Determination of 3D near fault seismic behaviour of Oroville earth fill dam using burger material model and free field-quiet boundary conditions

ABSTRACT In this study, the three-dimensional (3D) near-fault earthquake performance of the Oroville dam is examined considering a special material model and various seismic boundary conditions. The 3D finite-difference model of the Oroville EF dam is modeled using the finite difference method. Burger Creep (BC) material model is utilized for the foundation and dam body materials. Special interface elements are taken into account between the dam body and foundation. Fix, free field, and quiet seismic boundary conditions are considered for 3D nonlinear earthquake analyses. Total six various strong near-fault earthquakes are used in the 3D analyses. According to the non-linear earthquake analyses, principal stresses, horizontal and vertical displacements for three nodal points are assessed in detail and numerical results are compared for reflecting and non-reflecting seismic boundary conditions. It is clearly understood that seismic boundary conditions should not be utilized randomly for 3D modeling and analysis of EF dams.


Introduction
Earth-fill dams (EFDs) constructed on the strong near fault zones may undergo strong ground motions. If an EF dam failure, social and economic losses may occur. Thus, the seismic performance of these dams should be investigated in detail and this investigation is very critical to evaluate the safety and future of these water structures. The near-fault ground motions (NFGMs) have many important characteristic properties. One of them is NFGMs that can create strong seismic demands on the water structures constructed in the near-fault zones [1]. Another important property is NFGMs have different seismic damage properties when compared with far fault ground motions [2]. Moreover, the near-fault zones are exactly dependent on the earthquake magnitudes. When these significant seismic properties are considered, NFGMs should not be ignored for the design and seismic analyses of the EFDs [3].
In the literature, there are many studies related to numerical modelling and seismic analysis of rockfill dams considering near-fault earthquakes. The seismic behaviour of the Kiralkizi earth-fill dam was evaluated by using spectral ratios between (i) available crest and foundation records (C/F), (ii) horizontal and vertical components of the recorded motions (H/V), (iii) by performing two-dimensional finite difference-based seismic response analyses (Flac-2D), and (iv) ID elastic shear beam solutions. It was concluded that the earthquake response of the Kiralkizi earth-fill dam is comparable and within the prediction ranges of available analyses methods and is consistent with the expected response of a dam this height [4]. A strategy was dealt with for the maintenance of earth-fill dams and reliability analysis of the earth-fill dams was conducted considering the variability of the internal friction angle and the seismic hazard. Consequently, the probability of damage to the earth-fill dam over the next 50 years is calculated, and the effect of improving the earthfill is evaluated based on this probability [5]. In a study, the conducted correlation, spectral motion reconstruction and non-parametric stress-strain analyses of earth-fill dams were presented in detail. Numerical analyses revealed a complex three-dimensional dynamic response marked by non-uniform boundary conditions and a shear stress-strain behaviour slightly less nonlinear than what was observed in triaxial tests of soil samples taken from the dam core [6]. The nonlinear response of an earth-fill dam subjected to spatially varying ground motion, which includes the wave-passage, and effects of site response on earthquake response of an earth-fill dam were examined considering an equivalent linear method. It was observed that the variation in local soil conditions has important effects on the nonlinear response of earth-fill dams [7]. Then, intensity measures that best relate to earth-fill dam deformations based on nonlinear deformation analysis (NDA) results of two embankment dams with a large suite of recorded ground motions were determined taking into account engineering demand parameters of the site. Results of the study demonstrated that for the NDA model used, Arias intensity was found to be the most efficient predictor of earth-fill dam deformations [8]. It was investigated that the seismic behaviour of rockfill dams considering the strain-softening behaviour of rockfill materials. A new and efficient method was presented to assess the seismic behaviour of the dam. The seismic results indicate that this method is an effective approach to seismic reliability assessment from the stochastic viewpoint and it can directly reflect the failure probability [9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Furthermore, Karalar and Cavusli examined the seismic far-fault behaviour of the Oroville EF dam and they used six different far-fault earthquakes in the seismic analyses. According to earthquake analyses, the effects of far-fault earthquakes on the settlement and shear strain behaviour of the Oroville EF dam are determined by considering only non-reflecting boundary conditions [23]. As seen in these studies, many investigators examined the seismic behaviour of earth-fill dams in the past. However, the seismic effects of fix (reflecting) boundary conditions and free field (non-reflecting) boundary conditions on the 3D near-fault nonlinear seismic behaviour of earth-fill dams were not investigated by researchers in detail. These seismic boundary conditions are very specific for modelling and analysing EF dams. Besides, the visco-elastic constitutive law corresponding to a Burger Creep material model was not taken into account for seismic analysis of EF dams in the past. For this reason, this study provides very significant information to the literature.

