Settlement of the Kansai International Airport Islands

The literature on Kansai Airport does not appear to include any permeability data from direct permeability tests on Osaka Bay clay or sand layers.

For the present settlement analyses, the values of $k_{vo}$ for the Pleistocene clay layers were computed using the Mesri et al. (1994) equation together with representative values of prereclamation void ratio ($e_o$), clay-size fraction (CF), and activity ($A_c=I_p/\mathrm{CF}$) in Table 1. Rocchi et al. (2006) compared permeability data for Osaka Bay clays with $k_{vo}$ computed using the Mesri et al. (1994) equation, concluding that the empirical relationship provides a good fit to the experimental data for Osaka clays. The values of $k_{vo}$ for Pleistocene clays computed using the Mesri et al. (1994) equation are listed in Table 1.

The values of $k_{vo}$ for Ma13 clay sublayers, in the absence of reliable data on CF, were based on permeability data determined by Tanaka et al. (2003) by interpreting, using the Terzaghi theory of consolidation, compression rates observed in incremental loading oedometer tests. However, Mesri et al. (1994) showed that the values of permeability computed from $c_v$ and $m_v$ typically underestimate $k_v$ by a factor of 2. Therefore, the values of $k_{vo}$ for Ma13 in Table 1 were obtained by increasing the Tanaka et al. (2003) data by a factor of 2.

Permeability is expected to decrease with the decrease in void ratio, and for clays, the $e\text{-}\log k_v$, with slope $C_k=\mathrm{\Delta }e/\mathrm{\Delta }\log k$, is commonly used (Tavenas et al. 1983; Mesri et al. 1994). The value of $C_k$ for each sublayer listed in Table 1 was computed using $C_k=0.5e_o$ proposed by Tavenas et al. (1983) and confirmed by Mesri et al. (1994). Tanaka et al. (2003) showed that $C_k=0.5e_o$ is also applicable to Osaka Bay clays.

The sand layers in Osaka Bay play a significant role on the rate of consolidation of the clay layers and therefore on rate of settlement of the airport islands. Nakase (1987) listed the range of permeabilities for Pleistocene sand layers as ${10}^{-8}\hspace{0.17em}\text{to}\hspace{0.17em}{10}^{-5}\hspace{0.17em}\text{m}/\text{s}$. Mimura and Jang (2005) attributed the existence of undissipated pore-water pressures to low permeability and discontinuity of sand layers, considering the permeability question unresolved. For a settlement analysis of Island I, Mimura and Jang (2005) assumed Ds10 to be freely draining, Ds1 to have a high permeability of ${10}^{-2}\hspace{0.17em}\text{m}/\text{s}$, and assigned permeability values in the range of $2.5\times {10}^{-7}\hspace{0.17em}\text{to}\hspace{0.17em}4.5\times {10}^{-5}\hspace{0.17em}\text{m}/\text{s}$ to the remaining sand layers. In settlement analyses of Kansai Airport Islands, Shibata and Karube (2005) assumed permeability values in the range of $1\times {10}^{-5}\hspace{0.17em}\text{to}\hspace{0.17em}8.5\times {10}^{-5}\hspace{0.17em}\text{m}/\text{s}$ for the sand layers. Kobayashi et al. (2005), in terms of thickness and continuity, considered Ds1 and Ds10 to function as drainage layers.

The permeability of the Pleistocene sand layers was back-calculated for the present settlement analyses of Islands I and II using observed settlements and pore-water pressures. The same ILLICON procedure (Funk and Mesri 2014) to be described later, which was used for the long-term settlement analyses of the Pleistocene clay layers, was used for the back-analyses. In both back-analyses, to compute the permeability of the sand layers and long-term settlement analyses, one-dimensional vertical compression in clay layers and vertical and horizontal water flow in the clay layers were assumed. Horizontal flow in the sand layers was assumed. The horizontal drainage boundary is set at points where $\mathrm{\Delta }{\sigma }_v$ from reclamation load and therefore $u_o^{\prime }$ is small (influence factor for the vertical stress increase using the Boussinesq solution is less than 0.001). Sand layers Ds1 and Ds10 were assumed to be freely draining, and the back-analyses resulted in permeability of the remaining sand layers in the range of ${10}^{-7}\hspace{0.17em}\text{to}\hspace{0.17em}{10}^{-4}\hspace{0.17em}\text{m}/\text{s}$ (Funk 2013), comparable to the range of values reported by Nakase (1987), Mimura and Jang (2005), and Shibata and Karube (2005).

