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Understanding and predicting the distribution of fractures in the deep tight sandstone reservoir are important for both gas exploration and exploitation activities in Kuqa Depression. We analyzed the characteristics of regional structural evolution and paleotectonic stress setting based on acoustic emission tests and structural feature analysis. Several suites of geomechanical models and experiments were developed to analyze how the geological factors influenced and controlled the development and distribution of fractures during folding. The multilayer model used elasto-plastic finite element method to capture the stress variations and slip along bedding surfaces, and allowed large deformation. The simulated results demonstrate that this novel Quasi-Binary Method coupling composite failure criterion and geomechanical model can effectively quantitatively predict the developed area of fracture parameters in fault-related folds. High-density regions of fractures are mainly located in the fold limbs during initial folding stage, then gradually migrate from forelimb to backlimb, from limbs to hinge, from deep to shallow along with the fold uplift. Among these factors, the fold uplift and slip displacement along fault have the most important influence on distributions of fractures and stress field, meanwhile the lithology and distance to fault have also has certain influences. When the uplift height exceeds approximately 55 percent of the total height of fold the facture density reaches a peak, which conforms to typical top-graben fold type with large amplitude and high-density factures in the top. The overall simulated results match well with core observation and FMI results both in the whole geometry and fracture distribution.

Natural fractures influence the performance of many reservoirs around the world, including carbonate reservoir, deep tight sand reservoir and low-per- meability reservoir in the world [

As practiced in fractured reservoir exploration and production, fracture prediction is commonly based on geometric and/or kinematic models, such as analyses of fault-related folds and fold curvature [

Since the 1960s, there have been many studies on the mechanical methods of structural movement generating fractures, including rock failure criterion and strain energy density. Based on laboratory modeling experiments and tests, [

In this study, we use the finite-element-method (FEM) to better simulate when and where paleotectonic differential stress develop within a fault-propagation fold (D gas field) throughout the entire deformational history based on the analysis of the structural evolutional characteristics, rock mechanical test, and acoustic emission experiments. Then we quantitatively predict the development and distribution zones of tectonic fractures based on composite rock failure criterion and geomechanical model between fracture density and strain energy density. Meanwhile, the predicted results can be verified through the fracture density distributions identified from cores, boreholes and the capacity of gas wells. The ultimate goal is to develop several suites of geomechanical models and experiments for evaluating and analyzing how these important mechanical factors (e.g., stress field, slip displacement of fault, mechanical parameters difference among layers and uplift amplitude of fold) control and influence the development and distribution of these fractures in fault-propagation fold. According to the obtained results, the adopted methodology proved successful in predicting tectonic fractures of tight sandstone reservoirs. Such reality shows that the methods for predicting fractures can provide an important technological approach to exploration and development of gas field in the deep tight sandstone reservoirs.

The Kuqa Depression is located at the northern margin of the Tarim Basin between the South Tianshan Orogenic Belt and the Northern Tarim Uplift to the south (^{2}, displaying a fault-propagation anticline with structure amplitude more than 700 m, the top of which was cross-cut by large-scale Dinan fault and subsidiary Dibei fault striking EW to make it more complicated. The dip of southern limb ranges from 16˚ to 30˚ and the dip of northern limb, ranges from 19˚ to 33˚ (

The Qiulitage tectonic belt and D anticline was mainly characterized by three nearly SN or NNW 350˚ compression [

of up to 40 m in the study area and act as the role of the slip layer. The porosity of Paleogene reservoir ranges from 5% - 15% through core tests and permeability lies in the range of (0.05 - 1.0) × 10^{−3} μm^{2}. However, the fracture permeability can reach (1.00 - 10.00) × 10^{−3} μm^{2}. On the whole, the physical property of upper EII reservoir is slightly better than that of lower EI reservoir, Finally, all the above evidences prove that the D gas field belongs to tight sandstone reservoir with low porosity and low permeability.

