Soil Fatigue from Induced Seismicity

Induced seismicity and the effects on civil engineering systems are not completely understood and infrequently studied. One specific area that is not well known is soil fatigue which includes factors such as understanding the natural conditions of the subsurface as well as operational parameters under short duration impulse loads. With the increase of geoinduced seismic activity, soil fatigue becomes of greater concern to structures in the vicinity of this seismic load.,e foundations of these structures can be affected by impulse loads which can ultimately cause failure. ,e lack of quantitative data puts the reliability of these civil engineering systems at risk as they are not fully evaluated to determine if they are functioning as they are intended in the environments they are designed to support.


Introduction
Soil fatigue occurs prior to failure which makes it difficult to define as it is determined based on the acceptable level of risk the system can sustain. Determining factors for failure are usually based on social benefits and/or economic judgments that are difficult to quantify [1]. For purposes of this paper, soil fatigue can be defined as the magnitude of strain that a material can endure for a given number of cycles until a point of maximum strain where the soil begins to weaken. Similar to fatigue for other engineering structures bridges, roads, metals, etc., it is further defined as losing strength over time without catastrophic failure. However, such fatigue can ultimately lead to failure if left unchecked as it will continue to grow as the amount of applied impact load increases. e increase in geoengineered induced seismicity has created concerns for several civil engineering systems such as dams and levees. To date, the study of impacts from induced seismicity has been rare with indeterminate conclusions with significant volumes of research into the causality of geoengineered induced seismicity. However, little research has been completed into the accumulative effects of frequent colocated events as a single geoengineered event is assumed to be minor to cause any damage or degradation of the overlying soil structure [2][3][4].
ere is an abundance of literature regarding the study of single seismic event loading [5,6], as well as the behavior of partially saturated soils under cyclic loading [7,8]. However, these studies assume that the loading from geoengineered induced seismicity can be treated as isolated single events where the soil structure can fully recover before the next loading. Induced seismicity records from throughout the Central United States illustrate regions of close spaciotemporal small magnitude events, i.e., swarms, wherein any isolated event would typically be considered insufficient to cause any surficial expression of damage [2,3]. However, the cumulative effect of the close spaciotemporal swarms is not well understood and can potentially cause a fatigue condition within the soil.
To study soil fatigue, this paper presents a modified damage equation to account for degradation of soil structure as a result of low frequency impulsive loading, i.e., a proxy for spaciotemporal small magnitude events.

Geoengineered Activity and Induced Seismicity
Concerns regarding induced seismic activity have increased exponentially since 2009 due to the increase in the number of induced earthquakes magnitude (M) of 3.0 or larger [9]. Overall, the number of earthquakes in the central United States, M3.0 or larger, increased showing an average of around 300 earthquakes per year from 2009 to January 2016 [10]. In 2009 there were approximately 29 M3.0 or larger earthquakes with a large increase between 2009 and 2016 increasing to 330 M3.0 or larger earthquakes per year in 2016 [9].
A study was conducted in the western boundary of the stable Canadian craton using the three largest ground motion events: M4.0 and M4.2 near Fort St. John (FSJ), British Columbia, and an M3.9 in close proximity to the Rocky Mountain House (RMH) in Alberta that occurred between 30 July 2014 and 9 August 2014. e location selected for the study is a low-to-moderate seismic region which poses a large risk to infrastructure as it may not have been designed to resist strong ground motions because of the low probability of naturally occurring strong ground motions in the area [11]. In early investigations, the authors determined that moderate induced events (M4-5) could damage nearby infrastructure due to the shallow focal depth that can result in concentrated strong ground motions. e study was conducted using a sparse seismograph network to record the two events at FSJ, located anywhere from 15 km to several hundred km away. e recordings from these three events of M∼4 were then used to examine their ground motions along with their weakening with distance. When this study was conducted, the M4.2 event was the largest event related to hydraulic fracturing in the world. e two events at FSJ were determined through intesity assessments, ground motion characteristics, and focal depth estimations to be likely induced from hydraulic fracturing. ey occurred at shallow (2-5 km) depths that could be felt at distances over 200 km at a maximum intensity of M4.2 for the largest event. e third event at RMH was M3.9 and was the strongest event in Alberta in more than a decade. e focal depths were determined to be between 4 km and 8 km and the area shows no records of oil and gas drilling in recent years. e RMH event was felt by nearby residents and had reported intensity of M4-5 and caused a shutdown of a nearby gas plant and a power outage that lasted for many hours. All of these events were widely felt and had the potential to cause damage to infrastructure.
