Kinematic Interaction Research Articles

Empirical evaluation of kinematic soil-structure interaction effects in structures with large footprints and embedment depths

Kinematic soil-structure interaction (SSI) effects cause foundation-level motions to deviate from free-field motions. Simplified procedures to account for kinematic SSI effects are available in design guidelines for regular buildings and have been calibrated for regular buildings with limited foundation size and depth of embedment. As a result, their application to structures with much larger foundation footprints and deeper embedment depths is questionable. Kinematic interaction effects can be used to reduce foundation-level ground motions relative to those specified in the free-field, and this can be cost-effective especially for structures with larger footprints and embedment depths. The objective of this study is to quantify the extent of deviations between the use of available simplified procedures and empirical data for a select group of structures with larger footprints and embedment depths. In this study, a dataset of earthquake motions recorded at the instrumented structures in Japan is used to evaluate kinematic SSI effects, which are quantified in terms of the transfer function and the ratio of response spectra between foundation motions and corresponding free-field motions. Transfer functions represent the ratio between the free-field and the foundation level of a structure motion in the frequency domain and can be obtained by dividing Power Spectral Density functions of foundation motion and corresponding free-field motion. Finally, these empirical functions are compared to the available simplified formulations such as the semi-empirical transfer function and the ASCE/SEI 41–17 recommended ratio of response spectra, and the results are presented in terms of residuals. The overall trends of residuals indicate that the current simplified procedures tend to overestimate the foundation motions in structures with large footprints and embedment depths, and the extent of overestimation is higher for the ratio of response spectra compared to transfer functions. Thus, in future studies, these simplified procedures should be revised for applications in structures with large footprints and embedment depths.

Torque Reduction of a Reconfigurable Spherical Parallel Mechanism Based on Craniotomy Experimental Data

This paper deals with a robotic manipulator dedicated to craniotomy with a remote center of motion based on a Spherical Parallel Manipulator (SPM) architecture. The SPM is proposed to handle the drilling tool through the requested craniotomy Degrees of Freedom (DoF) with two rotations. The proposed architecture allows one degree of redundancy according to the total DoF. Thus, a first contribution of this work focuses on the experimental analysis of craniotomy surgery tasks. Secondly, its behavior is improved, taking advantage of the redundancy of the SPM using the spinning motion as a reconfiguration variable. The spinning angle modulation allows the reconfigurable manipulator to minimize its motor torques. A series of motion capture and force experimentations is performed for the analysis of the kinematic and force interaction characterizing Burr hole craniotomy procedures. Experimentations were carried out by a neurosurgeon on a human cadaver, ensuring highly realistic conditions.

Electronic spectrum and superconductivity in the extended [formula omitted]–[formula omitted]–[formula omitted] model

A consistent microscopic theory of superconductivity for strongly correlated electronic systems is presented within the extended t–J–V model where the intersite Coulomb repulsion and the electron-phonon interaction are taken into account. The exact Dyson equation for the normal and anomalous (pair) Green functions is derived for the projected (Hubbard) electronic operators. The equation is solved in the self-consistent Born approximation for the self-energy. We obtain the d-wave pairing with high-Tc induced by the strong kinematical interaction of the order of the kinetic energy ∼t of electrons with spin fluctuations which is much larger than the exchange interaction J. The Coulomb repulsion and the electron-phonon interaction give small contributions for the d-wave pairing. These results support the spin-fluctuation mechanism of high-temperature superconductivity in cuprates previously proposed in phenomenological models.

Tire Wear Reduction Based on an Extended Multibody Rear Axle Model

To analyze the influence of suspension kinematics on tire wear, detailed simulation models are required. In this study, a non-linear, flexible multibody model of a rear axle system is built up in the simulation software MSC Adams/View. The physical model comprises the suspension kinematics, compliance, and dynamics as well as the non-linear behavior of the tire using the FTire model. FTire is chosen because it has a separate tire tread model to compute the contact pressure and friction force distribution in the tire contact patch. To build up the simulation model, a large amount of data is needed. Bushings, spring, and damper characteristics are modeled based on measurements. For the structural components (e.g., control arms), reverse engineering techniques are used. The components are 3D-scanned, reworked, and included as a modal reduced finite element (FE)-model using component mode synthesis by Craig–Bampton. Finally, the suspension model is validated by comparing the simulated kinematic and compliance characteristics to experimental results. To investigate the interaction of suspension kinematics and tire wear, straight line driving events, such as acceleration, driving with constant velocity, and deceleration, are simulated with different setups of wheel suspension kinematics. The influence of the setups on the resulting friction work between tire and road is examined, and an exemplarily calculation of tire wear based on a validated FTire tire model is carried out. The results demonstrate, on the one hand, that the chosen concept of elasto-kinematic axle leads to a relatively good match with experimental results and, on the other hand, that there are significant possibilities to reduce tire wear by adjusting the suspension kinematics.