Main purpose and originality of study
In this study, the three-dimensional (3D) nonlinear near-fault earthquake performance of the Oroville dam which is one of the largest earth-fill dams (EFDs) in the world is investigated using the special seismic boundary conditions. Oroville earth-fill dam is modelled using finite-difference modelling method that was rarely used for 3D nonlinear modelling of high earth-fill dams in the past. This study supplies differences to the literature about optimum modelling of high earth-fill dams. Moreover, when literature is examined in detail, it is seen that the free field and quiet boundary conditions have rarely been practiced to the high earth-fill dams together. When these two seismic boundary conditions are applied to the 3D model of the dam together, it is ensured that the earthquake waves propagate correctly within the model. Therefore, this study contributes much important information to the literature about seismic boundary condition modelling of earth-fill dams. Besides, due to Burger-creep viscoplastic model used in this study being characterized by a visco-elastoplastic deviatoric behaviour and an elastoplastic volumetric behaviour, this model is a very special material model for time depending deviatoric and volumetric behaviour of dynamical systems. Moreover, because the Burger-creep model, one of the most effective constitutive models describes the creep behaviour of rocks, this model can be easily used for the creep behaviour of rocks and dams. This model is capable of accurately describing the creep law of rocks above long-term strength [24]. These properties are the biggest differences of the Burgercreep model from other models. In this study, this material model is used for dam body material and this material model was rarely used for seismic modelling of EF dams in the literature. Thus, this study contributes very special information about the modelling of body material of EF dams.
In this study, while modelling the Oroville EF dam, fix (reflecting) [25], free field (nonreflecting), and quiet (viscous) seismic boundary conditions are used for the main surfaces of the 3D model. Besides, while modelling this dam, Burger Creep (BC) material model is utilized for the foundation and dam body materials. Free field and quiet (viscous) boundary conditions are taken into account for only lateral boundaries of the 3D model of the dam as seen in Figure 1 and it is made up of a combination of load history and a viscous boundary. In the literature, these non-reflecting boundary conditions were rarely used for the earthquake analyses of EF dams. Thus, one of the most important aims of this study is to examine the effects of these seismic boundary conditions and the BC material model on the nonlinear near-fault earthquake behaviour of the Oroville EF dam. When these two seismic boundary conditions (free field and quiet) are applied to the 3D model of the dam together, it is ensured that the earthquake waves propagate correctly within the model (Figure 1).
Another purpose is to investigate the nonlinear horizontal displacement, vertical displacement and principal stress behaviour of three critical nodal points on the dam body surface considering various near-fault earthquakes. Moreover, this study aims to compare these nonlinear numerical results for reflecting and non-reflecting boundary conditions. For these purposes, a total of six various strong near-fault earthquakes are used in the 3D nonlinear earthquake analyses for 234 m (maximum water level) of reservoir water height. These near-fault earthquakes are the 1999 Chi-Chi earthquake, 1995 Kobe earthquake, 1989 Loma Prieta earthquake, 1994 Northridge earthquake, 1986 North Palm Springs earthquake, and 1979 Imperial Valley earthquake. According to seismic analysis results, significant numerical differences are observed when compared to these special seismic boundary conditions. In addition, it is seen the effects of near-fault ground motions on the 3D nonlinear earthquake behaviour of the Oroville EF dam.