The most frequently encountered fractures in the reservoir of the study area are planar discontinuities which are sub-perpendicular to the bedding. The fractures can be further divided into three basic types, namely shear fracture type, tenso-shear fracture type, and tension fracture type (

other two types, and, in most cases, it can cut through rock grains. The extension fracture, however, exposes dendritic structure and frequently bypasses rock grains with a relatively shorter distance [^{−1}) and volume density (m^{2}/m^{3}), and the former is an important parameter to illuminate the development and distribution characteristics of fractures [^{−1} to 1.5 m^{−1} and length and vertical extent often greater than 10 m (^{−1} to 1.1 m^{−1, that is characteristic of systematic joints as defined in } [

In order to obtain fracture density and occurrence from geomechanical modeling approach, and further analyze how the mechanical factors control the development and distribution of fractures in fault-propagation fold, a connection between the fracture density and geomechanical modeling results must be established. Accordingly, we used improved “Quasi-Binary Method”, i.e., composite failure criterion inducing strain-energy release as an indicator for fracture development, and establish a relationship between fracture density and strain energy density. And the details of this method could be found in research results of [

When a rock mass is subjected to spatial principal stresses σ_{1}, σ_{2} and σ_{3}, the strain-energy density at a given point can be expressed as [

ϖ = 1 2 ( σ 1 ε 1 + σ 2 ε 2 + σ 3 ε 3 ) (1)

where ϖ is strain energy density (J/m^{3}); and ε 1 , ε 2 , ε 3 respectively are the strains corresponding to three principal stresses.

Recalling the Hooke’s Law relations and substituting for the strain components into [

ϖ = 1 2 E [ σ 1 2 + σ 2 2 + σ 3 2 − 2 μ ( σ 1 σ 2 + σ 2 σ 3 + σ 1 σ 3 ) ] (2)

where μ is the Poisson’s ratio.

Deep tight sandstone is generally characterized by strong brittleness, high elasticity modulus and low Poisson’s ratio. According to brittle fracture mechanics theory and maximum tensile stress theory, when elastic strain energy release rate accumulating in brittle rocks equals to the energy per unit volume for generating fractures, rocks will break down. When the surrounding three-dimensional stress state reaches the rock strength, macro brittle fractures will occur with strain energy releasing, part of which will offset the surface energy of new fractures, and the rest of which will offset in form of elastic waves [

D v f = S f V = ϖ f J = ϖ − ϖ e J = 1 J ϖ − ϖ e J = a ϖ + b (3)

where D v f is fracture volume density per unit volume (m^{2}/m^{3}); ϖ f is strain energy density for new fractures (J/m^{3}); V is characterization of unit cell volume (m^{3}); S_{f} is surface area of new fractures (m^{2}); J is the required energy per unit area for fractures (J/m^{2}), i.e., fracture surface energy (here the energy is different from and far less than theoretical value of molecular dissociation); ϖ e is the necessary elastic strain energy to be overcome for new fractures (J/m^{3}); and a and b are the relative coefficients.

Furtherly, relationships between fracture volume density and strain energy density under uniaxial stress state, triaxial stress state will be established after formula transformation, the final fracture linear density is derived as following:

1) Commonly, tectonic fractures are divided into tensile and shear fractures based on the forming mechanism, and they can be discriminated with the Griffith Criterion and Coulomb-Navier Criterion (also called the Coulomb-Mohr Criterion), respectively [

σ 1 − σ 3 2 ≥ C 0 cos φ + σ 1 + σ 3 2 sin φ (4)

The Coulomb-Mohr Criterion suggests that a shear fracture only forms if the internal strength or cohesion of the rock (C_{0}) is exceeded, and depends on the magnitude of normal stress along a fracture plane. The relationships between fracture density, aperture and strain energy density, stress-strain are written as follows

{ w f = w − w e = 1 2 E [ σ 1 2 + σ 2 2 + σ 3 2 − 2 μ ( σ 1 + σ 2 + σ 3 ) − 0.85 2 σ p 2 + 2 μ ( σ 2 + σ 3 ) 0.85 σ ] p σ p = 2 C 0 cos φ + ( 1 + sin φ ) σ 3 1 − sin φ E = E 0 σ p D v f = w f J J = J 0 + Δ J = J 0 + σ 3 b D l f = 2 D v f L 1 L 3 sin θ cos θ − L 1 sin θ − L 3 cos θ L 1 2 sin 2 θ + L 3 2 cos 2 θ D l f b = | ε 3 | − | ε 0 | ε 0 = 1 E ( σ 3 − μ ( 0.85 σ p + σ 2 ) ) (5)