Evaluation of Physical Interaction during Walker-Assisted Gait with the AGoRA Walker: Strategies Based on Virtual Mechanical Stiffness.

Smart walkers are commonly used as potential gait assistance devices, to provide physical and cognitive assistance within rehabilitation and clinical scenarios. To understand such rehabilitation processes, several biomechanical studies have been conducted to assess human gait with passive and active walkers. Several sessions were conducted with 11 healthy volunteers to assess three interaction strategies based on passive, low and high mechanical stiffness values on the AGoRA Smart Walker. The trials were carried out in a motion analysis laboratory. Kinematic data were also collected from the smart walker sensory interface. The interaction force between users and the device was recorded. The force required under passive and low stiffness modes was and smaller than the high stiffness mode, respectively. An increase of for the hip range of motion, as well as the highest trunk’s inclination, were obtained under the resistive mode, suggesting a compensating motion to exert a higher impulse force on the device. Kinematic and physical interaction data suggested that the high stiffness mode significantly affected the users’ gait pattern. Results suggested that users compensated their kinematics, tilting their trunk and lower limbs to exert higher impulse forces on the device.

Centrifuge and numerical modelling of the seismic response of tunnels in two-layered soils

Soil deposits inevitably affect the seismic performance of underground structures, and underground tunnels are commonly constructed on sites composed of layered soil deposits. In this study, dynamic centrifuge tests and numerical modelling are conducted to enhance the fundamental understanding of the kinematic soil-tunnel interaction for tunnels constructed in layered soils that consist of muddy clay and silty clay. The site seismic response and tunnel seismic performance between the centrifuge and numerical modelling are compared. The acceleration time histories, amplification factors of the input motions, and the Fourier spectra between free field and structural field are experimentally and numerically investigated. For comparative purposes, parametric studies of tunnels in a single muddy clay and a single silty clay using verified numerical modelling are carried out. In addition, the dynamic bending moment and axial forces obtained by centrifuge and numerical modelling are compared with the solutions predicted by analytical methods in prior studies.

Effects of Soil-Foundation-Interaction on the Seismic Response of a Cooling Tower by 3D-FEM Analysis

This paper reports on the results of soil-foundation numerical modelling and the seismic response of a cooling tower founded on piles of a petrochemical facility located in the city of Augusta (Sicily, Italy). The city was affected in the past by some destructive earthquakes (1693, 1848, and 1990) that damaged a large territory of Southeastern Sicily, which was characterized by a very high seismic hazard. With this aim, the paper reports the FEM modelling of the seismic behaviour of the coupled soil-structure system. To determine the soil profile and the geotechnical characteristics, laboratory and in situ investigations were carried out in the studied area. The seismic event occurred in January 1693 and has been chosen as a scenario earthquake. Moreover, a parametric study with different input motions has also been carried out. A Mohr-Coulomb model has been adopted for the soil, and structural elements have been simulated by means of an elastic constitutive model. Two different vertical alignments have been analysed, considering both the free-field condition and the soil-structure interaction. The dynamic response has been investigated in terms of accelerations, response spectra, and amplification functions. The results have also been compared with those provided by Italian technical regulations. Finally, the seismic response of the coupled soil-structure system has been further examined in terms of peak bending moments along the pile foundation, emphasizing the possibility of a kinematic interaction on piles induced by the seismic action.