Oroville earth-fill dam and ground motion inputs
The Oroville Dam is a 234.7 m (770 ft.) tall earth-fill dam and it was built in 1968. It is the tallest dam in the United States of America and the fifth tallest earth-fill dam in the world [27][28][29][30]. It has 2109 m crest length and dam volume is 59,344,000 m 3 . Its spillway capacity is 4200 m 3 /s. Besides, the dam reservoir capacity is 4.36 km 3 . A cross-section of Oroville Dam, including seepage barriers and the seepage collection system, is shown in Figure 2. Moreover, an aerial view of the Oroville dam is shown in Figure 3. Dam body has different fill materials and material properties of Oroville EF Dam body are shown in Table 1.
In this study, a total of six different near-fault ground motions are used for the nonlinear seismic analyses. Besides, characteristic properties of near-fault earthquakes are shown in Table 2.

3D modelling stages of Oroville earth-fill dam
Earth fill dams under its probable maximum flood, the hydrostatic and uplift pressures can generate tensile stresses near the upstream and the foundation faces, possibly exceeding the strength of the material and causing a horizontal crack or opening of construction joints. The hydrostatic pressure acting inside the crack reduces the resistance and increases the penetration of water which exerts an uplift pressure [32][33][34][35]. However, seismic cracks within the dam are not a common damage situation in earth-fill   dams due to the downstream filters and drain control seepage and leakage and prevent sediment transport through any cracks in the central impervious core [36]. For earth-fill dams, transition zones and upstream filter zones also serve as a 'crack stopper' to supply cohesionless material that may help to self-heal a crack that occurs in the impervious core [36]. Moreover, earth-fill dams should be designed in such a way that there will be no cracks in the body during an earthquake [36]. For this reason, crack analysis was not examined in this study. The crack analysis is mostly examined in concrete dams or concrete-faced rockfill dams. Many researchers have analysed the effects of crack propagation in concrete dams [37][38][39][40][41][42][43][44]. While modelling the Oroville dam body-foundation system, specific material model and boundary conditions are utilized and practiced. The interaction between the dam body and the foundation under normal conditions has been obtained by defining the interaction elements between the dam body and the ground in this study. The theoretical background of the interaction between discrete surfaces is given below. In FLAC3D, the Interaction condition is represented by defining a normal and shear stiffness between two discrete planes (e.g. dam and foundation), which may contact one another as seen Figure 4 [24, [45][46][47]. FLAC3D uses a contact logic, which is similar in nature to that employed in the distinct element method, for either side of the interface [24,[45][46][47]. As seen in Figure 4, grid point N is checked for contact on the segment between grid points M and P. If contact is detected, the normal vector (n) is computed for the contact grid point (N) [45,24,46,47]. Besides, a length (L) is defined for the contact at N along with the interface. This length is equal to half the distance to the nearest grid point to the left of N plus half the distance to the nearest grid point to the right, irrespective of whether the neighbouring grid point is on the same side of the interface or the opposite side of N [45,24,46,47].  [23,45].
In this way, the entire interface is divided into contiguous segments, each controlled by a grid point. During each time step, the velocity (u � i ) of each grid point is determined. Since the units of velocity are displacement per time step, and the calculation of the time step has been scaled to unity to speed convergence [45,24,46,47]. The incremental displacement for any given time step is The incremental relative displacement vector at the contact point is resolved into the normal and shear directions, and normal and shear forces are determined by [24,[45][46][47] ; where the stiffnesses, k n, and k s , have the units of [stress/displacement] [45].
Reflecting boundary condition (fix boundary condition) does not provide true numerical results for the dynamic analyses because it reflects the seismic waves propagating in the model [24,46]. For this reason, the fix boundary condition does not represent reality [24,46]. In this study, the quiet (viscous) non-reflecting boundary condition is practiced to lateral boundaries of the 3D model. This special seismic boundary condition takes into account the seismic dashpots that were defined to the boundaries of the 3D model in the normal and shear directions. Thus, viscous normal and shear tractions are provided and these tractions can be defined as Equation (3) [24,46].
where v n is the normal component, v s is the shear component, C p is p wave velocity, C s is s wave velocity and ρ is the density [24,46]. Moreover, the free-field boundary is a special boundary condition for seismic analyses of water structures. In this study, the free-field boundary condition is defined to the lateral surfaces of the 3D model using special FISH functions [24,[45][46][47]. FISH is embedded deeply into FLAC3D at nearly every level. It can be used to parameterize data files so that many varying cases can be built into the same basic model [24,[45][46][47]. Every data type that makes up a FLAC3D model is also available for FISH to manipulate directly -before, after and during the solution [24,45].