where φ is the internal friction angle (˚); θ is the angle between normal to the newly formed fracture plane and the maximum principal stress (˚); σ 1 is the peak stress (MPa); σ 2 is the intermediate principal stress (MPa); σ 3 is the middle principal stress, (MPa); σ p is the rupture stress under action of σ 3 , different from the maximum principal stress; σ t is the tensile strength, (MPa); J 0 is fracture surface energy with no confining pressure or under unaxial compressive stress (J/m^{2}), Δ J is the additional surface energy caused by confining pressure σ 3 (J/m^{2}); E is the elasticity modulus with no confining pressure (GPa); b is the fracture aperture (i.e. paleo-aperture, here for reference only), m; D l f is the fracture linear density (1/m); ε 3 is the tensile strain under current state of stress, dimensionless parameter; ε 0 is the maximum tensile strain, dimensionless parameter, corresponding to tensile strain when crack beginning to form; E 0 is the proportionality coefficient related to lithology; and L_{1}, L_{2}, L_{3} are side length of the selecting representing element volume (REV) (refer to

2) When there exists tensile stress, for brittle tight sandstone material the Griffith Criterion is used, that is

When σ 3 ≤ 0 and ( σ 1 + 3 σ 3 ) ≥ 0 , the applied failure criterion is given as

( σ 1 − σ 2 ) 2 + ( σ 2 − σ 3 ) 2 + ( σ 3 − σ 1 ) 2 ≥ 24 σ T ( σ 1 + σ 2 + σ 3 ) (6)

cos 2 θ = σ 1 − σ 3 2 ( σ 1 + σ 3 )

When ( σ 1 + 3 σ 3 ) < 0 , the failure criterion is simplified to σ 3 = − σ T , θ = 0 .

If the failure criterion is reached, the relationships between fracture density, aperture and strain energy density, stress-strain are expressed as

{ w f = w − w e = 1 2 ( σ 1 ε 1 + σ 2 ε 2 + σ 3 ε 3 ) − 1 2 E σ t 2 D v f = w f J J = J 0 + Δ J = J 0 + σ 3 b D l f = 2 D v f L 1 L 3 sin θ cos θ − L 1 sin θ − L 3 cos θ L 1 2 sin 2 θ + L 3 2 cos 2 θ or D l f = D v f D l f b = | ε 3 | − | ε 0 | | ε 0 | = σ t E (7)

The above fracture mechanics models are all under local coordinates. However subsequent simulation of stress field and calculation of fracture parameters need to be transferred into global coordinates. In three-dimensional space, conformation of fracture strike and dip depend on reasonable projection method, e.g. X-axis agrees with east-west direction, Y-axis agrees with north-south direction, and Z-axis agrees with vertical direction. If direction cosine under global coordinate of normal direction vector of fracture plane is determined as n ¯ = { l m n } , and n ¯ is projected to x-o-z plane with angle between projection line and negative direction of z-axis, through the angle conversion α Z = arctan ( − l / n ) , the angle of strike α will be calculated.

If 0 ≤ α Z < 90 ∘ ，then α = 90 ∘ − α Z (8)

If 90 ∘ < α Z < 0 , then α = ( − 90 ∘ − α z ) + 360 ∘ (9)

From the geological point of view, fracture dip α d i p between x-o-z plane and fracture plane also can be defined as angle between the l x + m y + n z = 0 plane and y = 0 plane, that is α d i p ( 0 ∘ ≤ α d i p ≤ 90 ∘ ), which is expressed as

cos α d i p = | l ⋅ 0 + m ⋅ 1 + n ⋅ 0 | l 2 + m 2 + n 2 0 2 + 1 2 + 0 2 = | m | l 2 + m 2 + n 2 , 0 ∘ ≤ α d i p ≤ 90 ∘ (10)

The simulation approach used in this study utilizes the Finite Element (FE) technology, and geomechanical models will be run in order to simulate the distribution of tectonic stress for further predicting fracture development and distribution. This powerful tool allows for robust simulations of complex structures with non-linear material behavior or large deformation based on frictional contact mechanics [

The purpose of this step is to set up several suites of geomechanical models and experiments on the base of fold evolution and analyze the development and distribution of tectonic fractures in fault-propagation fold. The initial 2D geometric model (

Member of EII from top to bottom, respectively. The average thickness of the two mudstone interlayers are all set to 70 m, they are the first Mudstone Member of EI and the first Mudstone Member of EII from top to bottom, respectively. The target zone associated with the upper cover layers (i.e. Q. N. Formations) and basement (i.e. K. J. Formations)are considered as an isolated bodies or boundary conditions for simulation. The conformation of boundary conditions is important to demarcate the study area from the rest parts of Kuqa Depression, and eliminate the influence of boundary effect on the simulation results. Considering the Middle Himalaya Period after Miocene Jidike Formation sedimentary and the Late Himalaya Period after Pliocene Kangcun Formation sedimentary as the crucial time of fracture formation in the Paleogene reservoir, the cover layers are set to approximately 1200 m thick and 3400 m thick, respectively. In order to guarantee the accuracy of the simulation, the width of the 2D geometric model is set to 50m according to analogous theory of test model [

