# Instability Induced by Random Background Noise in a Delay Model of Landslide Dynamics
## 1 Introduction  
Landslides induced by external dynamical effects are common natural phenomena: there are many contemporary examples of massive landslides triggered by earthquakes [1; 2; 3], volcanic activity [4], or artificial vibrations [5; 6]. The mechanism of the dynamically triggered events is obvious: if the impact is strong, then the intensity of the vibrations themselves is causing the soil failure. On the other hand, if the intensity is rather low, then redistribution of pore pressure due to the duration of the event could induce soil failure along the potential sliding surface. However, it is well known that properties of the slope, i.e., the area susceptible to sliding, also significantly contribute to the final activation of sliding during the external dynamical event. In case a slope is composed of fresh, intact, and unweathered rock mass or soil with favorable shear strength parameters in dry conditions (or in a state of natural moisture), then stronger or longer dynamical events are required to trigger the landslides. Similarly, if the slope is on the verge of stability, then only a small event may be sufficient to trigger the instability. It is this case that is under the focus of the present research since slopes which are in a conditionally stable state may be susceptible to the critical effect of very small events such as background seismic noise. We consider this case to be of special interest since it is intuitively expected that strong earthquakes generate massive landslides; this phenomenon from the scientific viewpoint is not unexpected, and its mechanism is quite clear and obvious. What is not expected, and maybe with avague mechanism, is the effect of small-amplitude dynamic events on the possible slope destabilization in landslide-prone areas. In our opinion, such a scenario bears a higher level of natural hazard since the triggering mechanism is \"hidden\", so the landslide could occur without any apparent triggering event. Depending on the population of the area, such a scenario also bears a higher level of natural risk. We are showing in this paper that even the low-intensity background noise in certain conditions of the conditionally stable slope is sufficient to trigger the instability. One should note that recent research indicated a change in ambient seismic noise right before the commencement of the landslide movement [7; 8; 9] or during the landslide movement [10]. Apparently, previous research indicated a decrease in the seismic velocity of the sliding material for several days prior to the occurrence of landslides. Additionally, a significant drop in Rayleigh wave velocity was recorded with the acceleration of earthflow, indicating changes in shear stiffness and undrained strength. This change in ambient seismic noise due to landslide activity could have very positive implications for landslide monitoring and could help predict landslide activity in a very precise and quantitative manner [11]. Nevertheless, such ambient noise occurring due to landslide activity is not the subject of this paper. Instead, we are focused on the existing ambient seismic noise and its effect on the possible landslide triggering. Seismic background noise, although very well understood and monitored [12], has not been related to the onset of slope instability, i.e., landslide activation so far, except for the purpose of landslide monitoring using ambient seismic noise [11]. The main properties of the background seismic noise are the permanent presence, quasi-randomness, and variable amplitude, depending on the position, time, and frequency. We showed in one of our previous research that small-amplitude background noise is sufficient to trigger the unstable motion along the fault when the active fault is near the bifurcation curve, i.e., at the threshold of dynamic instability, when small external motion is sufficient to \"push\" the dynamics of the fault over the verge of stability [13]. The goal of the present research is to examine the effect of natural seismic noise on slope stability.