A study in Oklahoma [9] shows a definite increase in earthquakes beginning in 2009 with a steep increase from 2014 to 2015. Oklahoma does have a history of seismicity but recent studies show that it is highly unlikely that these are caused through natural fluctuations in the rates of earthquakes. Central Oklahoma has created cause for concern especially since it has had more than 60 earthquakes at M4.0 to M4.8 starting in 2009 to the middle of 2016. ere were larger events recorded in the same timeline that are currently under investigation due to the potential damaging effects of the seismic activity associated with the magnitude. One major earthquake was in Prague, Oklahoma, registered at M5.6 and was recorded [12] in November 2011. It destroyed 14 homes, injured two people, and buckled some parts of the highway and 17 other states could feel the tremble [13]. e largest earthquake documented was in Pawnee, Oklahoma, which was recorded at M5.8 causing substantial damage to infrastructure [9]. e M5.8 earthquake in Pawnee, OK, in September 2016, was the biggest recorded in the state and could possibly be related to wastewater injection.
ere is statistical data that supports this conceptual model that shows the seismic activity linked to the distance between the basement and the injection point.
is data provides regulators with information on how pore pressure develops through the knowledge of existing faults and ambient stress levels [14].
e study included a gas extraction process as studied in Groningen, e Netherlands. e process established for gas production compacts the reservoir that causes the build-up of stress along faults. Because of preexisting offsets, compartment reservoirs that have varying compaction levels meet along the faults. e compaction differences can increase the built-up stress at the faults which can in turn increase the occurrence of earthquakes [14].
rough subsidence measurements used to calibrate reservoir compaction in models, it identified seismicity concentrated in locations of high subsidence and compaction. ese induced events are recorded after a reduced reservoir pore pressure by ∼10 MPa with the outcome of an increase in rock stress that is of similar magnitude [14].
is conflicts with observations in Oklahoma that shows pressure disturbances of ∼0.1 MPa initiating earthquakes.
is shows that the crust is critically stressed and has a subset of faults that are near failure that can cause activation through a small amount of disturbance of stress [14].
In both of these activities, location and timing of the induced seismic activity are controlled by the distribution of space and the make-up of preexisting faults with existing stress conditions prior to subsurface work [14]. e current assumption regarding the size of induced events is that failures from induced activity are confined within the volume of rock that is affected by changes in stress of fluid pressure. However, recent studies by Van der Elst et al. [15] and Galis et al. [16] contradict this assumption and show that earthquakes induced from human activity could potentially fail outside of the volume that is affected. So that size of the induced earthquake can be manipulated through preexisting natural fluctuations of stress along the fault similar to natural events [14]. In either case, evidence suggests the need to understand preexisting faults as well as their stress level. Mitigation measures need to include both operational parameters, i.e., volume produced and volume injected, but must also include knowledge of the status of faults within the subsurface. is can be identified through hydromechanical modeling, operation parameters calibrated by independent measures through the use of InSAR to identify surface deformations [14].
