Landslide Simulation Research Articles

3D simulation of Vajont disaster. Part 1: Numerical formulation and validation

This work presents a numerical method for the simulation of landslides generated impulse waves and its application to the historical Vajont case study. The computational tool is based on the Particle Finite Element Method (PFEM), a Lagrangian strategy that combines the finite element solution of the governing equations with an efficient remeshing strategy to deal with large deformation problems. After presenting the numerical formulation, different landslide impulse wave problems with Froude number ranging from 0.5 to 2.8, are analyzed to validate the proposed methodology. The computational method is shown to be able to reproduce accurately the landslide runout, the momentum transfer between the sliding material and the impounded water, and the consequent wave propagation observed in experimental physical models. Then, the PFEM model is applied to the numerical simulation of the Vajont disaster, which is analyzed with a fully-resolved three-dimensional model. The numerical results are discussed and compared to the post-event observations and the numerical results of other computational methods. The results in terms of landslide velocity and runout, geometry of the deposit, maximum water runup, dam overtopping wave, and water discharge in the downstream valley are in good agreement with observations and reconstructions. The calibration and validation performed for this study form the basis for the PFEM analyses presented in a companion paper finalized to simulate different scenarios of the Vajont rockslide considered in the experimental tests done a year before the disaster.

Analysis and modeling of a landslide-induced tsunami-like wave across the Truong river in Quang Nam province, Vietnam

Landslide-induced waves are one of the most disastrous hazards that can post a great threat to human lives and properties. At about 4:00 pm, 5 November 2017, a landslide-induced tsunami-like wave suddenly occurred across the Truong river in Bac Tra My District, Quang Nam province, Vietnam. The water wave destroyed six houses at the opposite bank and caused one person dead and three others injured. This study seeks to investigate the initiation mechanism and process of the landslide and its impulse wave. First, we examined landslide characteristics through site investigations, unmanned aerial vehicle (UAV) surveys, and laboratory testing with a series of standard geotechnical tests on collected soil samples. Then, the initiation and motion of the rainfall-induced landslides were reproduced by the integrated landslide simulation model (LS-RAPID). Finally, a combined computer simulation of the landslide motion and its impulse wave was performed by using a landslide-induced tsunami simulation model (LS-Tsunami). In which, output data from the LS-RAPID was used as input parameters for LS-Tsunami. The analysis shows that the rainfall with very high intensity in a short-time period was the triggering factor of the landslide, which is common factor in the study area. The 12-, 24-, and 48-h accumulative precipitation prior to the landslide recorded to 530, 760, and 950 mm, respectively. In addition, the rainfall trigger presented a typical pattern of rainstorm events in a long duration. Simulation results show that the impulse wave was generated by the landslide mass rapidly entering the river, crossing the river, and directly causing the disastrous damage to the resident area opposite site of the fail slope. The landslide moved down at a maximum speed of 16.4 m/s when its body approached the water surface and generated a maximum wave height of 5 m. There is good agreement between the observed geomorphic evidences and water traces on the site and simulation results of the landslide and its impulse wave. The paper provides a good case study on the understanding of the mechanism and dynamic process of the whole event that significantly contribute to potential landslide hazard assessment and future disaster mitigation in the area.

A coupled hydrological-geotechnical framework for forecasting shallow landslide hazard—a case study in Halong City, Vietnam

Shallow landslides have posed significant threats to humans around the world. In order to reduce landslide disaster risk, the effectiveness of early warning systems and hazard zonation work needs to be improved. This research attempted to couple a landslide simulation model (LS-RAPID model) and a hydrological model (Rainfall-Runoff-Inundation (RRI) model) to exploit the advantages of each model for simulating and predicting landslide hazard (location and timing). The pilot area is a small catchment where a shallow landslide happened in July 2015 after 2 days of heavy rain. The landslide buried 3 houses and killed 8 people in Cao Thang Ward, Halong City, Vietnam. A soil sample was collected from the sliding surface and tested using an undrained ring-shear apparatus ICL-2 in the undrained condition. A thickness map of the potential sliding material was interpolated from the relationship between the depth of sandy soil layer and slope (based on 12 soil drill locations) and updated through field surveys in the study area. Different pore water pressure ratio scenarios were applied in the LS-RAPID model to simulate in 3D the initiation and motion of the rapid shallow landslide to create different hazard maps. The subsurface water level was monitored at two locations on the top of the shallow landslide. Based on the observed subsurface water and rainfall data, the RRI model was calibrated and then integrated with the LS-RAPID scenarios to generate Risk Index maps. The simulation results from the newly proposed coupled hydrological-geotechnical framework were compared with those from the observed landslide hazard and showed the reliability to predict the spatial and temporal occurrence of landslide hazard. This could be very useful for supporting decision-makers in rainfall-induced landslide hazard early warning and land use planning.