The ILLICON procedure used here for settlement analyses of the Kansai International Airport Islands is based on the assumption of uniqueness of the EOP void ratio–effective vertical stress relationship and the $C_{\alpha }/C_c$ law of compressibility. For each sublayer, such as those in Table 1, an EOP $e\text{-}\log {\sigma }_v^{\prime }$ relationship and a single value of $C_{\alpha }/C_c$ are required for settlement analysis. All published incremental loading and constant rate of deformation oedometer test data were used to define compressibility of the clay layers at the Kansai Airport site (Kanda et al. 1991; Tanaka et al. 2003, 2004; Tanaka 2005a, b; Furudoi and Kobayashi 2009). For the Pleistocene clay samples from depths below the seafloor range of 60–400 m, the values of ${\epsilon }_{vo}$, according to oedometer compression data, are in the range of 1.8–4.0%, suggesting a specimen quality designation of B to C (Terzaghi et al. 1996).

Published data on $e_o$, ${\sigma }_{vo}^{\prime }$, $C_r/C_c$, ${\sigma }_p^{\prime }/{\sigma }_{vo}^{\prime }$, and the nonlinear $e\text{-}\log {\sigma }_v^{\prime }$ relationship in the compression range beyond ${\sigma }_p^{\prime }$ were used to construct for each sublayer the EOP $e\text{-}\log {\sigma }_v^{\prime }$ relationship, which was input into the ILLICON computer program. The EOP $e\text{-}\log {\sigma }_v^{\prime }$ relationship of all clay layers starts at ($e_o$, ${\sigma }_{vo}^{\prime }$) in the recompression range. The representative values of $e_o$ in Table 1 were calculated from published $w_o$ data (Maeda et al. 1990; Akai and Tanaka 1999; Tanaka and Locat 1999; Tanaka et al. 2003, 2004; Imai et al. 2005) and $G_s$ data (Akai and Tanaka 1999). Prereclamation hydrostatic pore-water pressure from sea level was used to compute ${\sigma }_{vo}^{\prime }$ and to interpret postreclamation pore-water pressure measurements. The values of ${\sigma }_{vo}^{\prime }$ at MP2-II are shown in Fig. 4. The published total unit weight data for the clay and sand layers were used to calculate ${\sigma }_{vo}$ and therefore ${\sigma }_{vo}^{\prime }$.

The values of ${\sigma }_p^{\prime }/{\sigma }_{vo}^{\prime }$ for the clay layers at the Kansai Airport site were obtained from incremental loading (IL) and constant rate of strain (CRS) oedometer tests on undisturbed specimens. The value of ${\sigma }_p^{\prime }$ for IL tests was obtained using the EOP $e\text{-}\log {\sigma }_v^{\prime }$ relationship. It is well established that the value of ${\sigma }_p^{\prime }$ from CRS tests is a function of the imposed strain rate. Mesri and Feng (1986) recommended the EOP strain rate ${\dot{\epsilon }}_p$ to obtain the EOP $e\text{-}\log {\sigma }_v^{\prime }$ relationship from the CRS oedometer tests. For typical soft clay deposits, the value of ${\dot{\epsilon }}_p$ is $2.7\times {10}^{-7}\hspace{0.17em}{\text{s}}^{-1}$ (Mesri et al. 1994). The ${\sigma }_p^{\prime }/{\sigma }_{vo}^{\prime }$ data for Osaka Bay clays include CRS tests with ${\dot{\epsilon }}_I=3.3\times {10}^{-6}\hspace{0.17em}{\text{s}}^{-1}$ (Tanaka et al. 2003; Tanaka 2005a, b) and ${\dot{\epsilon }}_I=1.6\times {10}^{-6}\hspace{0.17em}{\text{s}}^{-1}$ (Watabe et al. 2002). Therefore, the reported values of ${\sigma }_p^{\prime }/{\sigma }_{vo}^{\prime }$ were reduced by a factor of 0.90 and 0.93, respectively, according to the empirical equation by Mesri and Feng (1986).

