A new reliability-based probabilistic model is developed for the estimation of liquefaction-induced lateral ground spreading, taking into consideration the uncertainties within the model functional form and the descriptive variables as well. The new model is also introduced as performance-based probabilistic engineering tool.

Following the 22 February 2011, MW 6.2 earthquake located on a fault beneath the Port Hills of Christchurch, fissuring of up to several hundred metres in length was observed in the loess and loess-colluvium of foot-slope positions in north-facing valleys of the Port Hills. The fissuring was observed in all major valleys, occurred at similar low altitudes, showing a contour-parallel orientation and often accompanied by both lateral compression/extension features and spring formation in the valley floor below. Fissuring locations studied in depth included Bowenvale Valley, Hillsborough Valley, Huntlywood Terrace–Lucas Lane, Bridle Path Road, and Maffeys Road–La Costa Lane. Investigations into loess soil, its properties and mannerisms, as well as international examples of its failure were undertaken, including study of the Loess Plateau of China, the Teton Dam, and palaeo-fissuring on Banks Peninsula. These investigations lead to the conclusion that loess has the propensity to fail, often due to the infiltration of water, the presence of which can lead to its instantaneous disaggregation. Literature study and laboratory analysis of Port Hills loess concluded that is has the ability to be stable in steep, sub-vertical escarpments, and often has a sub-vertically jointed internal structure and has a peak shear strength when dry. Values for cohesion, c (kPa) and the internal friction angle, ϕ (degrees) of Port Hills loess were established. The c values for the 40 Rapaki Road, 3 Glenview Terrace loess samples were 13.4 kPa and 19.7 kPa, respectively. The corresponding ϕ values were thought unusually high, at 42.0° and 43.4°.The analysed loess behaved very plastically, with little or no peak strength visible in the plots as the test went almost directly to residual strength. A geophysics resistivity survey showed an area of low resistivity which likely corresponds to a zone of saturated clayey loess/loess colluvium, indicating a high water table in the area. This is consistent with the appearances of local springs which are located towards the northern end of each distinct section of fissure trace and chemical analysis shows that they are sourced from the Port Hills volcanics. Port Hills fissuring may be sub-divided into three categories, Category A, Category B, and Category C, each characterised by distinctive features of the fissures. Category A includes fissures which display evidence of, spring formation, tunnel-gullying, and lateral spreading-like behaviour or quasi-toppling. These fissures are several metres down-slope of the loess-bedrock interface, and are in valleys containing a loess-colluvium fill. Category B fissures are in wider valleys than those in Category A, and the valleys contain estuarine silty sediments which liquefied during the earthquake. Category C fissures occurred at higher elevations than the fissures in the preceding categories, being almost coincident with bedrock outcropping. It is believed that the mechanism responsible for causing the fissuring is a complex combination of three mechanisms: the trampoline effect, bedrock fracturing, and lateral spreading. These three mechanisms can be applied in varying degrees to each of the fissuring sites in categories A, B, and C, in order to provide explanation for the observations made at each. Toppling failure can describe the soil movement as a consequence of the a three causative mechanisms, and provides insight into the movement of the loess. Intra-loess water coursing and tunnel gullying is thought to have encouraged and exacerbated the fissuring, while not being the driving force per se. Incipient landsliding is considered to be the least likely of the possible fissuring interpretations.