Influence of digital elevation models on the simulation of rainfall-induced landslides in the hillslopes of Guwahati, India

Topographic input parameters such as slope, curvature, and drainage area are derived from a Digital Elevation Model (DEM) representing the spatial elevation, and are widely used as important sources of geospatial information. Based on the chosen DEM and its derived paramters, physically based GIS models, such as TRIGRS, can compute the transient degradation of the hillslope stability due to rainfall infiltration to identify the landslide occurrences in the considered region. Hence, it is inadvertent that the accuracy of the DEM will significantly affect the outcome of the TRIGRS simulations. Obtaining a high-resolution DEM (using LiDAR, dGPS or other such ground based advanced surveying methods) for a large area is an expensive affair and unavailable in most cases. Hence, under such circumstances, DEMs available in public domain vis., CartoDEM, ALOS-AW3D30-DEM, SRTM-DEM, and ASTER-GDEM, serves to be the sole option. Each of these DEMs are obtained from varying sources using different data collection and processing techniques, thereby leading to DEMs of varying resolutions and different accuracies. Although there is ample literature on the effects of the resolution of specific DEMs, the influence of the varying accuracies of DEMs chosen for TRIGRS simulation has not been adequately reported. Considering the landslide scenario of Guwahati city as the study region, the effect of dissimilarity in DEMs on the prediction of the rainfall-induced landslides in the hillslopes of the study area is reported in this paper. Three rainfall events triggering landslides were considered as input into TRIGRS, and the simulation outcome of the different DEMs were compared with reported landslide locations. Significantly different outputs were obtained for the DEMs highlighting the importance of the analysis. Based on two different evaluation methodologies, i.e. the ROC and LRclass, landslide occurrences identified by ALOS-3D DEM provided the best agreements with the reported landslides, followed by those identified by Carto-DEMs.

Improvements to a smooth particle hydrodynamics simulator for investigating submarine landslide generated waves

SummarySubmarine landslides can exhibit complex rheologies, including a finite yield stress and shear thinning, yet are often simulated numerically using a Newtonian fluid rheology and simplistic boundary conditions. Here we present improvements made to a Smoothed Particle Hydrodynamics simulator to allow the accurate simulation of submarine landslide generated waves. The improvements include the addition of Bingham and Herschel‐Bulkley rheologies, which better simulate the behavior of submarine mudflows. The interaction between the base of the slide and the slope is represented more accurately through the use of a viscous stress boundary condition. This condition treats the interface between the seafloor and the slide as a fluid boundary layer with a user‐defined viscosity and length scale. Modifications to the pressure and density calculations are described that improve their stability for landslide generated wave scenarios. An option for pressure decomposition is introduced to prevent particle locking under high pressure. This facilitates the application of this simulator to landslide scenarios beneath significant water depths. Additional modifications to the reaveraging and renormalization routines improve the stability of the free surface and fluid density. We present the mathematical formulations of these improvements alongside commentary on their performance and applicability to landslide generated wave modeling. The modifications are verified against analytical fluid flow solutions and a wave generation experiment.

A scenario-based assessment of the tsunami hazard in Palermo, northern Sicily, and the southern Tyrrhenian Sea