The values of ${\sigma }_p^{\prime }/{\sigma }_{vo}^{\prime }$ for Holocene Clay Layer Ma13 are shown in Fig. 5 together with vertical line segments indicating the values that were used in the ILLICON settlement analyses. Similar plots were prepared for all Pleistocene clay layers, with four examples shown in Fig. 6. In Pleistocene clay layers, the values of ${\sigma }_p^{\prime }/{\sigma }_{vo}^{\prime }$ used for ILLICON analyses, listed in Table 1, ranged from 1.28 to 1.50. The preconsolidation pressure of Osaka Bay clays has mainly resulted from aging including secondary compression and thixotropic hardening and, possibly, some carbonate cementation (Mesri and Choi 1979; Tsuchida 2005).

The compression of Osaka Bay clays beyond the preconsolidation pressure, from IL and CRS oedometer tests, was summarized in terms of the secant compression index $C_c^{\prime }$ versus $\log {\sigma }_v^{\prime }/{\sigma }_p^{\prime }$, where ${\sigma }_v^{\prime }$ is the effective vertical stress for which $C_c^{\prime }$ is defined (Mesri and Choi 1985a; Terzaghi et al. 1996, Fig. 16.6). The $C_c^{\prime }\text{-}\log {\sigma }_v^{\prime }/{\sigma }_p^{\prime }$ plot for Holocene Marine Clay Layer Ma13 and the Pleistocene clays are shown in Figs. 7 and 8, respectively.

The EOP $e\text{-}\log {\sigma }_v^{\prime }$ relationship for each sublayer listed in Table 1 was constructed (Funk 2013) starting from point ($e_o$, ${\sigma }_{vo}^{\prime }$) with a recompression curve defined by $C_r/C_c=0.1$, where $C_c$ is the compression index from ${\sigma }_p^{\prime }$ to $2{\sigma }_p^{\prime }$, up to ${\sigma }_p^{\prime }$, and then defining the nonlinear compression curve using four to six values of ($C_c^{\prime }$, ${\sigma }_v^{\prime }/{\sigma }_p^{\prime }$).

The secondary compression of Osaka Bay clays following primary consolidation was defined using the $C_{\alpha }/C_c$ law of compressibility, which requires for each sublayer the EOP $e\text{-}\log {\sigma }_v^{\prime }$ relationship together with $C_{\alpha }/C_c$, where at any consolidation pressure ${\sigma }_v^{\prime }$, $C_c$ is a tangent compression index (Mesri and Godlewski 1977; Mesri and Castro 1987; Mesri 2001; Mesri and Ajlouni 2007). The values of $C_{\alpha }/C_c$ for Osaka Bay clays were determined from the published IL oedometer test data (Imai et al. 2005; Tanaka 2005a, b; Watabe et al. 2008; Funk 2013). A special procedure was also used to compute $C_{\alpha }/C_c$ for 11 Pleistocene clay layers using long-term incremental loading compression data by Tanaka (2005a, b). For each Pleistocene clay specimen, the EOP $e\text{-}\log {\sigma }_v^{\prime }$ curve and $e\text{-}\log t$ curves for two pressures in the recompression range were available. As is predicted by the $C_{\alpha }/C_c$ law of compressibility, the $e\text{-}\log t$ curve for the pressure near the preconsolidation pressure started with a small $C_{\alpha }$ proportional to the recompression index, rapidly increased to a maximum proportional to the maximum $C_c$ on the EOP $e\text{-}\log {\sigma }_v^{\prime }$ curve, and gradually decreased with time in accordance with the decrease in $C_c$ in the compression range. Therefore, the maximum $C_{\alpha }$ was used together with the maximum $C_c$ to define $C_{\alpha }/C_c$. The values of $C_{\alpha }/C_c$ for 11 clay layers from Dtc to Ma2 were in the range of 0.024–0.042, with an average value of 0.033, which is quite similar to the value from the published IL oedometer test data. The resulting value of $C_{\alpha }/C_c$ for each clay layer together with the EOP $e\text{-}\log {\sigma }_v^{\prime }$ curve were used to construct $e\text{-}\log {\sigma }_v^{\prime }$ curves for $t/t_p>1$. Four examples for the laboratory specimens are shown in Fig. 9, which also includes secondary compression measurements by Tanaka (2005b) at two consolidation pressures in the recompression range.