Evaluation on influences of inertial mass on seismic responses and structure-soil interactions of pile-soil-piers

This research is to assess the influences of the inertial mass from the girder on the dynamic characteristic, dynamic response, and structure-soil interaction of a pile-soil-pier subsystem in a scale-model of a cable-stayed bridge. Therefore, both connection configurations between the pile-soil-pier and girder, including the sliding and fixed connections, were designed to present various inertial mass from the superstructure delivered to the pile-soil-pier. The pile-soil-pier supported by a 3 × 3 pile-group in mixed soil placed in a shear box was tested using shaking tables. The dynamic characteristics, seismic responses, inertial interactions, and pile group effects of the pile-soil-pier between the sliding and fixed connections were analyzed under three input motions with different shaking amplitudes. These results showed that more inertial mass from the girder significantly increased the reinforcement strain and bending moment at the column bottom and pile top, displacement at the column top, inertial interaction effects, and pile group effects of the pile-soil-pier due to the sliding connection changing to the fixed connection. The inertial mass increment from the girder noticeably decreased the peak accelerations of the column of the pile-soil-pier when subjected to three input motions with different amplitudes. However, the inertial mass insignificantly affected the accelerations of the pile and free-soil. Therefore, the corresponding kinematic interaction effects were almost unaffected by the inertial mass. Additionally, the evident pile group effects were observed in the sliding and fixed connections between the pile-soil-pier and girder. The numerical model could approximately reproduce the macroscopic seismic responses of the pile-soil-piers with sliding and fixed connections and capture the typical response variations induced by the connection configuration change.

Dynamic analysis of combined piled raft system (CPRS)

High rise buildings constructed on the combined piled raft system (CPRS) have been rapidly increased in the recent years. Understanding of the load distribution mechanism between the pile and raft especially when these buildings are subjected to the earthquake is the main objective of this research. The kinematic interaction between the pile, soil, and raft is a principally 3-D problem. The main objective of this study is to evaluate the capability of the proposed numerical method by comparing its output with case study data. Further understanding of the raft-soil and pile interaction problem outside the verified case is therefore required by running a series of the parametric studies. These analyses indicate that the interaction mechanism of the raft-soil and pile is based on the inertia and kinematic interaction under seismic and vertical load. These interaction mechanisms are mainly evaluated by considering the load shared by soil beneath the pile tip after the earthquake while the sharing load by either pile or raft is quite stable after the earthquake. Efficiency of CPRS to mitigate the earthquake is demonstrated for the large raft stiffness more than 250 as in cases of (tp = 2 m, & S/D = 3), (tp = 3 m, &S/D = 3 or S/D = 4), and (tp = 2.5 m, &S/D = 3), or by employing long pile (Lp = 25 m). Also, employing the building stiffness to the increase inertia effect is almost not considered dominant in reducing the sharing load carried by CPRS, while the raft lateral displacement, acceleration, and bending moment express a relative increase. Another mitigation technique of the earthquake is adopted by applying the building stiffness assisted with the ductile or rigid base isolator. It proved that the ductile isolator is more effective technique in dissipating the earthquakes more than increasing the inertia of CPRS.

On the application of the beam model for linear dynamic analysis of pile and suction caisson foundations for offshore wind turbines

Piles and suction caissons are the most common foundation solutions for fixed Offshore Wind Turbines at intermediate water depths. They are generally used as a single element, presenting large diameters and short aspect ratios. These specific dimensions drastically differ from the ones of classical applications (offshore platforms, bridges, tall buildings etc.). Thus, in this paper the validity of their modelling as beam elements for the particular problem of OWT is revised. The results of a soil-beam model, based on the integral Reciprocity Theorem in Elastodynamics and specific Green’s functions for the layered half-space for the soil behaviour coupled with Timoshenko’s beam Finite Elements, are benchmarked against the ones of a soil-shell model, based on Boundary Elements for the soil coupled with shell Finite Elements. The comparative study is conducted in terms of foundation characterization variables (impedance functions and kinematic interaction factors). Their influence on the OWT seismic response is also studied through a substructuring procedure. From the results, some expressions for determining the applicability range of the beam simplification are proposed as functions of the relative foundation-soil stiffness ratio. It is observed that this applicability range goes beyond that the one commonly considered. .

