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Modelling risk effect using Monte Carlo Technique
Published in Stephen O. Ogunlana, Prasanta Kumar Dey, Risk Management in Engineering and Construction, 2019
A difficult situation occurs when the analyst wishes to define a distribution for a random variable but has no data available and has no idea what the shape of the distribution is, or should be. In these cases the analyst needs first to try at least the range of values – a minimum value and a maximum value. Then if there is any value or a range of values within the limits that might be more likely to occur than other values, triangular or trapezoidal distribution can be selected. If not, a uniform distribution may be suitable. If the most likely estimate for the random variable does not exceed a certain probability value (P), then the weighted triangular distribution can be used.
Effect of various initial excess pore water pressure distributions on 1-D consolidation of clays
Published in International Journal of Geotechnical Engineering, 2022
Amit Singh, Devindra Singh, Manash Chakraborty
Figure 1 describes ten different form of assumed u0 distribution (Case A–Case J) analysed in the present article. The grey shaded area displays the u0 loading generated instantaneously at the time of load application. The curves are drawn between two non-dimensional parameters, namely, normalized depth, Z (=z/Dp) and normalized u0 (u0/u0max); here, uomax is considered equal to q. The curves (symmetric/asymmetric) displayed in Figure 1 are not arbitrary. For a specific situation where a consolidating clay layer is sandwiched between two sandy layers, a triangular u0 distribution is likely to develop in the field due to the occurrence of either of the two conditions: (i) if there is a sudden rise/drop of the water surface in the upper sand while the piezometric level of the bottom layer is unaltered (Lambe and Whitman 1969) or (ii) if the lower sand layer is suddenly dewatered by destruction of an artesian condition without changing the water table at the upper sand (Olson 1980). Based on the hydraulic drainage and environmental conditions, upper/lower triangular distribution may evolve. A trapezoidal distribution is the combination of the rectangular and triangular surfaces. Figure 1(a–c) represents the linear distribution of u0 loading. The sinusoidal distribution in Figure 1(d) represents half sine wave, with uomax at the mid portion and zero pore pressure at both the boundaries. The sinusoidal distribution can be because of the fill applied at some previous time. Figure 1(e-g) displays other variants of the fundamental sinusoidal distribution. The composite shape, as shown in Figure 1(i), can be a combination of rectangular and parabolic/sinusoidal distribution. The arched distribution occurs for relatively tall sample in oedometer test due to the effect of skin friction, whereas the skewed distribution (top-skewed/ bottom-skewed) can arise after a certain degree of consolidation takes place from linear triangular u0 surface developed due to the previously placed fill. The shapes of all the considered distributions are mathematically expressed by the following normalized equation: Trapezoidal distribution