For reclamation loading in Osaka Bay, secondary settlement is expected to be a significant factor only for clay layers with a short duration of primary consolidation ($t_p$). This is only true for Holocene Marine Clay Layer Ma13 because of the use of vertical drains and for Pleistocene clay layers at great depth, e.g., Ma3 and lower in Fig. 2, where ${\sigma }_v^{\prime }$ is in the recompression range (Fig. 4) and therefore $t_p$ is small.

The ILLICON computer program was rebuilt using Microsoft Visual Studio 2010 (Redmond, Washington) to facilitate settlement and pore-water pressure calculation for the Kansai International Airport. A user interface that provides graphical output was created as a Windows Form Application, and the computational core was coded using Microsoft Visual C++. The current version of ILLICON, which is based on the Darcy flow equation, uniqueness of EOP $e\text{-}\log {\sigma }_v^{\prime }$ relationship, and the $C_{\alpha }/C_c$ law of compressibility, retains all features listed in Mesri and Khan (2012).

The hydrodynamic equation used for the Holocene Ma13 clay layer with vertical water flow into the sand blanket overlying Ma13, as well as the sand layer Ds1 underlying Ma13 and radial water flow into the vertical drain isThe hydrodynamic equation used for the Pleistocene clay layers with vertical water flow into sand layers that are treated as impeded drainage boundaries and horizontal water flow within the consolidating clay layer is (Funk 2013)

Because the length to width ratio of Kansai Airport Island I and Kansai Airport Island II is more than 3.5, the hydrodynamic equation for the Pleistocene clay layers was developed assuming vertical water flow plus horizontal water flow perpendicular to the length of each Airport Island (i.e., the $x\text{-direction}$).

The constitutive equation used in the ILLICON approach is (Mesri 2001)The compressibility parameters ${\left(\partial e/\partial {\sigma }_v^{\prime }\right)}_t$ and ${\left(\partial e/\partial t\right)}_{{\sigma }_v^{\prime }}$ are evaluated assuming the uniqueness of the EOP $e\text{-}{\sigma }_v^{\prime }$ relationship together with the $C_{\alpha }/C_c$ law of compressibility (Funk 2013). The explicit finite-difference approximation was used to solve the hydrodynamic and constitutive equations together (Funk 2013).

The compression of the Holocene Ma13 clay layer observed at CT, K-I, and MP1-I, together with ILLICON predictions, is shown in Figs. 10(a–c), respectively [for MP1-II and MP2-II, see Funk (2013)]. The settlements of the Pleistocene clay layers observed at MP1-II, together with ILLICON predictions, are shown in Fig. 11. The excess pore-water pressure observations in the Pleistocene sand layers at MP1-II, together with ILLICON predictions, are shown in Fig. 12. The settlements of Pleistocene clay layers observed at MP1-I, together with ILLICON predictions, are shown in Fig. 13. The excess pore-water pressure observations in the Pleistocene sand layers, together with ILLICON predictions, are shown in Fig. 14. The pore-water pressure increases in the Pleistocene sand layers through redistribution from the reclamation of Airport Island II. This pore-water pressure redistribution is expected to somewhat slow down settlement of Airport Island I, as suggested by the open and solid circles in Fig. 13.