Aggregation-Fragmentation of Clusters in the Framework of gTASEP with Attraction Interaction

This article provides summary of some of our results, concerning a model of aggregation and fragmentation of clusters of particles obeying the stochastic discrete-time discrete-space kinetics of the generalized Totally Asymmetric Simple Exclusion Process (gTASEP) with open boundaries. The model in essence is the ordinary TASEP with backward ordered sequential update with special kinematic interaction added, i.e., it has a second modified hopping probability $$~{{p}_{m}}$$ for particles in a cluster in addition to the standard hopping probability $$p$$ . We consider separately the two cases of attraction interaction ( $$p$$ < $$~{{p}_{m}}$$ ): (1) the limiting case of irreversible aggregation ( $${{p}_{m}}$$ = 1); and (2) the generic case of attraction, when $$~p$$ < $$~{{p}_{m}}$$ < 1 (then aggregation and fragmentation of clusters is allowed). We put special emphasis on the use of random walk theory in the study of gTASEP. It is applied to study the inter-cluster gaps time evolution, which helps to assess the properties of the nonequilibrium stationary phases of the system and the phase transitions between them. Theoretical conclusions are in agreement with the Monte Carlo simulations.

Implications of high-frequency decay parameter, “κ-kappa”, in the estimation of kinematic soil-structure interaction effects

In the present study, the difference between the peak seismic response measures recorded on building basements and those at nearby free-field conditions is studied by means of estimating the high-frequency spectral decay parameter, “κ” (known as “kappa”). Computation of “κ” is performed for selected accelerographic stations belonging to three strong motion networks, namely the Hellenic National Accelerographic Network (HNAN) in Greece, the Center for Engineering Strong Motion Data (CESMD) in California, USA and the Building Research Institute (BRI) in Japan. Parameter “κ” is computer according to Anderson and Hough (1984), while an automated signal energy-based procedure is developed to calculate the S-wave windows of each waveform, accounting for any errors. Site-specific restrictions on the upper frequency limit, f2, for the calculation of “κ” at the foundation level are imposed, based on the empirical transfer functions between foundation and free-field motions. Based on the above procedure, non-linear regression analyses are conducted to relate “κ”, as computed for free-field and foundation motions (κff, - κfnd), to magnitude Mw, source-to-site distance Repi and shear wave velocity VS30. Simulation of ground motions though the point-source stochastic method is accomplished, utilizing the regression expression to define “κ” and assess its effectiveness to predict the variation of intensity between free-field and foundation motions as a proxy for assessing soil-structure interaction effects. It is shown that the regression-based expressions, combined with stochastic simulations, consist a promising tool for correcting seismic motions recorded at a building foundation or basement levels and thus, for reliably predicting the corresponding intensity and characteristics of the actual “building-free” ground motions.

Lateral free-field responses and kinematic interaction of monopiles to obliquely incident seismic waves in offshore engineering

This paper studies the lateral free-field response and dynamic interaction of monopiles with a partially/fully saturated porous seabed under a seawater layer, subjected to vertically and obliquely incident P and SV wave excitations. The solution of the coupled three-dimensional water-pile-soil vibration problem is developed using a rigorous semi-analytical method. Results for the free-field soil displacement and kinematic interaction factors of the pile head are obtained: the presence of water layer will increase or decrease the lateral free-field displacement for the P wave case, depending on whether the soil is fully saturated or partially saturated; the presence of water layer will have little influence, increase or decrease the lateral free-field displacement for the SV wave case, depending on the incident angle. Besides, the non-dimensional lateral kinematic interaction factors for both P wave and SV wave cases, with different water depths, are illustrated over a broad non-dimensional frequency range. Similar to the free-field responses, monopile responses can generally be amplified or reduced with the presence of a water layer, depending on the saturation degrees of soil and incident angles in P wave case and SV wave case, respectively.

Surface slip distributions and geometric complexity of intraplate reverse-faulting earthquakes