Abstract Palermo is a populous city situated on the northern coast of Sicily, bordered by the Tyrrhenian Sea. This central part of the Mediterranean Sea features dramatic bathymetry, numerous subaqueous landslides and is also the epicentre to many subaqueous earthquakes. As such, the region is an area prone to tsunamis. This investigation uses the Cornell Multi-Grid Coupled Tsunami (COMCOT) tsunami modelling package to simulate five near-field landslides, and five near-field earthquakes regarded as worst-case credible scenarios for Palermo. The seismic simulations produced waves on a very small scale, the largest being c. 5 cm at its maximum height, and none of the earthquake-generated tsunami waves produced any measurable inundation. The landslide simulations produced larger waves ranging from 1.9 to 12 m in maximum height, two of which resulted in inundation in areas surrounding the Port of Palermo. Sensitivity analysis identified that fault width and dislocation as well as landslide-specific gravity did have significant influence over maximum wave height, inundation and maximum run-up wave height. There are methodological issues limiting the extent to which this study forms a comprehensive tsunami hazard assessment of Palermo, such as gaps in bathymetric data, computational restrictions and lack of a probabilistic element. These issues are counteracted by the fact that this study does serve as a robust first step in identifying that landslides in the region may produce larger tsunami waves than earthquakes, and that the directionality of mass movement is critical in landslide-driven tsunami propagation in the southern Tyrrhenian region.

A resolved CFD–DEM approach for the simulation of landslides and impulse waves

Landslides and subsequent impulse waves could result in destructive hazards, while most of the existing simulation methods are dependent on over simplifications or excessive hypothesis due to the numerical difficulties. In order to elaborately present the phenomenon of the strong coupling and the mechanism of the energy transfer between the fluid phases and the landslides, a novel resolved computational fluid dynamics-discrete element method (CFD–DEM) is proposed in this paper. The fluid phases, including the water and the air, are governed by the full Navier–Stokes equations in the Eulerian framework, whereas the landslide motion is modeled by the discrete element method using the Lagrangian description. The key challenge, namely the representation of the moving interfaces between the fluid and the landslides in different frameworks, is handled by the immersed boundary method. Meanwhile, the free surface of the impulse waves between the water and the air is captured by the conservative Level Set method, and the coupled system is solved by the partitioned method in an iterative way to obtain the strong coupling effect. Compared with the unresolved CFD–DEM method, the proposed approach calculates the fluid field with high resolution and reflects the mutual interaction precisely. After the verification of the overall performance by two benchmark cases, the resolved CFD–DEM method is applied to simulate the landslide movement and the subsequent generated waves in the Lituya Bay.

SPH Simulation of High-Volume Rapid Landslides Triggered by Earthquakes Based on a Unified Constitutive Model. Part II: Solid–Liquid-Like Phase Transition and Flow-Like Landslides

High-volume fast-moving landslides undergo a solid–liquid-like phase transition. In this study we apply the smoothed particle hydrodynamics (SPH) method to simulate the solid–liquid-like phase transition in earthquake-induced landslides based on a unified constitutive model. The feasibility analysis is carried out from two aspects: the governing equations in SPH and the unified constitutive model. A sand-collapse experiment simulating the fluidization motion is performed to verify the SPH model. Strong similarities between the SPH results and the experimental results are observed, confirming that the motion of geo-materials in different states can be simulated by the unified constitutive model. The entire process of the Tangjiashan landslide is reproduced. The SPH simulation shows that during the initiation process, the sliding-mass velocity was low as the geo-materials were in solid state. As shown in Part I of this study, a continuous slip surface formed at about 15[Formula: see text]s. The sliding body gains speed as it enters the fluid state. About 50[Formula: see text]s later, the mass gradually stops moving, reaches a steady state and returns to a solid phase. Besides, the SPH simulation based on elastic–plastic model clearly shows the advantage of the proposed model.

SPH Simulation of High-Volume Rapid Landslides Triggered by Earthquakes Based on a Unified Constitutive Model. Part I: Initiation Process and Slope Failure

Landslides triggered by seismic loading pose a great threat to human lives, property, and infrastructure. This paper embeds a unified constitutive model in the smoothed particle hydrodynamics (SPH) method and analyzes the initiation process of landslides. A seismic wave is applied to bottom boundary particles by imposing velocities calculated using the seismic wave. The bottom boundary is set as a no-slip boundary and the free field boundary is chosen to reduce seismic wave reflection. The reliability of the developed SPH method is first validated by the simulation of a benchmark problem of thin plate oscillation and stability analysis of a homogenous slope. Initiation of the earthquake-induced Tangjiashan landslide is then simulated as a case study. Formation of a shear zone under the action of seismic loading is followed by the formation of a continuous slip surface at about 15[Formula: see text]s. The sliding surface formed in the SPH simulation agrees well with the speculative sliding surface based on field observations. The velocities of monitored points during the initiation process are also captured by the SPH method.

