3D Mechanical modeling of faults planes based on stress fields: a case study of Saravan fault, SE Iran
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Abstract
This research aims to understand the response of the faults planes subjected to the certain stress fields. When an active fault ruptures, its geometry depends to the responsible mechanism at geological time. Therefore, it is important to study the faults behavior based on stress fields. We try to provide a process of modeling the fault plane. We first gain stress field by MATLAB scripting based on field data and stress–strain analyses. In addition, we compare the morphology of analogue models with the study area to improve our model. We design mechanical models based on finite element methods in Ansys so that have more adaptation with stress field and surface deformations. Finally, 3D fault plane appears as a narrow part of solid block. Selecting Saravan fault in SE Iran is because of its significant curvature along its strike and its recent activity. The model represents a compression and bulking affecting to the study area. The 3D deformed fault plane as a part of hanging wall block shows an upward progressive tear zone at the south end of the main fault.
Keywords
Stress field Mechanical model Finite element methodIntroduction
Many items including stress state, crustal geometry, rheology, rock type, frictional resistance, and fault activity interact to form tectonic phenomena (Rowshandel and NematNasser 1986; Niño et al. 1998; Chéry et al. 2004). Therefore we can use a continuous mechanical process to study the simultaneous effects of many geological events (Niño et al. 1998).
The aim of this study is applying a 3D mechanical model using stress fields to find out the geometry of the faults planes that here is Saravan fault (SF) as a case study. SF is an active right lateral reverse fault in SE Iran. An Mw 7.7 earthquake struck the Saravan region in SE Iran on 16 April 2013. According to the EMSC reports an almost pure normal focal mechanism with NE–SW fault plane, with a focal depth of 84 km (Zare and Shahvar 2013).
Since SF has reverse dip component and normal focal mechanism is unusual, we are interested to consider fault plane if there is another rupture at depth. By having an overall 3D view about fault plane, the judgment about seismic behavior of fault is more possible. We use a 3D finite element model and apply rock mechanical data to get a more realistic model.
Primitive investigators have considered elastic (e.g. Steketee, 1958; Chinnery 1961, 1970; Weertman 1965; Rybicki 1971) and viscoelastic (Nur and Mavko 1974) rheology in mechanical models. Considering of solid characteristics began with frictional resistance of rocks studies for strike slip faults and geodynamical models (Stuart 1979, 1981; Stuart and Mavko 1979; Rowshandel and NematNasser 1986; Carlson and Langer 1989; Willet et al. 1993; Byrne et al. 1993; Beaumont et al. 1996). However, the conception of modern mechanical models started with considering deformation fields and stress measurements (Niño et al. 1998; Chéry et al. 2001, 2004; Rhoden et al. 2012).
In this research, we improve mechanical models by taking stress field simulation and affecting rock mechanical data into account. Among main items for modeling, the state of stress is most important. By using MTLAB coding for structural field data, we simulate stress field. In this study, we try to design a mechanical model that works with simulated stress fields. We consider hanging wall block and then select narrow part of it to control boundary condition and study deformations of the fault plane. Therefore, Threedimension geometry of SF plane due to the responsible mechanics is the focus of this research.
Geological setting
General geology
The study area lies on the Nehbandan–Khash structural zone (Nabavi 1976) in southeastern Iran. However, there are some other names for this zone such as Iran’s East Mountain (Alavi 1991), Sistan suture zone (Camp and Griffis 1982), Zabol–Baluch zone (Berberian and King 1981), flysch zone (Eftekharnejad 1981), Makran mountain, and East of Iran (Stöcklin 1968). Sistan suture zone has tectonically changed by many events during a short geological time (Camp and Griffis 1982). A rifting system has parted Lut and Afghan blocks from each other. Afterwards an oceanic basin appeared that its evidence is thick flysch deposits. Northeastward subduction zone into the Afghan block occurred in Maastrichtian and collision of Lut block and Neh complex happened in Eocene. Continuing of the convergence caused the folds and conjugate strike slip faults that are visible on Oligocene and Miocene rocks (Camp and Griffis 1982). The subduction has been to the east direction where Afghan block exists (Tirrul et al. 1983). However, the number of Afghanistan volcanoes is trifle. Taftan volcano is a young and semiactive Pliocenequaternary volcanic that is located in 50 km far from Khash village in Baluchistan (Gansser 1966). Its height from the sea level is 4050 m and from surrounding planes is about 2000 m. This volcano has occurred on Eocene flyschs. The first eruptions involve lava, dacite, and rhyodacite pyroclastic rocks. The second activity of Taftan volcano consist upper Pliocene dacite and andesite lava with widespread agglomerate layers in 10 km far from its cone.
Lithological sequence
To have an overall view of the lithological sequence in the study area, we provide a general geological map by simplifying lithological units (Fig. 1). Although the main study area, including SF lies in eastern side of Taftan volcano (Fig. 2b) it spreads to the western side of Taftan volcano including Nosratabad and Bamposht faults. However, we mainly focus on eastern area of Taftan volcano to get analytical data from SF and nearby igneous rocks. We also consider general structural data from the western region to provide an overall model as discussed in the following. Cretaceous colored melange outcrops are oldest units in the study area (Fig. 1). In general, flysch facies developed in Eocene. Metadacites and intrusive granodiorites called KuheSefid developed in PaleoEocene and EoOligocene respectively (Fig. 1).
Main faults and related fractures
Strain and stress analysis
Calculating strain ratio along SF
Calculating stress field
Although simultaneous stress field studies led to insight into the mechanics that drives plate motions (e.g. Dwivedi and Hayashi 2010) but deductions will be difficult when studies encompass a more time range. A 2D stress distribution is possible to consider in two states. The first state includes a horizontal plane with two dimensions and the other one includes a plane with two horizontal and vertical planes (e.g. Islam and Shinjo 2012). Estimating of stress distribution is commonly from major to regional scale (Zhang et al. 2011). Nevertheless, according to conception of finite element analyses, we gather local data and generalize collected data to the whole area.
Threedimension mechanical model
Primary mechanical model
Rock mechanic data collected from different locations
Location latitude longitude  Rock type  Relative density (ASTM C97) g/cm^{3}  Uniaxial compressive strength (ASTM C170) MPa  Point load strength MPa  Young’s modulus ×10^{3} MPa 