The lateral surfaces of the 3D finite-difference model are merged to the free-field surfaces with viscous dashpots (quiet seismic boundary condition). This seismic condition is expressed in Equation (4) [24,46].
In this study, Burger creep material model is used for rockfill material and foundation. This model is very different from other material models [45,46]. Unlike other models, this model also reflects the creep behaviour of dam fill materials. Although it shows similar properties to the Mohr-Coulomb material model, it is also a different material model from the mohr coulomb material model in terms of reflecting the creep behaviour of the materials [45][46][47]. Burger viscoplastic model in FLAC is characterized by a viscoelastoplastic deviatoric behaviour and an elastoplastic volumetric behaviour. The viscoelastic and plastic strain-rate components are assumed to act in series [45]. The viscoelastic constitutive law corresponds to a Burger model (Kelvin cell in series with a Maxwell component), and the plastic constitutive law corresponds to a Mohr-Coulomb model [24,47]. The Burger model, one of the most effective constitutive models, is widely adopted to describe the creep behaviour of rocks. This model is capable of accurately describing the creep law of rocks above long-term strength [24,[45][46][47]. The Burger model is composed of a Kelvin model and a Maxwell model as seen from Figure 5.
The formulations and equations in the Burger material model are explained below. The symbols S ij and e ij are used to denote deviatoric stress and strain components [24,47]. Where and e vol ¼ 2 kk (8) Figure 5. Schematic of Burger model, with the definition of variables [24,[45][46][47].
Kelvin, Maxwell, and plastic contributions to stresses and strains are labelled using the superscripts K, M, and p, respectively. With those conventions, the model deviatoric behaviour may be described by the relations [24,47]: Strain rate partitioning: Kelvin model is expressed as follows [24,47]: Mohr-Coulomb model is expressed as follows [24,47]: Maxwell model is expressed as follows [24,47]: In turn, the volumetric behaviour is given by In those formulas, the properties K � and G are the bulk and shear moduli, and η is the dynamic viscosity (kinematic viscosity times mass density). The Mohr-Coulomb yield envelope is a composite of shear and tensile criteria. The yield criterion is f = 0, and in the principal axes formulation [24,47]: Shear yielding: Tension yielding: where C is the material cohesion, φ is the friction, Þ, σ t is the tensile strength, and σ 1 ,σ 3 are the minimum and maximum principal stresses (compression negative). The potential function g has the following form [24,47].
While modelling a structure in FLAC3D, an 'explicit' solution scheme is used (in contrast to the more usual implicit methods) [24,45]. Explicit schemes can follow arbitrary nonlinearity in stress/strain laws in almost the same computer time as linear laws, whereas implicit solutions can take significantly longer to solve nonlinear problems [24,[45][46][47]. Oroville dam has not got a flat dam body as other Earth-fill dams. It has an oval body structure and this oval geometry has three different angles [24,[45][46][47] (Figure 6).
The dam body has three different blocks and four different sections ( Figure 6). There are 3,961,591 nodal points in the 3D model of Oroville Dam [45][46][47]. To find the correct mesh width, a total of seven different mesh widths are created and stability analyses are performed for these mesh widths (Figure 7).
These widths are 10 m, 20 m, 30 m, 40 m, 50 m, 60 m and 70 m, respectively [47]. It is seen from numerical analyses that the maximum settlements on the crest of the dam do not change for less mesh width than 40 m [45][46][47] (Figure 7). Thus, mesh width is selected at approximately 40 m for seismic analyses. Locations of each material are different in the dam body and these materials are shown in detail in Figure 8.