And we mainly analyzed the contemporary faulting in this fault-controlled anticline. The southern boundary fault (i.e. Dinan fault) in the geological model began to develop mostly at the end of Miocene, and strongly reactivated at the end of Pliocene associated with stresses redistribution. In the Neotectonics Period, the same time the back thrust fault (i.e. Dibei fault) in the back limb rapidly formed as an accommodation structure along with rapid uplift of the D anticline and tending towards stability. In contrast, most fractures in D anticline were mainly controlled by the boundary Dinan fault in the forelimb, while were partly reactivated or influenced by the late-folding thrust fault (i.e. Dibeibackthrust fault) [

Generally, the vertical stress can be calculated from the bulk density of rocks based on Equation (11), and the horizontal stress component at the end of Miocene caused by the bulk density was less than 3 MPa in the Suweiyi Group and Kumugeliemu Group calculated by Equation (12) with an average depth of 1200 m. In the same way, the horizontal stress component at the ends of Pliocene and Pleistocene caused by the bulk density was less than 5 MPa.

σ z = ρ h g (11)

σ h = σ z ( μ 1 − μ ) 1 n (12)

where σ z is the vertical stress, σ h is the horizontal stress caused by the bulk density, μ is the Poisson’ ratio, ρ is the density, g is the gravitational acceleration, and n is a constant related to the nonlinear compression and is 0.67 here [

Note that our intention is to precisely simulate the overall deformation history of the D anticline under horizontal compressive stresses and capture real-time development and distribution of strain energy density and fractures. Based on the sustainability of tectonic movement on the earth, each thrusting movement can be subdivided into two critical stages, so that a total of 6 deformation stages numbered in geological models are conducted through finite element analyses. From beginning to the end, a horizontal stress of 50 MPa, 60 MPa, 80 MPa, 100 MPa, 90 MPa, and 70 MPa from northern Tianshan Mountain is applied to the geological model.

Material properties are assigned to the elements representing the various lithologies. The finite element models can describe elastic and plastic rock deformation to adequately simulate the folding behavior. The exposed strata and corresponding lithology can be obtained from the stratigraphic data of the Kuqa Depression. To begin the examination of macroscopic effects, the geological model of this study was divided into the following major types of unit: the sandstones, mudstone interlayers, basement, and fault. The mechanical parameters of the EI group and EII group are assigned with the different values because of lithologic differences respectively, which had certain effect on the simulation results. These parameters were determined by the testing of rock mechanics (

Layers | Density (g/cm^{3}) | Young’s modulus (GPa) | Poisson’s ratio | Internal friction angle (˚) | Cohesion (MPa) | Tensile strength (MPa) |
---|---|---|---|---|---|---|

Upper Sandstone of EI | 2.62 | 57 | 0.24 | 34.27 | 84.61 | 7.12 |

Lower Sandstone of EI | 2.63 | 56 | 0.25 | 36.14 | 92.14 | 7.44 |

Sandstone of EII | 2.60 | 60 | 0.23 | 28.63 | 87.88 | 6.91 |

Mudstone of EI | 2.64 | 35 | 0.29 | 46.72 | 73.18 | 9.78 |

Mudstone of EII | 2.67 | 35 | 0.31 | 48.10 | 66.51 | 9.44 |

Faults | 2.45 | 35 | 0.31 | 48.10 | 66.51 | 4.67 |

Basement | 2.64 | 50 | 0.24 | 34.27 | 84.61 | 10.12 |

The definition of mechanics parameters in fault zones is extremely significant to the modeling results, however exact mechanical parameters for fault zones are unavailable. Based on previous studies [

The Ansys software was used to construct a geological model that was meshed based on area distribution, rock structure, and lithology distribution of the target stratum. The geological model was meshed in the form of hexahedron elements with 8 nodes by an artificial mesh-generation method. In general, the fault zones and targeted layer are divided by finer elements, whereas other layers were meshed by coarse elements. The geological units of the whole model are meshed by setting the element length from small to large. Each layer was meshed and then connected with one another in space for a 2D mesh model. The model contained a total of 12,576 elements and 2796 nodes (

