For a quantitative assessment of debris flow risk, it is essential to consider not only the hazardous process itself but also to perform an analysis of its consequences. This should include the estimation of the expected monetary losses as the product of the hazard with a given magnitude and the vulnerability of the elements exposed. A quantifiable integrated approach of both hazard and vulnerability is becoming a required practice in risk reduction management. This study aims at developing physical vulnerability curves for debris flows through the use of a dynamic run-out model. Dynamic run-out models for debris flows are able to calculate physical outputs (extension, depths, velocities, impact pressures) and to determine the zones where the elements at risk could suffer an impact. These results can then be applied to consequence analyses and risk calculations. On 13 July 2008, after more than two days of intense rainfall, several debris and mud flows were released in the central part of the Valtellina Valley (Lombardy Region, Northern Italy). One of the largest debris flows events occurred in a village called Selvetta. The debris flow event was reconstructed after extensive field work and interviews with local inhabitants and civil protection teams. The Selvetta event was modelled with the FLO-2D program, an Eulerian formulation with a finite differences numerical scheme that requires the specification of an input hydrograph. The internal stresses are isotropic and the basal shear stresses are calculated using a quadratic model. The behaviour and run-out of the flow was reconstructed. The significance of calculated values of the flow depth, velocity, and pressure were investigated in terms of the resulting damage to the affected buildings. The physical damage was quantified for each affected structure within the context of physical vulnerability, which was calculated as the ratio between the monetary loss and the reconstruction value. Three different empirical vulnerability curves were obtained, which are functions of debris flow depth, impact pressure, and kinematic viscosity, respectively. A quantitative approach to estimate the vulnerability of an exposed element to a debris flow which can be independent of the temporal occurrence of the hazard event is presented.

The results of 167 full-scale field load tests were used to examine several issues related to the load-displacement behavior of footings in cohesionless soils under axial compression loading, including (1) method to interpret the “failure load” from the load-settlement curves; (2) correlations among interpreted loads and settlements; and (3) generalized load-settlement behavior. The L1 - L2 method was found to be more appropriate than the “tangent intersection” and “10% of the footing width” methods for interpreting the failure load. The interpreted loads and displacements indicate that footing load-settlement behavior is less elastic and more nonlinear than that of drilled foundations. The results show that the footing behavior will be beyond the elastic limit for designs where a traditional factor of safety between 2 and 3 is used. A normalized curve was developed by approximating the load-settlement curve for each load test in the database by hyperbolic fitting, and the uncertainty in this curve was qu...

A probabilistic method is presented to estimate the differential settlements of footings on cohesionless soils, considering the uncertainties in both the load and capacity sides of the design equation. A random field approach is employed to characterize the inherent soil variability. This method is first compared to typical limit values from the literature to denote critical combinations of design parameters that can lead to exceedance of tolerable differential settlements. Then, reliability-based design equations are developed for the serviceability limit state (SLS) design of footings on cohesionless soils. The key parameters controlling the SLS are the allowable angular distortion, site variability, and footing spacing. The results are given in a straightforward design format and indicate that currently suggested deformation factors (resistance factors for SLS) equal to 1.0 are likely to be unconservative for most design situations.

An extensive database of full-scale field load tests was used to examine the bearing capacity for footings in cohesionless soils. Each load test curve was evaluated consistently to determine the interpreted failure load (i.e., bearing capacity) using the L1 - L2 method. This test value then was compared with the theoretical bearing capacity, computed primarily using the basic Vesić model. The comparisons show that, for footing widths B>1 m , the field results agree very well with the Vesić predictions. However, for B<1 m , the results indicated a relationship between B and the predicted-to-measured bearing capacity ratio. Accordingly, a simple modification was made to the bearing capacity equation, and the resulting predictions are very good.