Moreover, special interface elements are used between the dam body and foundation to represent the interaction condition of discrete surfaces in this study [23]. Normal (k n ) and shear (k s ) interaction stiffness values are considered as approximately 10 8 Pa/m between the dam body and foundation [47]. The reservoir water is modelled considering the hydrostatic pressure and leakage in the dam body. All surfaces exposed to the hydrostatic pressure are separately grouped in the 3D model to apply hydrostatic water pressure to these surfaces [23]. Hydrostatic water loads were applied from the crest to the foundation surface. These water loads are contacted to each node. To obtain the water leakage, a water table was applied to the upstream part of the dam taking into account the maximum water height (234 m) [23]. Free field and quiet (viscous) boundary conditions are applied only to lateral surfaces of the 3D model. Firstly, free field special seismic boundary condition is defined to software using special FISH functions [23,24]. Afterwards, the quiet boundary condition is considered to lateral surfaces of the 3D model. These special seismic boundary conditions are shown in Figure 9.

Nonlinear seismic analysis results
The nonlinear seismic behaviour of the Oroville dam is investigated graphically taking into account 6 various strong near-fault ground motions [23]. Three nodal points are selected on the dam body surface to better see changing of nonlinear seismic behaviour of the dam [23]. These points are shown in Figure 10 in detail.
Moreover, the numerical analysis algorithm for seismic analyses is presented in Figure 11. As a result of the seismic analysis, principal stresses, horizontal displacements and vertical displacements are presented and assessed graphically for three nodal points [23]. In addition, these numerical results are compared for reflecting and non-reflecting seismic boundary conditions [23].  In this study, the time history analysis method is practiced to 3D nonlinear model of Oroville dam [23]. This method is very important for structural engineering because of time history analysis method calculates the response of the structure subjected to earthquake excitation at every instant of time [24]. Various seismic data are necessary to carry out the seismic analysis i.e. acceleration, velocity, displacement data, etc., which can be easily procured from seismograph data's analysis for any particular earthquake [24,46]. It is an important technique for structural seismic analysis especially when the evaluated structural response is nonlinear [45][46][47].

Principal stress results
During strong earthquakes, very significant principal stresses may occur in the earth-fill dams (EFDs) by the effect of strong earthquake loads and these seismic stresses may give rise to important damages in the dam body. In this section, the nonlinear principal stress behaviour of the Oroville EF dam is graphically examined considering various near fault earthquakes in Figures 12,13 and Table 3. Total six different near-fault ground motions are used in the 3D seismic analyses. These earthquake analyses are compared with each other considering reflecting (fix) and non-reflecting (free field and quiet) seismic boundary conditions. According to Figure 12, nonlinear principal stresses for three different nodal points on the dam body surface are evaluated for the Kobe earthquake.
As seen in Figure 12(a), approximately 8.9 MPa maximum principal stress is observed for Point 2 at 13.1th second of the earthquake and minimum stress occurred on Point 1. In Figure 12(b), approximately 16 MPa maximum principal stress is obtained for Point 2 at 18.7th second of the earthquake. During the first 4 s, very small principal stresses are observed for three nodal points for reflecting and non-reflecting boundary conditions. According to Figure 13, the effect of the Loma Prieta earthquake on the nonlinear seismic performance of the Oroville dam is graphically investigated for both boundary conditions. For the fix boundary condition, 8 MPa maximum principal stress is observed for Point 2 at the 11th second of the earthquake and significant stresses occurred for Point 1 as seen in Figure 13(a). However, when examined Figure 13(b), approximately 11 MPa maximum principal stress is observed for Point 2 at 19.4th second of the earthquake.