After establishing several suites of mathematical models, we used the Ansys software to simulate the paleotectonic stresses fields during the Himalayan Period and Neotectonics Period in the D area, Kuqa Depression. The simulation results included the distribution of the maximum principal stress, minimum principal stress intermediate stress and differential stress, which provided stress parameters for fracture prediction (_{1}, indicative of compression, range from 140 MPa to220 MPa. The σ_{2} (i.e. vertical stress) indicative of compression, are generally between 56 MPa and 123 MPa, and the σ_{3}, indicative of both compression and tension, ranges from −30 MPa to 15 MPa (_{3} subtracting σ_{1}, indicative of possible damage zone, mainly ranges from 0 to 85 MPa (

along the fault plane and uplift of fold amplitude, the stress and strain gradually focus in the thrust fault. Along with the shorting and folding of D anticline, the differential stress gradually increases and the positive values of minimum principal stress migrates from the back limb to the forelimb, indicating a successive transition from regional stress field to local tensile stress field in the core of fold. For comparison, considering the mechanical differences between sandstone member and mudstone interlayers, a series of inconsistent deformation phenomena occur near the lithologic interfaces, accompanied with obvious bed-parallel slip, wide development of tensile stress in sandstones and concentration of differential stress. The distributions of three principal stresses are similar to each other, all of them are mainly fold-controlled and secondly fault-controlled. In addition, both the highest values of tensile stress and differential stress are all located in the hanging wall of fault and top areas of D gas field (

The simulation of the 2D tectonic stress field may be used to calculate the tensile stress and compressive stress of rocks during tectonic movement. The rock rupture criteria in Equation (4) and Equation (6) may then be employed to determine whether ruptures will occur in rocks. D v f , D l f and α d i p are used to express the development degree of the tensional and shear fractures comprehensively. According to Equation (5) and Equation (7), the fracture parameters related to stress, strain and strain energy density are calculated or directly extracted from the above numerical simulation of paleotectonic stress field. Firstly, based on abundant mechanical experiments [_{c} (σ_{c} is compressive strength of rock), the number of fractures explode instantaneously and the number of large-scale fractures increase faster than that of small-scale fractures, which can be considered as damage threshold indicating a key stage of abundant microcracks coalescence and macrocrack initiation. At this key stage, the corresponding strain density energy is close to ϖ e in theory, hence, we assume that ϖ e is strain energy density at σ = 0.85 σ c . Recalling the Hooke’s Law the ϖ e and ϖ can be obtained [^{2}, and the average E 0 is 112.6. Secondly, putting J 0 and E 0 into the Equation (5) and combining with formulas of D v f , D l f , b and J , the fracture volume density D v f , the fracture linear density and fracture aperture b under triaxial state of stress can be calculated, in that order. Thirdly, considering appearance of tensile stress, the fracture parameters D v f , D l f and α d i p are obtained using the same method, which is built into the Ansys platform to calculated spatial distribution of fracture parameters (

To gain insight into the stress field and damage zone during fault-related fold- ing, we conducted six simulations for different combinations of mechanical stratigraphy (thickness and mechanical properties of the rock layers), continuous contraction of the fold, and strength of bedding surfaces. In sum, the final geomechanical finite element modeling result during the six step matches well with cores observation and imaging logging interpretation results both in the whole geometry and facture distribution (

Commonly, the development of tectonic fractures is generally controlled by

tectonic stress field [

For all simulations in the geological model, the horizontal pressure of each key construction period is set to 50 MPa, 60 MPa, 80 MPa, 100 MPa, 90 MPa, and 70 MPa in turn. For further study of continuous influences on development of fractures in fault-propagation fold, the horizontal pressure of 30 MPa, 110 MPa, 120 MPa and 130 MPa is respectively added to the geological model as a supplement. The stresses intensity is computed at the center of elements, which is identified in

y = 0.7426 ln x − 1.1603 ( R = 0.9572 )

where y is the simulated fracture density in model (m^{−1}), x is the differential stress (i.e., σ_{1} − σ_{3}), and R is the correlation coefficient.

