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The Approach to Data Linearity and Slope Failure; A Method to Increase Predictive Confidence

Updated: Apr 8, 2020


Unlike most slope monitoring technologies, ground-based slope monitoring radar can scan an entire unstable slope surface in minutes. Combing the quick scan time with the submillimeter accuracy of the ground-based InSAR (GBInSAR) system, the approach to data linearity can visually and statistically increase confidence in slope movement trend analyses in near-real-time. Data linearity means an unstable surface is beginning to move at nearly the same rate, and areas exhibiting different rates begin to coalesce over time, further increasing the visual representation of data linearity. Assisting the visual observation of an approach to linearity is a sequence of regression analyses (R2) that can show both a decreasing or increasing confidence levels.


What does the approach to data linearity mean during the monitoring of an unstable slope surface with data acquisition intervals of 4-minutes or less? First, consider a mental picture of an unstable slope surface, "is displacement occurring at the same rate at the same time everywhere on the slope surface? If the acquired movement rates are all moving at the same rate, the resulting data curve would be a smooth line. Typically, movement occurring on an extensive surface area exhibits different rates of movement during much of its unstable history. The different rates at various intervals affect the presentation of data, exhibiting what is often described as noise. The observed variability in data can be seen in cumulative displacement but is distinctly exhibited in velocity and inverse velocity data. Many agree that the observed variability in the data is inconsistent movement on the slope surface. Slope surface movement is influenced by friction, rock strength, geologic structure, pore water pressure, fractures, joints, thermal effects, and the pull of gravity, all creating a complex order of obstacles for a rock mass to overcome. Once some of the restrictive challenges are overtaken, acceleration can begin, often acceleration is gradual and displays variability between each acquisition interval while exhibiting an overall accelerating trend. Continued acceleration that begins to exhibit less variability between acquisition intervals or an approach to linearity is often an observational indicator of a possible failure.


Increasing confidence with predictive accuracy for slope failures during acceleration requires observing inverse velocity data followed by a series of regression analyses as the acceleration continues. Increasing data linearity should correlate to higher regression analysis values and together indicate that acceleration is becoming more consistent, supporting a higher level of confidence for predicting a slope failure.


Radar data from numerous sites have generally shown the most visually significant data variability, or noise occurs during regressive movement trends and low rate steady movement trends for both cumulative displacement and inverse velocity data. Alternatively, moderate to high rate steady trends generally exhibit less variability, and progressive or accelerating trends show a distinct approach to linearity. The approach to linearity also suggests that the resisting forces of friction, rock strength, geologic structure, have begun to lose their battle to pore water pressure and gravity.

The image above displays inverse velocity data from two different areas on the same unstable slope. From left to right, the red curve displays a regressive trend and exhibits an increase in data variability as the rate decreases (upward trend). The blue curve from left to right exhibits an initial regressive trend and then a short steady trend before changing to an acceleration trend. The acceleration data clearly shows an approach to linearity to the point of a phase ambiguity, which designates the point in time when the accelerating slope mass exceeds the maximum rate of the radar's scan interval. Or if the phase ambiguity is occurring, the slope is failing.


Unstable slopes vary in size from small surficial failures to large failures exceeding millions of tons of rock, and there appears to be an undocumented, correlation between the volume of an unstable slope and the time to failure. It appears from several sites that the time-to-failure occurs much faster for small rock volumes and much longer for larger rock volumes. Using inverse velocity data during acceleration and a best-fit trend line through the data to the x-axis (time axis) provides the best method for determining the possible time of slope failure. However, our experience has shown that not all acceleration events result in a slope failure as any number of factors can interrupt acceleration. Hence, the importance of employing data observations with multiple regression analyses using inverse velocity data as the acceleration event progresses.


The GBInSAR systems have resoundingly put to rest the myth that slope failures occur instantaneously with no warning as some in the media and others have proclaimed. It was widely broadcasted by local politicians that the massive failure occurring in Oso, Washington in 2014, that killed 43 people occurred instantaneously, and that massive landslides are impossible to predict. Unfortunately for Oso, no monitoring was in place before the failure, even though numerous professionals knew of the danger the slope presented. Two years before the Oso failure, I predicted a 5-million ton failure 3-days in advance of the actual failure time. During the same year of the Oso tragedy, the most massive historic landslide to occur in North America was successfully predicted at the Bingham Copper Mine in Utah with no fatalities or injuries. The volume of the Bingham slide was estimated to be about 70 million tons and registered an amazingly 3.2 magnitude on the Richter Scale. Both the Bingham Copper Mine and the 5-million ton mine failure used GBInSAR and the inverse velocity failure prediction method.

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