuring inflows during excavation. Thus, the dependence of any natural reduction in inflow upon flow dimension must be confirmed at actual excavation sites. This work investigated whether major inflows that occurred during excavations at the Horonobe URL changed in a manner that was dependent upon the flow dimension estimated from pre-excavation packer tests in surface-based boreholes. Faulted and fractured siliceous rocks occur in and around the URL, and data from inflow monitoring and geological mapping during the excavations are available in addition to data from preexcavation packer tests in four boreholes near the URL; thus, the Horonobe URL is a suitable site for this case study.

Geological setting
Neogene-to-Quaternary marine siliceous rocks occur in and around the URL and consist of siliceous mudstone (the Wakkanai Formation) and overlying diatomaceous mudstone (the Koetoi Formation; Fig. 1b,c). These siliceous and diatomaceous mudstones are composed mainly of opal-cristobalite/ tridymite (40-50 wt%) and opal-A (40-45 wt%), respectively . Although both have a small amount of smectite (Hiraga and Ishii 2008), they have poor swelling capacity (Niunoya and Matsui 2005).
Fault zones are developed in the Wakkanai Formation, where the fault cores (thickness < decimeters) consist of fault rocks such as fault breccia and gouge, and the surrounding damage zones (width < meters) are characterized by the development of tensile and hybrid fractures and shear-band-based shear fractures (Ishii 2017b;Ishii et al. 2011). The faults are bedding-parallel and bedding-oblique (Table 1), and the cores of the beddingparallel faults are typically tephra-derived clay-rich (smectiterich) shear zones (Ishii 2019). The hydraulic transmissivity of fault zones decreases with increasing depth, depending on the effective mean stress normalized to the tensile strength of the intact rock; this normalized mean stress is defined as the ductility index, DI (Ishii 2015(Ishii , 2021. The hydraulic connectivity of fault zones is also related to the ductility index, as follows; i.e., (1) fault zones are poorly hydraulically connected in the deep domain (DI > 2; deeper than ~400 m below ground level, mbgl) due to the high effective normal stress acting on the fault planes (Ohno and Ishii 2022), but are hydraulically well connected in the shallow domain (DI < 2), as indicated from the flow dimensions estimated from pressure derivative results from packer tests (Ishii 2018); (2) the flow dimension is more than 1 in the shallow domain but predominantly 1 or less in the deep domain (Ishii 2018); and (3) the flow dimension varies gradually with depth around the domain boundary at DI = 2 (Ozaki et al. 2022). These hydrogeological characteristics lead to pressure anomalies indicating low effective permeability in the deep domain ( Fig. 4a), thus trapping fossil seawater, while the shallow domain allows intrusion by surface water though fault zones and fractures (Fig. 4b;Ishii 2018;Mochizuki and Ishii 2022). The porosity and hydraulic conductivity of the intact rock in the Wakkanai Formation are 30-50% and of the order of 10 −12 -10 −11 m/s, respectively .
Numerous shear-band-based shear fractures are developed in the Koetoi Formation (Table 1), and only a few fractures are hydraulically connected to form flow paths (Ishii 2017a;Ishii et al. 2011). The porosity and hydraulic conductivity of the intact rock in the Koetoi Formation are  Ishii and Fukushima (2006) e Ishii (2019) f Ishii (2018), Ishii and Fukushima (2006), and Ozaki et al. (2022) g Ohno and Ishii (2022) (Muraoka et al. 2022), and biogenic methane and carbon dioxide are abundantly dissolved in the groundwater Sasamoto et al. 2011). Furthermore, excavation-damaged zones (EDZs) have formed along the tunnels and shafts; their thicknesses are typically <0.6 m for the side walls of tunnels and <1.6 m for the floors of tunnels in the Wakkanai Formation, and <1.2 m for the side walls of tunnels in the Koetoi Formation (Aoyagi and Ishii 2019;Aoyagi et al. 2014;Tokiwa et al. 2018).