Application of the Chebyshev spectral method to the simulation of groundwater flow and rainfall-induced landslides

In this paper, the potential of the Chebyshev spectral method (CSM) is examined for the numerical solution of time-dependent variably saturated Darcian flow problems described by the Richards equation (RE). Generally, the computational efficiency of the traditional finite difference method (FDM) is not high because it requires a high mesh density to improve accuracy. Therefore, the Chebyshev spectral method (CSM) was extended to model groundwater transient flow in unsaturated soils. Furthermore, the Gardner model (soil-water characteristic curve) was adopted to linearize the RE for an inclined slope. The test results demonstrated that the accuracy, efficiency, and robustness of the CSM are better than those of the traditional FDM. A comparison of the analytical solutions of each method showed that the computational accuracy (L2(h*)) of the CSM was less affected by the grid size than that of the FDM. Simultaneously, the CSM was not sensitive to the initial conditions. The results demonstrated that the numerical accuracy of the CSM was stable in the order of 10−6 to 10−7, whereas that of the FDM was in the order of 10−3 to 10−6; it achieved higher accuracy with fewer grid points. The CSM was successfully applied to solve the one-dimensional transient flow problem on unsaturated soil slopes. The numerical results indicated that the proposed method solved the transient flow problem related to rainfall-induced landslides with high accuracy. This proposed approach can be developed to analyze rainfall-induced landslides.

Variation patterns of landslide basal friction revealed from long-period seismic waveform inversion

A catastrophic landslide struck the Xiaoba village in Fuquan, Guizhou, southwestern China at about 8:30 p.m. (Beijing Time, UTC + 8) on August 27, 2014. The landslide and induced impulse water waves destroyed two villages and killed 23 persons. By reprocessing seismic signals from a seismic network deployed in the surrounding area of the landslide, we recognized the event from low-frequency seismic signals and subsequently performed a long-period seismic waveform inversion to obtain its force–time history. The inversion results reveal that the maximum force for the landslide is 5 × 109 N, and the duration of the landslide is 38.4 s. The landslide reached its maximum velocity of 12.4 m/s at 13.2 s after its initiation, and the mass center plugged into the quarry at 24.2 s. Based on the inversion results, we estimated basal friction of the landslide. We found the friction coefficient rapidly reduces to a relatively steady-state value of ~ 0.4 at a steady-state distance of 35 m and subsequently reduces in a near-linear manner that satisfies the empirical formula mu = - 1.4d + 0.44 , where d is sliding distance in km. The reduction in friction revealed by the formula is compatible with the finding of previous studies for landslides of similar volume in landslide acceleration stage. However, our result does not make it possible for the friction coefficient to increase again in landslide deceleration stage that a velocity-dependent friction law would allow. The friction variation patterns can be used to constrain input parameters in numerical landslide simulation, which can predicate runout distance and deposit areas for massive landslides to carry out landslide hazard assessment.

Three-dimensional distance potential discrete element method for the numerical simulation of landslides

The study focuses on the kinetic process of landslides, including associated travel trajectory and endangered area. A three-dimensional distance potential discrete element method for the movement process of landslides is developed in this work. Benefited from a new definition of the distance potential function with a clear physical meaning, a holonomic system of the calculation algorithm for the contact interaction is established, accounting for the influence of the tangential contact force. Performance of the new approach is validated with well-known benchmarks, which consist of a block impact simulation, a sliding/toppling test of a joint rock slope, and block response to induced acceleration in the foundation. The results are in good agreement with the analytical solutions, showing an ability of the newly method in capturing the microscopic mechanical behaviors and macro-motion characteristics of individual blocks. After the verification of the overall performance by three cases, the proposed method is applied to simulate the Tangjiashan Landslide trigged by the Wenchuan Earthquake in 2008.