N: 28°15′ E: 61°44′  Granodiorite  2.67  175.3  12.1  60.2 
N: 28°20′ E: 61°41′  Granodiorite  2.64  174.2  11.9  59.8 
N: 28°11′ E: 61°46′  Diorite  2.84  204.1  14.3  77.3 
N: 28°17′ E: 61°43′  Tonalite  2.74  190.4  13.2  65.1 
N: 28°13′ E: 61°45′  Tonalite  2.75  191.1  13.4  66.2 
N: 28°15′ E: 61°37′  Metadacite  2.71  193.5  13.1  65.7 
N: 28°28′ E: 61°32′  Metadacite  2.67  192.9  12.9  65.4 
N: 29°34′ E: 61°34′  Gneiss  2.68  163.4  12.8  45.5 
N: 28°15′ E: 61°33′  Schist  2.65  82.4  6.1  35.3 
Combined mechanical model
Simulation

Definition a set of elements connected at nodes

Computation of stiffness matrix K ^{(e)} and force vector F ^{(e)} for each element

Assembling the contribution of all elements into the global system Ka = f

Modifying the global system by imposing essential (displacements) boundary conditions

Solving the global system and obtaining the global displacements a
Therefore, it is possible to compute the reactions F _{1}, F _{3}, F _{4} after the computation of the global displacements.
Conclusions
3D model of the SF plane based on stress field and mechanical simulated models suggests the combined stress field effects as an important item that influence fault plane. It also show the mechanical behavior of the fault plane could vary from surface to the depth in different stress fields. Two gained main groups of stress fields represent S_{Hmax} orientation range from N10E to N85E. Comparing results of analogue models (i.e. Dominguez et al. 1998; Marques and Cobbold 2002; Zweigel 1998) and our primary models suggests for existence of a compression in the beginning until Eocene, a volumetric strain in OligoMiocene, and continuing of both simultaneously. Existence of a tear zone (Fig. 12) at the south end of the fault maybe justifies normal focal mechanism of Saravan earthquake on 16 April 2013. In conclusions, while other items may contribute to the geometry of fault plane, the most important finding in our model is effects of resultant stress fields in inhomogeneous deformations of faults planes. However, the more accurate information about underground fault mechanisms needs more works. We have not considered accurate displacement vectors in this model. Affecting a more range of kinematic data to determine boundary conditions that are more accurate is one of the future objects.
Notes
Acknowledgments
We thank E. Gholami from University of Birjand who shared his information and knowledge about SF and general geology. Analysis of the rock mechanic data to support this article in Table 1 has performed by us in the Rock Mechanics Laboratory at University of Tabriz and has not published anywhere else. We also thank officials at University of Tabriz and laboratory expert M. Sharghi for cooperation.
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