In Table 3, the principal stress behaviour of the Oroville EF dam is summarized for 6 different strong ground motions. As seen in Table 3, approximately 9.3 MPa maximum principal stress is observed on Point 3 at 18.8th second of the North Palm Springs earthquake and minimum stress occurred on Point 2. However, when examined nonreflecting boundary condition, 10.9 MPa maximum principal stress is observed for Point 2 at 6.9th second of the earthquake, and minimum stress is obtained at the lowest nodal point (Point 3). When comparing both boundary conditions, it is seen that greater stresses are observed for non-reflecting boundary conditions during the Imperial Valley earthquake (Table 3). 5.6 MPa maximum principal stress is acquired for Point 2 at 17.8th second of the earthquake. However, although the same earthquake and same 3D model is used in the seismic analyses, very different principal stress values are observed for non-reflecting boundary condition. Approximately 8.9 MPa maximum principal stress occurred for Point 2 at 18.7th second of the earthquake. According to Tables 3, 12.3 MPa maximum stress value is obtained for Point 2 at 17.1th second of Northridge earthquake, and minimum stress value is observed on the Point. For non-reflecting boundary condition, 15.1 MPa maximum principal stress is observed for Point 2 at 19.6th second of the earthquake. In Table 3, the effects of the Chi-Chi earthquake on the principal stress behaviour of the Oroville dam are examined in detail. 6.3 MPa maximum principal stress   is observed on Point 3 for reflecting boundary condition. In addition, approximately 1 MPa maximum positive principal stress occurred for Point 3 at the 36th second of the earthquake. 6.6 MPa maximum principal stress is observed on Point 2 at 30.1th second of the earthquake for non-reflecting boundary condition (Table 3). These seismic results indicated that seismic boundary conditions should not be used randomly for the earthquake analysis of EF dams. Moreover, it is seen from all numerical analyses, the largest principal stresses occur on the middle point (Point 2) during the earthquake.

Horizontal displacement results
In this section, HD results of three nodal points on the dam body surface are shown considering 6 various near-fault ground motions in Figures 14,15 and Table 4. Moreover, these results are compared for reflecting (fix) and non-reflecting (free field and quiet) boundary conditions. In Figure 14, the effect of the Kobe earthquake on the HD behaviour of the Oroville dam is graphically presented in detail. As seen in Figure 14(a), HDs are observed in positive and negative directions during the earthquake. Approximately 1 m maximum negative HD is observed for Point 3 at the 11th second of the earthquake. According to Figure 14(b) (for non-reflecting boundary condition), very different displacements are observed when compared to fix boundary condition. 1.8 m maximum negative HD is obtained for Point 2 at 17.7th second of the earthquake. When examined in Figure 15, it is seen the effect of the Loma Prieta earthquake on the HD behaviour of the Oroville dam. In Figures 15(a), 0.9 m maximum positive HD is observed for Point 3 at 18.1th second of the earthquake. However, for non-reflecting boundary condition, 1.2 m maximum positive HD is obtained for Point 3 at 17.5th second of the earthquake. As Figures 15(a,b) are compared, less horizontal displacements occurred on three nodal points for reflecting seismic boundary condition.
In Table 4, horizontal displacements are examined for the North Palm Springs earthquake considering reflecting and non-reflecting boundary conditions. For the fix boundary condition, 0.7 m maximum positive HD is observed for Point 3 at the 16th second of the earthquake and no significant HDs occurred during the first 3 s of the earthquake. However, for non-reflecting boundary condition, larger displacement results are acquired. Approximately 0.9 m maximum negative and positive maximum HD is observed for Point 3. According to the Imperial Valley earthquake, positive displacements are observed between the 4th and 7th seconds of the earthquake and negative HDs occurred between the 7th and 11th seconds of the earthquake for three nodal points. In Tables 4, 0.52 m maximum negative HD is obtained for Point 3 and minimum displacements are observed for Point 1. However, for non-reflecting boundary condition, 0.68 m maximum negative displacement is observed for Point 3 at 7.2th second of the earthquake. In Table 4, the effect of the 1994 Northridge earthquake on the nonlinear horizontal displacement behaviour of the Oroville dam is examined in detail. According to fix boundary condition, approximately 1.5 m negative HD is obtained for Point 3 at 12.3th second of the earthquake. However, for non-reflecting boundary condition, approximately 2 m negative maximum HD is observed for Point 2 at 10.2th second of the earthquake. The effect of the Chi-Chi earthquake on the horizontal displacement behaviour of the Oroville dam is presented in Table 4 in detail. During the first 12 s of the earthquake, significant horizontal displacements are not observed on the dam body surface. However, after the 12th second, very important HDs occurred. 0.5 m maximum positive horizontal displacement is obtained for Point 3. In addition, for non-reflecting boundary condition, 0.7 m positive maximum displacement occurred for Point 3 at the 28th second of the earthquake (Table 4).