Inflows during excavations
The URL has three shafts (ventilation, east access, and west access) and three galleries at depths of 140, 250, and 350 m (Fig. 5), which were constructed from 2006 to 2014. The shafts were mechanically excavated using a breaker or roadheader or excavated by blasting in vertical steps of 1.0 m; they were lined with 0.4 m-thick concrete after every 2.0 m excavated. During lining, drain sheets were also installed between the concrete and rock surfaces in eight directions (i.e., N, NE, E, SE, S, SW, W, and NW) to allow groundwater to flow from the rock surfaces to the shaft (Fig. 6). The inner diameters of the ventilation and access shafts are 4.5 and 6.5 m, respectively.
The horizontal galleries were mechanically excavated using a breaker in horizontal steps of 1.0 m. After each step, 0.2 m-thick shotcrete and a steel arch rib were installed. The inner diameter of each gallery is typically 4.0 m. The rock surfaces at the tunnel floors were exposed for some time between excavation and being invert-concrete lined, and drainage systems comprising a drainpipe and gravel filters were installed between the invert and floor rock surfaces during lining to enable groundwater to flow from the rock mass into the galleries through the drainage systems and EDZ.
Groundwater flowing into the shafts and galleries has been continuously pumped up to the ground, and the flow rates have been monitored at different locations in the URL using electromagnetic flowmeters during and after the excavations. The saline groundwater includes abundant boron and ammonia and has been discharged into a river near the URL after processing. The maximum discharge is regulated to be 750 m 3 /day by agreement with a local fishermen's union; thus, the URL's total inflow must be kept below 750 m 3 /day. As preliminary borehole investigations predicted this limit to be exceeded during the excavation of highly permeable fault zones in the shallow domain of the Wakkanai Formation, preexcavation grouting was prepared and applied to locations where highly permeable fault zones were predicted to occur (Japan Atomic Energy Agency 2015; Sato et al. 2017).
Major inflows (tens of cubic meters per day or more) occurred at six locations during excavations, as indicated by monitoring inflows at various locations in the URL and geological observations of inflows at excavation faces. The data are reported elsewhere (Aoyagi and Kawate 2015;Inagaki 2014;Inagaki et al. 2011Inagaki et al. , 2012Inagaki et al. , 2013Sakurai and Aoyagi 2016;Sano et al. 2009). In order of occurrence, the six locations are E250_H26 in the Koetoi Formation, and V268, V285, H350_E011, H350_LGE228, and H350_LGEH013 in the Wakkanai Formation (Figs. 5 and 7). Another major inflow occurred at 250 mbgl in the ventilation shaft (Ozaki et al. 2022); specifically, it was at 256.7 and 266.0 mbgl in a vertical borehole (diameter 86 mm; bottom depth 266.0 mbgl) drilled from the excavation floor. As it was not from the excavation face, it is not considered in the present study.
The geological characteristics of the six locations are as follows: • The inflow at E250_H26 was mainly from well-connected shear fractures that were not pre-excavation grouted and from EDZ fractures (Fig. 8a). Stable isotope composition of groundwater and porewater sampled from the boreholes. After Ishii (2018) and Ozaki et al. (2022). DI ductility index • The inflow at V268 was mainly from EDZ fractures near a bedding-parallel clay-rich shear zone and from partially pre-excavation-grouted damage-zone fractures; the groundwater effervesced through the degassing of methane and carbon dioxide (Figs. 7a and 8b). • The inflow at V285 was from a partially pre-excavationgrouted fault breccia (Figs. 7a and 8c). • The inflow at H350_E011 was from a rock immediately below a fault breccia that burst suddenly after excavation (Figs. 7b and 8d).
• The muddy inflow (~20 L/min) at H350_LGE228 occurred from a partially pre-excavation-grouted, bedding-parallel, clay-rich shear zone immediately after excavation (Figs. 7b and 9a). The clay materials were increasingly washed out into the tunnel with groundwater. After the excavation face was shotcreted, the shotcrete covering the inflow point was broken, and a larger inflow ensued (>800 L/min; Fig. 9b; Ishii and Furusawa 2017). The total inflow at the URL exceeded the 750 m 3 / day limit, and postexcavation grouting was conducted. • The inflow at H350_LGEH013 occurred from a fault breccia at the innermost part of a hollow (diameter ~0.5 m) that resulted from the collapse of the left-side wall during excavation; the groundwater was effervescent by degassing ( Fig. 9c,d). The collapsed part was immediately shotcreted, and drainpipes (diameter 3 cm) were installed to allow groundwater to discharge into the tunnel. This inflow location was also postexcavation grouted.