A study was conducted by Zalachoris and Rathje [17] to develop ground motion models (GMMs) for small to moderate sized, potentially induced earthquake events in Texas, Oklahoma, and Kansas. e team created a database with events with epicenters in those specific locations through the use of the Incorporated Research Institutions for Seismology (IRIS), 2018. Events that had at least 3 ground motions and at magnitudes that were greater than 3.0 were used for this effort which included 4,528 ground motions that were recorded during 376 events with hypocentral distances at less than 500 km. In an effort to quantify site amplifications, the team used the P-wave seismogram method that uses theoretical wave propagation considerations as well as recordings from seismic stations to estimate the VS30 at 251 seismic station locations within the defined area. In addition, the team investigated the relationship between geologic conditions and VS30 estimates at each location. is new model predicts smaller ground motions than other models and predicts an increase in ground motions at hypocentral distances less than or equal to 20 km. e newly scaled VS30 was determined to be weaker than other models and less amplified at VS30 <600 m/s [17]. It should be noted that there is an abundance of research into the source initiation and spectral characteristics of induced seismicity (see, e.g., [18][19][20]). ere have been several notable studies investigating the seismic vulnerability of structures to induced seismicity (see, e.g., [21][22][23][24][25]). ese studies illustrate that there exists the potential for structural susceptibility for moderate to slight damage from induced seismicity. While the severity of the potential damage to structures from induced seismic events may not be as significant as HAZUS models based on the New Madrid Seismic Zone, these results clearly indicate that the potential damage is not insignificant. To further illustrate damage potential on structures from the increase in seismicity in parts of the central United States, a recent study by Liu et al. [25] identified that nonstructural components of structures have the potential to sustain damage from induced events as well as increased risk towards potential building collapse. In particular, Chase et al. [22] indicated that in the case of lightframe wood structures the structural damage and fragility did not seem to be accumulating with sequential seismic loadings. Liu et al. [25] calculated life-safety risk from the USGS 2016 one-year seismic hazard model as well as the fragility curves that are defined in the 2015 NEHRP (National Earthquake Reduction Program) Provisions. ese results indicate that life-safety risks for modern buildings, in areas that are close to active induced seismic zones, have the potential to exceed the risks calculated from the 2015 NEHRP provisions' report that considers natural seismicity alone [25]. erefore, if nonstructural components can sustain damage and increase the potential risk of structural collapse from induced seismicity, then the logical question is as follows: "Can the fatigue of the subsurface yield similar increased risk?" Moreover, do sequential induced seismic events have an accumulative effect on the fragility or fatigue of the subsurface?

Laboratory Observations of Soil Fatigue for Impulsive versus Cyclic Loading
To determine the reliability of a system, an object is assessed to determine failure which is the lack of ability of a system to function normally under the same specified conditions for the same amount of time [1]. In the case of soil mechanics, the point of failure is determined via an ultimate, or peak, failure condition, typically occurring when the strains exceed between 2% and 5%. However, failure of the soil structure can occur at a significantly lower strain [26,27]. is loss of soil structure stiffness can result in small-scale collapses, i.e., small-strain compression, yielding, or settlement, as the soil element transitions to the next quasi-stable soil structure. If the excitation sources, e.g., impulses from pile driving, occur at a rate where the soil structure is continually forced to transition to the next quasi-stable state, the summation of the small-strain compression can cause superstructures, e.g., buildings and infrastructure, to exceed allowable design tolerances without causing an ultimate failure, e.g., structural collapse. is behavior defines the soil fatigue process. As subjective as failure is, soil fatigue is as well and far more difficult to identify as the experience which is usually known as the factor of safety is unknown [1]. is makes it difficult to quantify soil fatigue from close proximity spaciotemporal small magnitude events.
In a study conducted by the Engineering Research and Development Center, Geotechnical and Structures Laboratory (ERDC-GSL), laboratory tests were conducted to show the difference in dynamic behavior of near-surface partially saturated sand in reference to the potential for liquefaction from both cyclic and impulse loadings [28]. e outcome of these tests identifying the effects of near-surface soils with equivalent sinusoidal loads does not show the same strains as impulse loads to represent seismic waveforms that are irregular [28]. e 0.3% axial strain yield threshold is used based on a study conducted by [29] to identify significant limiting strain at the beginning of movement from pile strikes that began around 0.3% ε da . e study consisted of a series of cyclic tests shown in Table 1 with the number of cycles needed to attain a certain double amplitude axial strain, ε da , as shown in Figure 1. e results suggest that an exponential increase in the rate of strain starts to occur at around 0.3% ε da , which is prior to the ultimate failure threshold of 5% ε da . Additionally, it was observed that 47% of the completed tests reached 0.1% ε da within the first cycle which suggests that the use of 0.1% as a yield initiation threshold would be overly conservative. Further tests identified that the capacity at 0.3% ε da is about half of the difference of 0.1% and 5% ε da and is about the mean of the distribution of the capacity-strain threshold, as shown in Figure 1 [29]. erefore, a yield initiation, or fatigue, threshold of 0.3% ε da as the maximum allowable fatigue stain for saturated dynamic loading is justified.