Vertical displacement results
During the strong ground motions, significant vertical displacements may occur on the dam body surface by the effect of strong earthquake loads and hydrostatic pressure. In this section, vertical displacement (VD) results are graphically   Table 5). According to Figure 16, the effect of the Kobe earthquake on the vertical displacement behaviour of the Oroville dam is evaluated considering reflecting and non-reflecting seismic boundary conditions. In Figures 16(a), 0.78 m maximum VD is observed for Point 3 at the 19th second of the earthquake and minimum displacement occurred for Point 1. When examined Figure 16(b), significant VD differences are observed for non-reflecting boundary condition compared fix boundary condition. 0.9 m maximum VD occurred for Point 3 at 17.2th second of the earthquake. When investigated Figures 17(a,b), vertical displacement results for reflecting and non-reflecting boundary conditions are close for Points 1 and 2. However, obvious displacement differences are observed between Figures 17(a,b) for Point 3. 0.63 m maximum settlement occurred on Point 3 for reflecting boundary condition (Figure 17(a)). In addition, 0.78 m maximum VD is observed on Point 3 for nonreflecting boundary condition (Figure 17(b)).
In Table 5, vertical displacements for three nodal points on the dam body surface are examined for the 1986 North Palm Springs earthquake considering reflecting and non-reflecting seismic boundary conditions. For the fix boundary condition, 0.72 m maximum VD is observed for Point 3 at 12.5th second of the earthquake and minimum displacement occurred on Point 1. However, for non-reflecting boundary condition, 0.85 maximum displacement is obtained for Point 3 at the 12th second of the earthquake. According to Table 5, the effect of the 1979 Imperial Valley earthquake on the vertical displacement behaviour of the Oroville dam is examined considering reflecting and non-reflecting boundary conditions. 0.68 m  Table 5, it is seen the effect of the Chi-Chi earthquake on the vertical displacement behaviour of the Oroville dam. Significant differences are observed between reflecting and non-reflecting boundary condition. For the fix boundary condition, 0.76 m maximum VD is observed for Point 3 at the 29 th second of the earthquake. However, for free field and quiet boundary condition, approximately 0.8 m maximum settlement occurred for Point 3 at 39 th second of the earthquake.

Conclusions
In this paper, the nonlinear seismic behaviour of the Oroville earth-fill (EF) dam is examined for 6 various near-fault ground motions considering reflecting (fix) and non-reflecting (free-field and quiet) seismic boundary conditions. The effects of reflecting and non-reflecting seismic boundary conditions and Burger Creep material model on the nonlinear near-fault earthquake behaviour of the Oroville dam is evaluated as below: • For six various near-fault ground motions, maximum principal stresses are observed on the middle nodal point (Point 2) of the dam body surface and minimum principal stress occurred on the lowest nodal point (Point 1). For nonreflecting boundary condition, when compared 6 various earthquakes with each other, maximum principal stress is observed on Point 2 for the Kobe earthquake and its numerical value is 16 MPa. In addition, for reflecting boundary condition, 6.3 MPa minimum principal stress occurred on Point 3 for the Chi-Chi earthquake. • According to nonlinear near-fault analysis results, maximum horizontal displacements are observed on Point 3 (top nodal point) and minimum horizontal displacements occurred on Point 1 (lowest nodal point). Moreover, for non-reflecting boundary condition, when considering all earthquake analyses, 2 m maximum displacements are obtained from Point 3 for the Northbridge earthquake. Moreover, for reflecting boundary condition, 0.5 m minimum displacement occurred for the Chi-Chi earthquake. • As examined settlement analysis results, maximum vertical displacements are observed on Point 3 (top nodal point) and minimum settlements are obtained on Point 1 (lowest nodal point). For all earthquake analysis results, maximum settlement is acquired on Point 3 for the Northridge earthquake and its numerical value is 1 m. • Since free field and quiet boundary conditions are some of the most suitable boundary conditions for the propagation of seismic earthquake waves within the finite difference model, these boundary conditions can give similar results when applied to other dam types.

Disclosure statement
No potential conflict of interest was reported by the author(s).

Funding
This study was not funded. Strain rate λ � a parameter that is nonzero during plastic flow