Pre-excavation packer tests in boreholes
Preceding the excavation of the six inflow locations, packer tests were performed for sections including fault rocks and/ or fractures in four boreholes (HDB-3, HDB-6, PB-V01, and SAB-1 in Fig. 5a,b; inner radius 82.5 mm). Slug withdrawal tests (SWs), pressure recovery tests after shut-in of SW (SWSs), constant rate withdrawal tests (RWs), and    Fig. 4. Figure 5a shows this depth in the Wakkanai Formation to be 463 mbgl for HDB-3 and 379 mbgl for HDB-6, PB-V01, and SAB-1; however, the flow dimension in the Wakkanai and Koetoi formations has not yet been quantified in detail.

Basis of the relationship between inflow and flow dimension
Following the diffusion equation for fluid pressure, a change in inflow with time q(t) (m 3 /s) can be related to the flow dimension by the following equations, based on assumptions of an infinitesimal source and an infinite flow regime, referring to Barker (1988): (1) q(t) = ΔH • 4 1− Kb 3−n ∕r 2 • −1 (− , u) (2) = 1 − n∕2 Fig. 9 Photographs of inflows during excavations and related information including the orientations (dip direction/dip) of faults and fractures and the inflow rates estimated during geological observations. a-b Inflow from a partially pre-excavation-grouted, bedding-parallel, clay-rich shear zone before the excavation face was shotcreted at H350_LGE228. After shotcreting, a larger inflow occurred at the same point, breaking the shotcrete. c-d Inflow from the excavation sidewall that collapsed during excavation at H350_LGEH013  Fig. 10 Examples of a circular area on a single fault or fracture with a nonintegral flow dimension (radius = 2.1 m). When water is injected into (or pumped from) the center of the circle, numerical simulation indicates a flow dimension of a 1.9 and b 0.8 for a hydraulic diffusiv-ity of 1 × 10 −2 m 2 /s for void areas and 1 × 10 −7 m 2 /s for contact areas, assuming a constant-head outer-boundary condition. The proportion of contact area is 41% (a) and 64% (b). The red hexagons in the figures show locations for injection (or pumping) and/or monitoring pressure where ΔH is the constant differential head maintained at the inflow location in the tunnel or shaft (m), K is the hydraulic conductivity of the fault/fracture system feeding the inflow (m/s), b is the extent of the inflow location (m), n is the flow dimension in the fault/fracture system, r is the radius of the tunnel or shaft (m), S s is the specific storage of the fault/fracture system (m −1 ), t is time (s), and Γ (a, x) is the complementary incomplete Gamma function. When the flow dimension is integral and u < 0.01, q(t) can be expressed by the following equations (Barker 1988): The flow dimension along a single fault or fracture may be a nonintegral value as shown in Fig. 10, and therefore the flow dimension in a fault/fracture system may also be a nonintegral value. If packer tests indicate a flow dimension of >2.0 in a fault/fracture system, the individual faults or fractures that contain the main flow paths must link with each other in three dimensions, and the higher flow dimension requires greater connectivity among the faults/fractures and a higher flow dimension (e.g., ~2.0) along the individual faults/fractures, as shown in Fig. 10a. On the other hand, if packer tests indicate a flow dimension of <1.0 for a fault/fracture system, the flow dimension along the individual faults or fractures that contain the main flow paths must be <1.0, as shown in Fig. 10b. Thus, the flow dimension of a fault/ fracture system obtained by packer tests is determined by a combination of the flow dimension along individual faults or fractures that contain the main flow paths and the threedimensional (3D) connectivity of those faults or fractures. Figure 11 shows inflow data for each location, expressed as cumulative inflow per day (06:00 to 06:00 the next day; m 3 / day). Flowmeters were installed at two locations when the inflows occurred at E250_H26, V268, and V285 and at four locations when inflows at H350_E011, H350_LGE228, and LGEH013 occurred. The installed positions were moved    depending on the excavation progress. The inflow data at each location are based on the flowmeters that best represented the inflow, but also include inflows from other locations. The inflow data for V268 and V285 may also include water used for working during excavation. Under these conditions, the net inflow at each inflow location was defined as the difference from the baseline value (the mean value of inflow for 10 days immediately before the inflow; Fig. 11). The evaluation period at each location ended when the location of the flowmeter changed (Fig. 11a,b), when the net inflow became clearly undetectable (Fig. 11c), or when postexcavation grouting was effectively begun (Fig. 11d,e).