Abstract Earthquake ground surface ruptures provide insights into faulting mechanics and inform seismic hazard analyses. We analyze surface ruptures for 11 historical (1968–2018) moment magnitude (Mw) 4.7–6.6 reverse earthquakes in Australia using statistical techniques and compare their characteristics with magnetic, gravity, and stress trajectory data sets. Of the total combined (summative) length of all surface ruptures (∼148 km), 133 km (90%) to 145 km (98%) align with the geophysical structure in the host basement rocks. Surface rupture length (SRL), maximum displacement (MD), and probability of surface rupture at a specified Mw are high compared with equivalent Mw earthquakes globally. This is attributed to (1) a steep cratonic crustal strength gradient at shallow depths, promoting shallow hypocenters (∼1–6 km) and limiting downdip rupture widths (∼1–8.5 km), and (2) favorably aligned crustal anisotropies (e.g., bedrock foliations, faults, fault intersections) that enhanced lateral rupture propagation and/or surface displacements. Combined (modeled and observed) MDs are in the middle third of the SRL with 68% probability and either the ≤33rd or ≥66th percentiles of SRL with 16% probability. MD occurs proximate to or directly within zones of enhanced fault geometric complexity (as evidenced from surface ruptures) in 8 of 11 earthquakes (73%). MD is approximated by 3.3 ± 1.6 (1σ) × AD (average displacement). S-transform analyses indicates that high-frequency slip maxima also coincide with fault geometric complexities, consistent with stress amplifications and enhanced slip variability due to geometric and kinematic interactions with neighboring faults. Rupture slip taper angles exhibit large variations (−90% to +380% with respect to the mean value) toward rupture termini and are steepest where ruptures terminate at obliquely oriented magnetic lineaments and/or lithology changes. Incremental slip approximates AD between the 10th and 90th percentiles of the SRL. The average static stress drop of the studied earthquakes is 4.8 ± 2.8 MPa. A surface rupture classification scheme for cratonic stable regions is presented to describe the prevailing characteristics of intraplate earthquakes across diverse crustal structural-geophysical settings. New scaling relationships and suggestions for logic tree weights are provided to enhance probabilistic fault displacement hazard analyses for bedrock-dominated intraplate continental regions.

Effects of Stratification on Soil–Foundation–Structure Interaction: Centrifugal Observation and Numerical Simulation

It is essential to reduce structural damages caused by earthquakes in severe conditions, such as layered ground, especially when a soft soil layer is close to the surface. In this study, the kinematic and inertial interactions, two mechanisms of soil–foundation–structure interaction (SFSI), of different soil–foundation–structure systems (SFS) were investigated on uniform and layered grounds. Two layered soil profiles composed of a low stiffness layer laid over another were prepared in an equivalent shear beam container. Nine centrifuge experiments were carried out for three structures located on the surface of each ground and exposed to the Hachinohe earthquake while increasing the peak acceleration of the input motion. Numerical simulations were performed to simulate the centrifuge tests. It was found that roof motion (RM) of the tall structure increased in layered profile even though the free-field motion (FFM) decreased compared to homogeneous ground. The appearance of a soft layer beneath structures modifies the SFS system’s stiffness that causes kinematic and inertial interactions to alter to those on uniform soil profile.

Kinematic interaction and condensation factor in two-dimensional quantum Heisenberg ferromagnet

We investigate the influences of Dyson’s kinematic and dynamic interaction on the physical properties of two-dimensional quantum Heisenberg ferromagnet with O(3) rotational symmetry. It is found that the repulsive potential led by dynamic interaction modifies the third large term with $$T^{3}$$ in the low-temperature series of specific heat. Under mean-field approximation, the kinematic interaction transforms the occupation-number configuration into a coherent-state configuration and significantly improves the result of modified spin wave theory in the high-temperature limit. In the low-temperature limit, the kinematic-interaction contribution to specific heat is negligibly small. For finite-size systems, it is found that a crossover temperature can be used to characterize the transition to a single-domain-type magnet. In the thermodynamic limit, the condensation factor (the number of zero-mode magnons) dominates the isothermal compressibility of magnon gas although there is not a real phase transition at finite temperatures. The asymptotic behavior of static structure factor depends on the relative size of the spin-wave wavelength with respect to the correlation length.

Lateral soil pile structure interaction assessment for semi active tuned mass damper buildings

Using Lateral load-displacement curves (p-y curves) which is recommended by American Petroleum Institute (API) guideline, is typically used as a design approach for analysis of soil-pile-structure interaction due to its simplicity. The soil-pile structure interface has two separate parts of interaction; kinematic and inertial interaction. Both types of interaction must be measured accurately for the structures with dampers to determine the optimum parameters for design. For structures equipped with semi active tuned mass damper (STMD) on deep foundation, determination of the optimum STMD characterizations are completely related to the dynamic attitude of the structure. Hence, in this study, first the accuracy of general p-y equation for buildings with STMD which have short period on deep foundations are evaluated. Then, three dimensional continuum method (finite element method) is used and the general equation of API are updated to provide compatibility. The results showed that the accuracy of spring method (p-y curves method) is very poor in estimation of dynamic response of the structure. A modified API equation is proposed to improve the accuracy and reduce the degree of error for the data set provided. However, it is concluded that the three dimensional continuum method is still a more trustworthy approach for the type of problem investigated in this paper.