Runout simulation of seismic landslides using discontinuous deformation analysis (DDA) with state-dependent shear strength model

The reliable numerical simulation of the landslide process contributes to the establishment of evidence-based disaster mitigation measures in seismically active zones. To achieve this goal, a simple and unified state-dependent shear strength model of discontinuities is presented to describe the shear strength degradation in a seismic landslide process. The proposed model establishes a relationship between the shear strength parameters and the global safety factor of the slope by assuming that the slope instability (or landslide initiation) is accompanied by an instantaneous shear strength degradation of discontinuities. To realize the model numerically, the algorithms for the computation of global safety factor and the modification of shear strength parameters were incorporated into the discontinuous deformation analysis (DDA). Subsequently, the kinematic accuracy of the improved DDA method was validated by comparisons with theoretical solutions for the dynamic sliding of a block on an inclined plane. Numerical simulations of the Daguangbao landslide triggered by the Wenchuan earthquake were performed using the improved DDA method. The results illustrate that the shear strength degradation of discontinuities affect the evolution process, travel distance, and post-failure shape of the seismic landslide significantly.

Geoelectrical characterization and monitoring of slopes on a rainfall-triggered landslide simulator

In this paper, we present the results of time-lapse electrical resistivity tomography (ERT) monitoring of rainfall-triggered shallow landslides reproduced on a laboratory-scale physical model. The main objective of our experiments was to monitor rainwater infiltration through landslide body in order to improve our understanding of the precursors of failure. Time-domain reflectometry (TDR) data were also acquired to obtain the volumetric water content. Knowing the porosity, water saturation was calculated from the volumetric water content and we could calibrate Archie's equation to calculate water saturation maps from inverted resistivity values. Time-lapse ERT images proved to be effective in monitoring the hydrogeological conditions of the slope as well as in detecting the development of fracture zones before collapse. We performed eight laboratory tests and the results show that the landslide body becomes unstable at zones where the water saturation exceeds 45%. It was also observed that instability could occur at the boundaries between areas with different water saturations. Our study shows that time-lapse ERT technique can be employed to monitor the hydrogeological conditions of landslide bodies and the monitoring strategy could be extended to field-scale applications in areas prone to the development of shallow landslides.

Numerical Simulation of Subaerial and Submarine Landslides Using the Finite Volume Method in the Shallow Water Equations with (<i>b</i>, <i>s</i>) Coordinate

Numerical Simulation of Subaerial and Submarine Landslides Using the Finite Volume Method in the Shallow Water Equations with (<i>b</i>, <i>s</i>) Coordinate

A conservative and consistent Lagrangian gradient smoothing method for earthquake-induced landslide simulation

Numerical study of earthquake-induced landslides plays an important role in the disaster prevention and post-earthquake managements. Thanks to its mesh-free feature, the SPH (Smoothed Particle Hydrodynamics) method has significant advantages over the traditional grid-based methods in dealing with extremely large deformation problems such as high-speed fluid-like landslides. However, SPH is unstable when the material is in tension, which is widely known as the ‘tensile instability’ problem in SPH. Although the instability issue can be removed to certain stand by particular ad-hoc techniques, the root cause of the problem is not addressed. In addition, such ad-hoc techniques require additional user-defined parameters, which is difficult to make universally applicable. In this study, a conservative and consistent Lagrangian Gradient Smoothing Method (L-GSM) is proposed for fluid-like landslide simulations based on the recently developed meshfree L-GSM. In the present L-GSM, the strong-form of governing equations is discretized using the GSM gradient operator in a conservative and consistent manner. Moreover, a simple and accurate boundary treatment for free surface and solid boundary is newly proposed for L-GSM to handle the complicated free surface and solid boundary existed in the landslide problems. Finally, the proposed conservative and consistent L-GSM framework is validated by a soil column collapse benchmark and three real landslide problems. Results show that our L-GSM can give an accurate and reliable solution to the fluid-like landslide problem with a high efficiency. The treatments for free surface and solid boundary are also proven very effective in producing desired boundary conditions. Both cohesive soil column collapse example and Wangjiayan landslide example demonstrate that L-GSM is indeed free from the tensile instability problem.

Development of a Coupled DDA–SPH Method and its Application to Dynamic Simulation of Landslides Involving Solid–Fluid Interaction