Estimation of flow dimension at the six inflow locations
The flow dimension at each location was estimated using the inflow data in Fig. 11. Although flow dimensions are usually estimated by fitting observed data and simulated results, the net inflows at the six locations fluctuated significantly, and the flow dimensions were hard to determine by fitting analyses. Thus, the flow dimension was estimated by a diagnostic method, where type curves for changes in inflow for 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0 flow dimensions were created for each location using a simulator, nSIGHTS (n-dimensional Statistical Inverse Graphical Hydraulic Test Simulator; Beauheim et al. 2014; Nuclear Waste Management Program 2011). During the simulation, the fault/fracture system around each location was modeled as an infinite aquifer with transient laminar flow assumed. Then, inflows (cumulative inflow per day, m 3 /day) for the evaluated periods were simulated with a time step of 1 day under the conditions of constant-head withdrawal testing. Finally, the simulated inflows were normalized to the inflows on the first day, and type curves of relative inflow (i.e., the normalized inflow) were created at each location and compared with the observed inflow data.
Parameters affecting each type curve are the radius of the inflow location and the hydraulic diffusivity of the aquifer; other parameters such as the imposed differential head and the aquifer's thicknesses are irrelevant to the type curve. The radii of inflow locations were 2.2 m for E250_H26, H350_ E011, and H350_LGE228; 2.65 m for V268 and V285; and 0.5 m for H350_LGEH013. Possible hydraulic diffusivities of the aquifers were 0.001-0.1 m 2 /s for E250_H26 in the Koetoi Formation and 0.01-10 m 2 /s for the other locations in the Wakkanai Formation. These values are based on previous studies Ozaki et al. 2022) that established the hydraulic conductivity and specific storage of the Koetoi Formation to be of the order of 10 −8 -10 −6 m/s and 10 −5 m −1 , respectively, and those in the Wakkanai Formation to be of the order of 10 −8 -10 −5 m/s and 10 −6 m −1 , respectively. Positive skin zones along the tunnels and shaft were also modeled for the cases of high hydraulic diffusivity (i.e., 10 m 2 /s) at V268, V285, H350_E011, and H350_LGE228 in the Wakkanai Formation to consider the effects of pre-excavation grouting. The thickness of each skin zone was inferred to be the same as the radius of the tunnel or shaft based on the grouting area (e.g., Fig. 7b), and the hydraulic diffusivity of the skin zone was given a value one order of magnitude lower than that of the high hydraulic diffusivity of the aquifer (i.e., 1 m 2 /s), assuming partial preexcavation grouting. Regarding the cases of low hydraulic diffusivity (i.e., 0.01 m 2 /s), the effects of pre-excavation grouting were not considered, as the hydraulic diffusivity is already low and would not be practically reduced further by pre-excavation grouting (Japan Atomic Energy Agency 2015). Although positive skin zones can also be created by degassing, the areas of degassing are smaller than the areas of pressure-propagating zones. The effects of these limited skin zones can be approximately considered by estimating the imposed differential heads to be lower (Doughty 1995). However, the imposed differential heads themselves do not affect the type curves, as mentioned previously; thus, the effects of degassing were not explicitly considered in the simulation. Finally, the observed change in inflow at each location was also normalized to the inflow on its first day, and by comparing it with the created type curves, the flow dimension at each location was determined with an accuracy of 0.5.