Taylor et al. [28] identify changes in dynamic behavior of near-surface partially saturated sand illustrating the strain potential from comparable cyclic and impulse loading wherein ten partially drained triaxial impulse and cyclic tests were conducted on poorly graded medium-fine beach sand with 24% saturation with a confinement of 10 kPa. An ultimate failure criterion of 2.5% axial strain was imposed based on samples tested through triaxial testing for a qualitative comparison of the loading requirements needed to cause an ultimate failure condition; see Figure 2 and Table 2 [28]. e test results showed no signs of liquefaction Advances in Civil Engineering or symptoms of uncontrolled straining as observed in saturated conditions, e.g., Taylor [29]; however, the impulse tests did reach the 2.5% straining threshold where an equivalent cyclic load did not. All of the impulse load tests exceeded the failure criteria of 2.5% ε a between 9 and 19 cycles with an average of 12 cycles to failure. Only three of the cyclic test reached the 2.5% failure criteria with an average of 100 cycles to failure. is study identifies the need to Advances in Civil Engineering study cyclic and impulse loads with respect to near-surface seismic resistance. As shown by the data, cyclic loads, the increase in axial strain is nonlinear and has a logarithmic trend with a low number of cycles followed by a large increase at 50 cycles which identifies the potential for softening of the soil; however, this is not enough to reach liquefaction. On the other hand, impulse loads showed the increase in strain to be linear after an initial loading spike which identifies a constant strain [28].

Determining Damage Potential from Soil Fatigue
It is feasible through innovative processes to determine damage from soil fatigue that will allow engineers to identify when the system is not functioning as it should.
Most studies are focused on the effects of cyclic soil degradation on soil strengths but neglect including potential damage from impulse loads. In addition, the damage accumulation effects from earthquake swarm events are largely unknown. Newmark's [30] sliding block analysis touches on this concept but focuses on a single earthquake with a distinct number of times the acceleration exceeds the threshold. e focus of this paper is to consider multiple events in close proximity where each event has a single time the acceleration exceeds a threshold value. Based on Taylor et al. [28], it is important that cyclic and impulse loading tests are treated differently so equation (1) is introduced to identify a more accurate picture of liquefaction from induced seismic events. To consider the seismic design of a structure in this paper, a conceptual model is provided to analyze the equations presented in this paper. e pseudostatic slope stability method is a commonly used procedure to determine slope stability under seismic loading that was introduced by Seed [31]. It was further improved by Bray and Travasarou [32,33] to better rationalize the identification of the seismic coefficient used in the analysis.
is method uses a probabilistic seismic slope displacement model to determine slope stability under seismic loading. It uses the yield coefficient (k y ), the initial fundamental time period of the sliding mass (T s ), along with a degraded time period of spectral acceleration (S a )1.5T s , (M) being the moment magnitude of the earthquake, and ε being the normal distributed random variable. Equation (1)  (1) e example presented in this paper is created as an example for potential settlement from earthquake swarm events on a standard office building. e below slope stability analysis was completed through the use of the Seismic Landslide Movement Modeled using Earthquake Records (SLAMMER) program created for the USGS [34]. e program is used to analyze permanent deformations of slopes to identify how they behave during an earthquake. e Bray and Travasarou [32] method was used for this analysis with the use of existing data incorporated into the SLAMMER system as well as assumptions that were used to calculate displacement. Using the data included in the SLAMMER system, shown in Figures 3 and 4, the below record was used as a sample product for the calculations used in the Bray and Travasarou flexible (coupled) method with a modification of the earthquake magnitude from M7 to M4 to represent the potential for damage at small magnitudes [34]. e Bray and Travasarou flexible coupled method was selected to estimate permanent displacement from a single deterministic event or the probability of exceeding specific permanent displacements [34]. e flexible analysis estimates the nonzero displacement as well as the probability of   zero displacement. Figure 5 shows the correlation of the yield coefficient to the median displacement from data shown in Table 3. e data shows little to no displacement based on the above parameters.