Landslides involving solid–fluid interaction such as submarine landslides and landslide dams occur frequently around the world, which may bring severe damage to human lives and properties. Investigation of such landslides is thus of significance to hazard prevention and mitigation. To conduct the analysis, there are three key points to be addressed: (a) the landslide failure process, (b) the free surface flow, and (c) the solid–fluid interaction process. Discontinuous deformation analysis (DDA) method is suitable for analyzing discontinuous blocky systems and has outstanding advantages in simulating the landslide failure process. Meanwhile, smoothed particle hydrodynamics (SPH) method is well-suited for modeling the free surface flow. However, the consideration of solid–fluid interaction in these two methods is seldom, which somehow restricts their applications. With the aim to take advantages of these two methods, a coupled DDA–SPH method in two-dimensional case is proposed, in which the solid–fluid interaction is forced using a penalty approach. The SPH formulations are implemented into DDA code. Several numerical examples are presented to check the validity of the proposed method. A dam-break test is first investigated to show the success of implementing SPH into DDA code for modeling the fluid flow in later simulations of fluid–solid systems. Subsequently, the performance of the coupled DDA–SPH method is validated through a submarine rigid landslide, and the simulation results are in good agreement with the experimental data. Further, an extension study on the submarine deformable landslide is performed, in which the landslide mass consists of multiple blocks and a sensitivity analysis on the interface friction angle between blocks is conducted. Finally, a designed landslide dam is simulated to show the applicability and feasibility of the coupled DDA–SPH method.

Numerical Simulation of a Creeping Landslide Induced by a Snow Melt Water

In this study, a finite element based numerical method has been considered to evaluate the creeping behavior of a landslide induced by snow melt water. A two-dimensional elasto-viscoplastic constitutive model was used to simulate the creeping behavior owing to groundwater level fluctuations of the Tomuro landslide of Gunma, Japan as a case study. Two new control constitutive parameters were incorporated in the numerical model for the first time to better understand the creeping behavior of a landslide induced by snow melt water. Such control constitutive parameters are estimated based on the relation between the total factor of safety, calculated by the Janbu's Simplified Method (i.e., Limit Equilibrium Method), and the field monitoring displacement rate of the Tomuro landslide of Gunma prefecture, Japan. The snowfall precipitation was also considered during the calculation of total factor of safety. Others required material parameters for landslide simulation were obtained from the field investigation and laboratory tests of the collected blocked samples. The simulation results of deformation pattern and shear strain pattern were presented and discussed to understand the creeping behaviour of the Tomuro landslide. Moreover, the predicted and measured time histories of horizontal displacement of the Tomuro landslide were compared for the validity of the proposed numerical model, and found in good agreements with each other. Therefore, it is believed that the proposed numerical method will be applicable to understand the creeping behavior of a landslide induced by snow melt water in the future and at the same time, long-term monitoring and management of such landslide will be much easier.

Physically based modeling and animation of landslides with MPM

Landslide is a disaster which may cause huge losses of human life and block the traffic on hilly area. In this paper, we present a new physically based model to simulate the dynamic flow of landslides, under a modified MPM (material point method) framework. To realistically simulate the characteristics of fracture and flow of soil medium in landslide, we introduce the modified Cambridge clay model (MCCM) from soil dynamics into the yield surface criterion to model the dynamic process of landslides. The interaction between soil and rock in the landslide is simulated by a level-set-based two-way fluid–solid coupling algorithm. Meanwhile, we propose a GPU-based optimization to calculate the signed distance function in level set to improve the efficiency of collision detection. We also simplify the hardening and softening parameter calculation algorithm of MCCM to reduce the calculation involved in landslide simulation. By choosing different values of the material yield surface parameters, various kinds of landslide disaster scenes with different cover area are successfully generated, including rocks rolling from hill, soil and rock collapsing, landslide flowing, and covering the road and cars. Experimental results demonstrate the potential of our method.

Trough OpenMP Platform for Reducing Computational Time Cost in Underwater Landslide Simulation on Inclined Bottom

Simulation of underwater landslide becomes important, since underwater landslide phenomena is very dangerous in real life. One of the enormous disasters caused by this phenomena can be a Tsunami. Computer simulation of underwater landslide can reduce cost of time and money from conventional simulation (using laboratory). However, to obtain high resolution of computer simulation, large discrete points should be computed. In this paper, the numerical simulation of underwater landslide using two-layers shallow water equations (SWE) and OpenMP platform is elaborated. Here, the finite volume method framework using upwinding dispersive correction hydrostatic reconstruction (UDCHR) scheme is used. The results of numerical simulation is in a good agreement with the numerical simulation using Nasa-Vof2d numerical scheme. In parallel performance, speedup and efficiency of this numerical simulation are observed 2.8 times and 76% respectively at t=0.8 s final time simulation.