Estimation of flow dimension using pressure data during packer tests
Flow dimension is closely related to the pressure derivative dp/dln(t) during packer tests, based on Eq. (1) (Mishra 1992). The pressure derivatives during packer tests (SWS and RWS; Table 2) in HDB-3, HDB-6, PB-V01, and SAB-1 were analyzed by fitting measured and simulated pressure derivatives to determine the flow dimension by using nSIGHTS and considering the test sequences during each packer test. During the fitting analysis, the fault/fracture system around each test section was modeled as an infinite aquifer with assumed transient laminar flow. Fitting parameters were the compressibility of the test section, the hydraulic conductivity of the aquifer, and the flow dimension. The thicknesses and initial pressure of each aquifer were given the lengths of the test section and the pressure immediately before the test, respectively. The specific storage of each aquifer was set to be that of the surrounding intact rock, following Ozaki et al. (2022) (i.e., 3.5 × 10 −6 m −1 for the Wakkanai Formation and 1.4 × 10 −5 m −1 for the Koetoi Formation). When the pressure derivative could not be well fitted, a skin zone around the test section was also modeled; its radial thickness and hydraulic conductivity were also added to the fitting parameters (its specific storage was considered equal to that of the intact rock). Under these conditions, 50 simulations were performed for each packer-test section, and the mean value and error (2σ) of the simulated flow dimension were determined. However, when the simulation estimated the hydraulic conductivity to be comparable to that of the intact rock, the flow dimension was not determined as the result indicates the flow dimension of the intact rock rather than that in the fault/fracture system. Although packer test no. 9 in SAB-1 (SWS; 470.35-512.80 mbgl) was conducted (Table 2), the flow dimension was not determined, as the timing of shut-in was too late and sufficient data were not obtained for fitting analysis. Figure 12 shows the relative inflows observed at each location. The relative inflow is the rate normalized to that on its first day; however, the relative inflows at E250_H26 and H350_E011 were normalized to the rates on the second and fourth day, respectively, as the peak of each on the first day was not clear (Fig. 12a,d). Qualitative evaluation of the relative inflows at the six locations indicates that those at V268 and V285 fluctuated significantly without any systematic reduction with time (Fig. 12b,c). On the other hand, those at H350_LGE228 and H350_LGEH013 were significantly reduced, by between one half and two thirds, within the first several days (Fig. 11e,f). The relative inflows at E250_H26 and H350_E011 showed reductions between the cases described above (Fig. 11a,d). The relative inflows 22-36 days after the first day at H350_E011 are not shown in the figure as the monitoring conditions were different from those before and after that period. Figure 12 also shows the simulated type curves. The plot of relative inflows at E250_H26 lies between the type curves for 1.5 and 2.0 flow dimensions when the hydraulic diffusivity is 0.1 m 2 /s, and it is between the type curves for 2.0 and 2.5 dimensions when the hydraulic diffusivity is 0.001 m 2 /s (Fig. 12a). The differences between the type curves for the cases of high and low hydraulic diffusivity are largest when the flow dimension is 2.0 (Fig. 12a). Considering the influence of altering the hydraulic diffusivity, the flow dimension at E250_H26 is estimated to be within 1.5-2.5. At V268, the positive skin effect by pre-excavation grouting is also considered for the case of high hydraulic diffusivity, and the differences between the cases considering and neglecting the skin effect are largest when the flow dimension is 2.0 (Fig. 12b). When also considering the effect of pre-excavation grouting, the plot of relative inflow at V268 is generally between the type curves for 2.0 and 3.0 flow dimensions (Fig. 12b), thus the flow dimension is estimated to be within 2.0-3.0. Similar assessment applied at the other inflow locations estimated flow dimensions of within 1.5-3.0 for V285, 1.0-2.0 for H350_E011, 1.0-2.0 for H350_LGE228, and 1.0-1.5 for H350_LGEH013 (Fig. 12c-f). Figure 13 and Table 2 show the flow dimensions estimated at the test sections of packer tests. The pressure derivatives at all the test sections can be well reproduced by fitting analysis (Appendix), and the estimated flow dimensions are valid. Following previous studies (Ishii 2018;Ozaki et al. 2022), the estimated flow dimensions in the Wakkanai Formation are compiled in relation to the relative depth (meters below depth of DI = 2) in Fig. 13a, and those in the Koetoi Formation are shown in relation to depth (mbgl) in Fig. 13b. In the Wakkanai Formation, the flow dimensionality clearly decreases with increasing relative depth, being 1.5-3.0 between −150 and −50 m, 0.9-1.8 between −50 and 50 m, and 0.4-1.1 between 50 and 150 m (Fig. 13a). The flow dimensions at the no. 5-1 and no. 5-2 test sections in HDB-6 and no. 6 section in SAB-1 were not estimated, as the hydraulic conductivities at those sections were estimated to be comparable to that of the intact rock ( Table 2). The flow dimensions at the test sections in the Koetoi Formation were estimated to be 1.1-2.9, and no systematic variation with depth was shown (Fig. 13b).