Effect of kinematic interaction on seismic response of offshore wind turbines on monopiles

AbstractInterest in renewable energy over the past decade has motivated a remarkable research on offshore wind energy. Due to the environmental loading conditions in the early developments of offshore wind farms, the focus of the research and engineering has been on aerodynamic and hydrodynamic subjects. However, earthquake has turned out to be a major design concern in seismic areas such as East Asia, Southern Europe, and United States. The topics include, among others, nonlinear response of foundations, soil liquefaction, and their impacts on foundation performance. An important topic in seismic soil‐structure interaction (SSI) analysis is the kinematic seismic response of foundations. This information is crucial for analyses based on the substructuring approach where both kinematic response and foundation impedances are key parameters. While considerable research has been spent on the latter topic, very little has been reported on the kinematic interaction. Large monopoles with low aspect ratios tend to rotate much more than regular piles in pile group foundations due to seismic waves. The rotation leads to additional load on the tower and the turbine. This article uses a rigorous numerical model for monopole‐soil interaction in layered soil and computes both rotational and horizontal responses at the pile head (seabed) as functions of frequency. A suite of generic homogeneous and heterogeneous soil profiles with shear moduli representative of clay (generally linear) and sand (generally parabolic) are considered in these analyses. Through representative analyses, both in frequency domain and time domain, it is illustrated how the kinematic interaction influences the earthquake loads imparted to an offshore wind turbine (OWT).

Modal dynamics of boundary-interior coupled structures. Part 1: A general approach using components Green’s function

In Part 1 of this series papers (Part 1 & Part 2 (Guo and Rega, 2020) [1]), a general operator-based boundary analysis approach is proposed for free vibrations of coupled structural systems, with the new coupled modal frequencies and modal shapes being directly extracted in a systematic manner from the uncoupled components Green’s functions. Therefore, ad-hoc re-modelling of the whole augmented structural system is avoided. It turns out that a hybrid decomposition of the original coupled system into two sub-problems at the coupling interface, i.e., one excited kinematically at the boundary and the other excited by an interaction force in its interior domain, is of vital importance. Using general operator arguments and reciprocity-based operator equality, the dynamic coupling is imposed by combining the boundary kinematic effects and interaction force effects. The orthogonality of the coupled modal shapes is further established (and in Part 2 (Guo and Rega, 2020) [1] a general full interpretation of mode localization phenomenon will be presented). Finally, two coupled structural systems, i.e., string-oscillator and string-beam, are attacked by this operator formulation as examples, with coupled frequencies/modal shapes being obtained in a systematic way.

Fault inversion in central Iran: Evidence of post Pliocene intracontinental left lateral kinematics at the northern Iranian Plateau margin

Structural inversion of strike–slip faults in response to plate kinematic changes and interactions of large–scale basement blocks is a significant phenomenon in continental collision zones. In the Alborz Mountains, at the northern margin of the Iranian Plateau, Late Cenozoic kinematic of major fault systems changed in the late Pliocene from dextral to sinistral strike–slip. This kinematic change has been attributed to the clockwise rotation of the rigid South Caspian Block. However, the spatial extent and distribution of this kinematic change toward the south and into the Iranian Plateau is controversial. Here we present a detailed structural analysis of the West Saveh fault system located at the northwestern margin of the Iranian Plateau to unravel the regional distribution of this kinematic change. The West Saveh fault system is composed of the WNW–ESE trending Kushk–e Nosrat, Khalkhab, Saveh, and Nashveh faults. We identified several different sets of strike–slip related structures, which are classified into three categories based on their cross–cutting relationship and superimposition of kinematic indicators. We document dextral, dextral transpression and sinistral kinematics and their relative timing since Miocene time in the West Saveh fault system. Our structural analysis indicates recent slip sense inversion from dextral transpression to sinistral strike–slip, which possibly occurred in post Pliocene time. This kinematic change is regional and can be explained by the clockwise rotation of the South Caspian Block similarly to the kinematic change documented in the Alborz Mountains. We propose that the kinematic change due to South Caspian Block rotation is not restricted to the Alborz Mountains, but also affected the Iranian Plateau during post Pliocene time.