La interfaz web

High-frequency pore-pressure fluctuations having magnitudes large enough to locally liquefy the bed were measured only if the near-surface bed sediment was wet as it was overridden and subsequently entrained by debris flows (e.g., Figures 4.5, 4.6, 4.8, 4.13, 4.19). Iverson et al. [2011] observed a similarly strong control of θ on the generation of p in sediment during debris-flow passage. When bed sediment had θ < 22%, no significant pressure response was measured, which contrasted with p large enough to nearly liquefy the bed with θ > 22%. Such measurements support the hypothesis that rapid loading and deformation of wet bed sediment by overriding debris flows can cause significant increases in sediment pore pressures and aid entrainment [e.g., Hutchinson and Bhandari, 1971; Bovis and Dagg, 1992; Sassa, 1984; Hungr et al., 2005; Sassa and Wang, 2005]. The strong control of θ on pore-pressure development in overridden bed sediment can be better understood by exploring at how differences in the compressibility and viscosity of water versus air affect various mechanisms of pore-pressure generation. In a recent theoretical analysis, Iverson [2012] demonstrated that for loosely-packed, water-saturated beds, the observed growth of bed-sediment pore pressure likely resulted from bed-sediment consolidation due to compressional loading and shear deformation by overriding debris flows. Starting with a constitutive equation for changes in bed-sediment porosity, Iverson [2012] derived a pore-pressure diffusion equation

103 that includes two types of pore-pressure forcing, both of which are modulated by pore-pressure diffusion. The first type of forcing is pore contraction due to increases in mean normal effective stress that arise from changes in flow depth or bed-sediment height. The second type of forcing is pore contraction resulting from shear-driven consolidation.

Our measurements of bed-sediment pore pressures provide evidence for pore-pressure gener- ation by both types of forcing proposed by Iverson [2012] and highlight that each type of forcing generates pressure fluctuations with unique frequencies due to the contrasting timescales over which they operate. Long period fluctuations in p, on the order of 10 s, generally had small peak ampli- tudes for both wet and dry beds (∼ 1 kPa), and were correlated with similar long-period fluctuations in both flow stage and basal normal stress σ associated with the arrival of deep surges (e.g., Figures 4.7, 4.8, and 4.13). Such a correlation suggests that long-period pore-pressure fluctuations were generated by gravitational compression of bed-sediment pores in response to the increasing weight of the overriding flow, or for completely saturated beds, direct loading of the static water column. In contrast, high-frequency pore-pressure fluctuations with periods < 0.1 s and amplitudes exceed- ing 10 kPa, were only measured in wet sediment, were commonly uncorrelated with fluctuations in σ, and were much too short to be correlated to changes in flow depth. This lack of correlation suggests that high-frequency fluctuations were generated during shear deformation of bed sediment [Iverson et al., 2011; Iverson, 2012]. Because the magnitude of pore-pressure fluctuations due to changes in flow depth were small relative to those due to shear deformation, we focus on the latter. To dynamically generate high fluid pressure in bed sediment at the scale of a pore, the rate of

pore-pressure generation via pore contraction Λgmust be faster than the rate at which pore pressure

will decrease Λd due to diffusion [Iverson and LaHusen, 1989]. Λg is likely controlled by pore-fluid

compressibility Cf and the timescale of pore contraction Tc, Λg = (1/Cf)/Tc. In turn, the velocity

of sediment grains in the sheared layer ug and the grain diameter δ will set Tc = δ/ug [Iverson

and LaHusen, 1989]. Λd can be expressed as P/Td, in which P = ρgδ cos α is a characteristic

pressure scale, Td= δ2/D is the diffusion timescale, and D is the hydraulic diffusivity. The ratio of

104 non-equilibrium pore pressure

I = Λg Λd = Td TcCfP = δug DCfP . (4.4)

Iverson [2012] used a similar nondimensional number to scale a normalized shear-driven pressure- forcing term. If I is large, the rate of pore-pressure generation exceeds that of pore-pressure diffusion and development of large pore pressures during shear deformation is expected.

Because water and air differ markedly in their compressibility and viscosity, equation 4.4 sug- gests a strong contrast in the potential for shear deformation of water-saturated and air-saturated sediment to generate high-frequency pore-pressure fluctuations. D is a function of pore-fluid ma- terial properties, in addition to granular-matrix properties, and can be written as

D = K Ss = kρpfg/µ ρpfg(Cm+ nCf) = k µ(Cm+ nCf) (4.5)

where K is the hydraulic conductivity, Ss is the specific storage, k is the intrinsic permeability,

ρpf is the pore-fluid density, g is the gravitational acceleration, µ is the dynamic viscosity of the

pore fluid, Cm is the matrix compressibility, which is the inverse of the bulk modulus of elasticity,

n is the matrix porosity, and Cf is the compressibility of the pore fluid [Freeze and Cherry, 1979].

Using reasonable values for variables in equation 4.5 (listed in Table 3.4), it is clear that D for water-saturated sediment can be orders of magnitude larger or smaller than D for the same air- saturated sediment. For the bed sediment in this study, which was characterized as sandy gravel

(Cm ∼ 10−8 Pa−1), D for air-saturated and water-saturated sediment can be similar. Equation 4.5

also emphasizes that potentially large decreases in D could be possible if k was reduced at depth due to compaction. The compressibility of air is approximately four orders of magnitude larger than the compressibility of water (Table S1). As a result, I for certain air-saturated sediment could be orders of magnitude smaller than I for the same water-saturated sediment. Such a large difference in I for air- versus water-saturated sediment might explain why dramatic increases in near-surface pore pressures were only measured once θ in the near-surface bed sediment rose above zero, even if D was similar for both water-saturated and air-saturated portions of the bed (e.g., Figure 4.6, 4.7, and 4.8).

105