Results
The flow dimensions in the Wakkanai Formation estimated at the six inflow locations showed similar depth dependence to those at the packer-test sections: the flow dimensions are 1.5-3.0 near a relative depth of −100 m and 1.0-2.0 near a relative depth of −30 m (Fig. 13a). The flow dimension estimated at E250_H26 in the Koetoi Formation is 1.5-2.5, which is within the range of 1.1-2.9 estimated at the packer-test sections in the Koetoi Formation (Fig. 13b). Although the flow dimensions estimated at the packer-test sections show some heterogeneity, even at similar relative or absolute depths, those estimated at the six inflow locations are consistent with those at the packer-test sections (Fig. 13).

Discussion
The flow dimensions estimated at the six inflow locations and the packer-test sections were consistent (Fig. 13). Thus, flow dimensions at inflow locations that emerge during excavation are potentially predictable by pre-excavation packer tests in surface-based boreholes. Furthermore, the subsequent changes of an inflow also appear to be predictable using simulations based on Eq.
(1), as demonstrated in Fig. 12. This result is further discussed considering the skin effects along a tunnel or shaft and the practical applicability of the relationship between changes in inflow and the flow dimension at actual excavation sites.

Effects of positive skin zones along tunnels and shafts
Of the six inflow locations, V268, V285, H350_E011, and H350_LGE228 were pre-excavation grouted (Fig. 7). Preexcavation grouting reduces the hydraulic conductivity near the excavation, thus reducing inflow. However, although simulations confirm some differences in the relative inflows between the cases considering and neglecting the skin effect when the flow dimension is assumed to be 2.0, significant differences are not seen for all cases (Fig. 12b-e). The flow dimensions estimated at the four pre-excavation-grouted locations were also consistent with those estimated at the related packer-test sections (Fig. 13a). The following reasons may account for this: (1) the present study considers relative inflows rather than net inflows themselves, and (2) the effects of skin zones on changes in relative inflow when viewed on a daily time scale (i.e., m 3 /day) for several days or more can be negligible, as the hydraulic diffusivity at inflow locations is expected to remain high (e.g., >0.01 m 2 /s), even if the location is pre-excavation grouted, owing to insufficient (partial) grouting (e.g.,Figs. 8b,c,and 9a). This can be explained by the following simple simulation. As shown in Fig. 14, the pore pressure at 2.2 m from the wall of a tunnel of radius 2.2 m decreases significantly within a few hours of excavation, but thereafter remains almost stable. Thus, the effects of pre-excavation grouting are limited when inflows are viewed as changes in relative inflow on a daily timescale for several days or more.
Positive skin zones along tunnels or shafts can be also caused by degassing. In the Horonobe URL, degassing of methane and carbon dioxide dissolved in the groundwater has occurred by reduction in water pressure near the tunnels and shafts (e.g., Figs. 8b and 9d; Mochizuki et al. 2020). Degassing can reduce hydraulic conductivity (Jarsjö and Destouni 2000;Persoft and Pruess 1995); however, the flow dimensions estimated at the six locations were consistent with those estimated at the packer-test sections (Fig. 13). This may be due to the effects of degassing being approximately expressed by estimating a reduced imposed  (Doughty 1995) and by the actual differential heads themselves not affecting the type curves, as described in section 'Estimation of flow dimension at the six inflow locations'.
Other possible factors causing positive skin zones along tunnels or shafts include the effective stress redistribution induced by excavation (Mas Ivars 2006) and the scale effects of channel densities in fault/fracture systems (Black and Barker 2018;Black et al. 2016). However, the skin zones caused by these factors are also limited to the areas close to tunnels and shafts and are unlikely to significantly affect changes in relative inflow on a daily time scale for several days or more.