In an effort to identify soil fatigue from earthquake swarms and show that induced seismic events have shorter dominating peak accelerations as well as shorter durations (2) was modified from Allotey and Nagger [35] damage equation to replace cyclic loading with impulse loading as well as adding an additional nonlinear stress dependent variable: where D is the constant stress-controlled loading, fatigue damage function that is assumed to be a single valued deterministic figure that is nondimensional, and nondecreasing part of the stress ratio under a given number of  cycles. N is the current number of cycles elapsed at the stress ratio S and N f (S) is the number of cycles of the stress ratio, S, to reach failure. Failure is defined as soil fatigue which is determined to be the magnitude of strain that a material can endure for a given number of cycles until a point of maximum strain where the soil no longer functions as intended. e stress ratio, S, is the initial mean effective confining stress and Θ is a nonlinear function with loading cycles that is a stress dependent variable in the applied stress (CSR) and confining pressure. As the stress levels vary, the damage rate   changes; depending on the sequence of loading, the life of fatigue can be less than or greater than one [36]. A threshold of 0.3% strain allows a comparison of cyclic loading vs impulse loading [29]. In contrast to the previous analysis from Bray and Travasarou [32] that did not register damage, Table 4 and Figure 6 show that when being modified from cyclic loading to impulse loading, the damage rate changes at varying stress levels. ese results identify degradation to the soil structure that might not be seen immediately but overtime can cause failure if left unchecked. is level of damage can be catastrophic in infrastructure that is constructed to a certain level based on the existing seismic design criteria. Using this method, the data identifies the potential failure from settlement due to earthquake swarms and should be considered in seismic evaluations.

Conclusion
Induced seismicity or induced earthquakes have become of great concern in recent years as rates of these events continue to grow. e inducement of seismicity from underground and surface mining, extraction of oil and gas, reservoir impoundments, and injection of fluids into geologic formations at the subsurface has been understood for some time now; however, these studies neglect incorporating the potential effects that these impulse loads may have on civil engineering systems. One of these potential effects is soil fatigue which can be considered a slow weakening of material because of sources external to the structure that act upon the reliability of it.
is should be considered in current evaluation standards and studied to determine if the structure can sustain impulse loading that occurs at shallow depths to identify issues with the foundation prior to failure. e introduction of a new damage equation is an extension of the Allotey and Naggers [35] model that modifies the loading criteria to impulse in lieu of cyclic to get a better depiction of soil degradation from induced seismic events. It was further modified to include a nonlinear function with loading cycles that is a stress dependent variable for both applied stress and confining pressure. e limitation of the Allotey and Nagger [35] model to determine soil degradation from induced seismic events was based on cyclic loads which do not depict strains that develop from impulse loads. Based on the reformulation of the equation, a better picture of potential damage effects to soils near the surface under impulse loading can be attained. is redundancy is needed as the existing process to access damage to infrastructure from induced seismicity is not adequate as it requires a better understanding of the failure modes and threshold limits within the Seismic Hazard and vulnerabilities structures that are not well equipped to survive seismic loading. Moreover, the difficulty in quantifying the seismic hazard for induced event continues as the hazard is not completely understood and changes in geoengineered locations, activities, and technologies are ever present. However, thorough innovative processes and further studies on this particular topic will allow for a better assessment and determination of detrimental degradation to be observed at the subsurface.

Data Availability
All data used to support the findings of this study can be obtained via the published references.

Conflicts of Interest
e authors declare that they have no conflicts of interest.