There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Poisson's ratio values for rocks

The extraction of groundwater can generate land subsidence by causing the compaction of susceptible aquifer systems, typically unconsolidated alluvial or basin-fill aquifer systems comprising aquifers and aquitards. Various ground-based and remotely sensed methods are used to measure and map subsidence. Many areas of subsidence caused by groundwater pumping have been identified and monitored, and corrective measures to slow or halt subsidence have been devised. Two principal means are used to mitigate subsidence caused by groundwater withdrawal—reduction of groundwater withdrawal, and artificial recharge. Analysis and simulation of aquifer-system compaction follow from the basic relations between head, stress, compressibility, and groundwater flow and are addressed primarily using two approaches—one based on conventional groundwater flow theory and one based on linear poroelasticity theory. Research and development to improve the assessment and analysis of aquifer-system compaction, the accompanying subsidence and potential ground ruptures are needed in the topic areas of the hydromechanical behavior of aquitards, the role of horizontal deformation, the application of differential synthetic aperture radar interferometry, and the regional-scale simulation of coupled groundwater flow and aquifer-system deformation to support resource management and hazard mitigation measures.

Review: Regional land subsidence accompanying groundwater extraction

Abstract Knowledge of the spacing and size of discontinuities in a rock mass is of considerable importance for the prediction of rock behaviour. The characteristics of discontinuities can be estimated using scanline surveys but the precision of the estimates must be obtained and the bias caused by linear sampling must be eliminated before they can validly be used. Initially, an expression is presented which gives the degree of confidence that can be assigned to the measured mean discontinuity spacing. A reduced form of this expression is obtained for cases where the discontinuity spacings follow the negative exponential distribution. The precision of discontinuity frequency and RQD estimates is also explained. The distribution of trace lengths produced by the intersection of planar discontinuities with a planar rock face is used to determine the distribution of trace lengths, the distribution of semi-trace lengths and the distribution of censored semi-trace lengths intersected by a randomly located scanline. Comparison of the actual and sampled distributions demonstrates the bias introduced by scanline sampling of trace lengths. Relations between the distributions can be used to produce analytical or graphical methods of estimating mean trace length from censored measurements at exposures of limited extent.

Estimation discontinuity spacing and trace length using scanline surveys

Large earthquakes initiate chains of surface processes that last much longer than the brief moments of strong shaking. Most moderate‐ and large‐magnitude earthquakes trigger landslides, ranging from small failures in the soil cover to massive, devastating rock avalanches. Some landslides dam rivers and impound lakes, which can collapse days to centuries later, and flood mountain valleys for hundreds of kilometers downstream. Landslide deposits on slopes can remobilize during heavy rainfall and evolve into debris flows. Cracks and fractures can form and widen on mountain crests and flanks, promoting increased frequency of landslides that lasts for decades. More gradual impacts involve the flushing of excess debris downstream by rivers, which can generate bank erosion and floodplain accretion as well as channel avulsions that affect flooding frequency, settlements, ecosystems, and infrastructure. Ultimately, earthquake sequences and their geomorphic consequences alter mountain landscapes over both human and geologic time scales. Two recent events have attracted intense research into earthquake‐induced landslides and their consequences: the magnitude M 7.6 Chi‐Chi, Taiwan earthquake of 1999, and the M 7.9 Wenchuan, China earthquake of 2008. Using data and insights from these and several other earthquakes, we analyze how such events initiate processes that change mountain landscapes, highlight research gaps, and suggest pathways toward a more complete understanding of the seismic effects on the Earth's surface.

Earthquake-Induced Chains of Geologic Hazards: Patterns, Mechanisms, and Impacts

https://ir.nctu.edu.tw:443/bitstream/11536/25894/1/000286853100006.pdf

Logistic regression model for predicting the failure probability of a landslide dam

https://ir.nctu.edu.tw:443/bitstream/11536/460/1/A1997XU58600009.pdf

Direct tensile behavior of a transversely isotropic rock

https://ir.nctu.edu.tw:443/bitstream/11536/6681/1/000269553300011.pdf

Discriminant analysis of the geomorphic characteristics and stability of landslide dams

SUMMARY We rederive and present the complete closed-form solutions of the displacements and stresses subjected to a point load in a transversely isotropic elastic half-space. The half-space is bounded by a horizontal surface, and the plane of transverse isotropy of the medium is parallel to the horizontal surface. The solutions are obtained by superposing the solutions of two infinite spaces, one acting a point load in its interior and the other being free loading. The Fourier and Hankel transforms in a cylindrical co-ordinate system are employed for deriving the analytical solutions. These solutions are identical with the Mindlin and Boussinesq solutions if the half-space is homogeneous, linear elastic, and isotropic. Also, the Lekhnitskii solution for a transversely isotropic half-space subjected to a vertical point load on its horizontal surface is one of these solutions. Furthermore, an illustrative example is given to show the e⁄ect of degree of rock anisotropy on the vertical surface displacement and vertical stress that are induced by a single vertical concentrated force acting on the surface. The results indicate that the displacement and stress accounted for rock anisotropy are quite di⁄erent for the displacement and stress calculated from isotropic solutions. ( 1998 John Wiley & Sons, Ltd.

https://ir.nctu.edu.tw:443/bitstream/11536/32583/1/000074569100002.pdf

Elastic solutions for a transversely isotropic half-space subjected to a point load

https://blogs.uakron.edu/ernianpan/files/2014/09/065_2003IJRMMSWangTzengPanLiao.pdf

Jyh-Jong Liao

Papers

Logistic regression model for predicting the failure probability of a landslide dam

Direct tensile behavior of a transversely isotropic rock

Discriminant analysis of the geomorphic characteristics and stability of landslide dams

Elastic solutions for a transversely isotropic half-space subjected to a point load

Displacements and stresses due to a vertical point load in an inhomogeneous transversely isotropic half-space