From the preceding, positive skin effects by factors such as pre-excavation grouting and degassing are unlikely to significantly affect changes in relative inflow when viewed on a daily timescale of several days or more, as demonstrated in Fig. 12.

Practical applicability of predicting the natural reduction in inflow based on flow dimension
The present study demonstrates that the flow dimensions at possible inflow locations during excavation are predictable by pre-excavation packer tests in surface-based boreholes, and that the progression of unexpected inflows can be predicted based on their location's assessed flow dimension; however, data from packer tests are not always available. Also, even if the data were available, effective prediction is difficult for largely heterogeneous flow dimensions like those in the Koetoi Formation (Fig. 13b). In these cases, it is possible to estimate the flow dimension at an inflow location from the changes in relative inflow during the first several days and then predict subsequent changes in inflow based on the derived flow dimension. As shown in Fig. 12, the actual changes in inflow are not simple-for example, the first peak of inflow does not necessarily appear on the first day (e.g., Fig. 12a,d), and inflows may fluctuate significantly (e.g., Fig. 12b,c). These effects can be due to different factors including the effects of degassing and excavation processes as well as difficulties in measuring inflows; however, the changes in inflow at H350_LGE228, and H350_LGEH013 clearly reduced by between one-half to two-thirds within the first several days (Fig. 11e,f). These results suggest that if an inflow that emerges during excavation clearly reduces by at least half within the first several days, the flow dimension at that location is close to 1, and further reduction in inflow can be expected subsequently, as shown in Fig. 3. This inference may allow excessive postexcavation grouting to be avoided and could thus improve the efficiency of excavation.
Finally, the effects of far-field boundary conditions are mentioned. The present study analyzed changes in each inflow for the first 14-46 days (Fig. 11). The periods of the packer tests were 19,330-143,827 s (0-2 days), as shown in Table 2; however, any consideration of changes in inflow over longer times should include the effects of outer (far field) boundary conditions (e.g., Doughty 1995)-for example, if a fault or fracture system is surrounded by less-permeable domains, further natural reductions in inflow can be expected, as such domains can have no-flow boundary effects. Hydraulic interference among pressure diffusions from multiple inflow locations (e.g., Jia et al. 2016) can also contribute to further natural reductions; however, if a fault or fracture system is connected to a constant-head boundary (e.g., river or ocean), further natural reductions might not be expected

Conclusions
• Based on the diffusion equation for fluid pressure, major inflows occurring during excavation in faulted or fractured rock masses hardly decrease when the flow dimension is close to 3 but can significantly decrease by twothirds in the first 10 days and by >90% in the first 100 days when the flow dimension is close to 1. • Actual inflows during excavation can be affected by different factors including grouting, degassing, the excavation processes, and outer boundary conditions; however, those effects are limited when relative inflow is considered on a daily time scale for several days to several weeks immediately after the inflow commenced. The changes in relative inflow can be strongly influenced by the flow dimension. • The flow dimensions at locations during excavation are predictable from pre-excavation packer tests in surfacebased boreholes, and any natural reduction in inflow can be estimated using the flow dimensions. • When pre-excavation packer-test data are not available, or when the flow dimension in a rock mass is largely heterogeneous, the flow dimensions at locations of major inflows during excavations may be inferred from the changes in relative inflow during the first several days. The flow dimension is estimated to be close to 1 when the inflow clearly reduces by at least half within the first several days. In such cases, further reduction is expected (e.g., to one-tenth of the original inflow during the next 100 days) if no constant-head boundary exists near the inflow location. • Predicting the natural reduction in inflow based on the flow dimension can be helpful when planning excavations or for determining if postexcavation grouting is urgently required or whether a natural reduction would likely obviate remedial measures against a major inflow encountered during excavation.

Fig. 16
Examples of best estimates obtained by fitting analyses for pressure derivatives during packer tests in the Koetoi Formation (red symbols are measured data; blue lines are simulations). p is water pressure (MPa), K/S s is hydraulic diffusivity of the aquifer and skin zone (m 2 /s), c is compressibility of the test section (Pa −1 ), n is the flow dimension in the aquifer and skin zone, and r s is the radial thickness of the skin zone (m). Raw data are available in the ESM