Critical notch depths for failure of coastal limestone cliffs: case study at Kuro‐shima Island, Okinawa, Japan

Abstract

Development of a notch at the base of a cliff reduces cliff stability and often induces a collapse. Pleistocene limestone coastal cliffs of elevation 5 m in Kuro-shima, Ryukyu Islands, have a prominent notch with a depth of 3-4 m at their bases. Around these coastal cliffs, collapses different from previous studies of cliff collapses in the Ryukyu Islands were found; collapses in Kuro-shima have a horizontal failure surface. The horizontal failure surface, situated at the height of the failure surface corresponding to the retreat point of the notch, is bounded by vertical joints cutting the whole cliff and the reef fl at in front of the cliff. Two types of horizontal failure surface were found, triangular and quadrangular; the distinction appears to depend on the angle between the vertical joints and the front face of the cliff. Prior to collapse, these cliffs appear to have been separated from the adjacent cliffs by the development of vertical joints. Consequently, a cliff that will collapse can be identifi ed in advance; cliff instability is strongly dependent on the development of a notch. To study the effect of notch development on cliff collapse, the notch depth at which collapse occurs was calculated using stability analysis. Instability of a cliff increases with notch depth; collapse occurs at the horizontal failure surface when the ratio of the notch depth to the seaward length of the cliff is approximately 0·5-0·7 for a triangular failure surface, and 0·7-0·9 for a quadrangular failure surface.

Short-term retreat statistics of a slowly eroding coastal cliff

“…Geologic discontinuities (e.g. joints and faults) can exert strong control on cliff failure dimensions (Kogure and Matsukura, 2010), and likely affected the observed failure geometries. The larger area, infrequent failures contributed substantially to the mean (cliff-wide) retreat over the entire study period.…”

Instability of coral limestone cliffs due to extreme waves

“…Based on the observed correspondence of geometries of the boulder and the scar of cliff collapse, the boulder has been cleaved from the cliff. Kogure and Matsukura (2010) have also reported the existence of an upset boulder (Figure 2c and 2d) having a notched face, as seen on cliffs around the boulder ( Figure 2d); this was on a cliff with a scar of collapse at the south-eastern coast of Kuro-shima (Figure 1). Stability analysis from the previous study Our previous paper (Kogure and Matsukura, 2010) discussed the possibility of gravitational collapse in Kuro-shima.…”

“…Kogure and Matsukura (2010) have also reported the existence of an upset boulder (Figure 2c and 2d) having a notched face, as seen on cliffs around the boulder ( Figure 2d); this was on a cliff with a scar of collapse at the south-eastern coast of Kuro-shima (Figure 1). Stability analysis from the previous study Our previous paper (Kogure and Matsukura, 2010) discussed the possibility of gravitational collapse in Kuro-shima. In summary, collapses of coastal cliffs with vertical joints in Kuro-shima have been classifi ed into two morphological types, according to the number and direction of vertical joints and the shapes of the failure surface: H q -type or H t -type (see Figure 3a).…”

“…Stability analyses showed that most boulders were produced by gravitational collapse, although some collapses occurred when the notch depth was not large enough. Moreover, Kogure and Matsukura (2010) found that one boulder had been turned over on a shoulder of a cliff with the scar of collapse as mentioned in the next section. This upset boulder suggests that attack by extreme waves has induced cliff collapses.…”

“…We therefore refer to the collapses as gravity-induced collapse (GC). From a similar viewpoint, Kogure and Matsukura (2010) have discussed the collapses of coastal cliffs with height below 5 m using stability analyses (details are in the next section) in Kuro-shima, which is a small island in the Ryukyu Islands. Stability analyses showed that most boulders were produced by gravitational collapse, although some collapses occurred when the notch depth was not large enough.…”