As is shown in

Besides, the simulated developed areas of fracture density coincide with the areas with high tensile stress, including the hinge of anticline and the northerns and stones near the lithologic interfaces (

Of interest here is the relation between different slip displacements and uplift amplitude with fault-parallel slip. Generally, vertical amplitudes that develop during folding are affected by the interaction between slip displacements along fault plane and differential stress with different mechanical properties [

The influence of slip displacement and fold amplitude on the development and distribution of fractures in fault-propagation fold is observed and discussed (

y = 0.839 ln x − 2.6501 ( R = 0.8823 )

where y is the simulated fracture density in model (m^{−1}), x is the uplift height (m), which is equivalent to curvature in folding process, and R is the correlation coefficient.

As is shown in ^{−1}) in initial segment of the curve then slowly increases until the end. The corresponding height to this peak point of fracture density is about 240 m, which is regarded as the most critical stage of fracture development. However, as in

At the same time, a power relationship is barely established between the fracture linear density and corresponding distance from fault surface (

y = 9.3044 x − 0.482 ( R = 0.7749 )

where y is the predicted fracture linear density in model (m^{−1}), x is the distance from fault (m), and R is the correlation coefficient.

As illustrated in ^{−1}), and in this process some abnormal points seriously deviate from the curve track indicating a minor quantitative effect of fault activity on development of fracture density.

For comparison, another integrated logarithmic relationship is confirmed between the fracture linear density and corresponding slip displacement as follows (

y = 0.7309 ln x − 2.6306 ( R = 0.9481 )

where y is the predicted fracture linear density in model (m^{−1}), x is the slip displacement along fault during folding (m), and R is the correlation coefficient.

As is shown in ^{−1}). Considering the difference of buried depth, within the first three stages the high-value areas of fracture density are located in upper EI sandstones, however, in the late three stages the high-value areas are transferred to the lower EII sandstones, which is similar to the results of hybrid cellular automata numerical technique [

For the model results described above, the spatial variation of fracture dip during folding is a result of stress state transformation under sustaining loadings. As with an elastic-plastic model, the Mohr-Coulomb and Griffith criterions give the different rupture angles in extension and compression. Therefore, an experimental linear relationship is established between the fracture dip and corresponding uplift height of folding as follows (

y = 0.1684 x + 11.33 ( R = 0.503 )

where y is the predicted fracture dip in model (˚), x is the uplift height during folding (m), and R is the correlation coefficient.

It should be emphasized that this obvious linear relationship is only occurred in upper EI formation (

As mentioned above, the fractures observed in cores and identified in FMI can be divided into four sets, and the fracture Set I and Set II mainly presenting in hinge and limbs, are interpreted as a low-angle conjugate fracture system at initial folding stage. Along with increase of depth, the compressional stress state gradually converts to typical strike-slip stress environment, which usually is marked by a series of strike-slip fractures. This result agrees with the simulated distribution characteristics of fracture density and dipping region as shown in first three stages (

In general, the lithology influences the development of tectonic fractures in reservoirs basically [

deformation [

Statistical analysis from cores and thin sections, shows that lithology still has effect on fracture development and distribution to a certain extent in anticline. As is shown in

Our non-linear 2D FE models of a fault-propagation fold (the D gas field) developed in a mechanically stratified sequence of the Kuqa Depression are analyzed to understand the development and distribution characteristics of fractures during different folding stages. As a result, the overall geomechanical FE modeling results are in agreement with field observation results both in the geometry and in the fracture development and distribution. Clearly, the Strain Energy Density and Fracture Density used here as indicators are not appropriate for all types of fractures, however, if combined with fracture criterions, it might be useful indicators in the present study and the reliability of this premise is acceptable. Certainly, aiming at more complicated structures, the improved and elaborate anisotropic geomechanical models including various lithologies and relatively true structural feature should be constructed for more accurate analysis based on more advanced software platform and theory.

Several important geological factors, such as the differential stress, tensile stress, distance from fault, slip displacement, uplift height and lithology are discussed and analyzed quantitatively based on the simulated results and measured results. A logarithmic relationship between fracture linear density and stress density, fracture density and uplift height, fracture density and slip displacement was established respectively. However, unlike the formers, relationship between fracture linear density and tensile stress values accords with good linear trend, which implies that the derived tension stress field during folding has the most influence on fracture development. Moreover, a negative power relationship between fracture density and distance to major fault surfaces is roughly established through scattered data points, which indicates during the Early Initial Compressional Stage and Mid-term Strong Thrusting and Uplift Stage, most fractures probably are co-controlled by folding faulting activities. Additionally, the potential evolutionary relationship between fracture dip and uplift height during folding is studied. On the whole, along with the increasing of fold amplitude the facture dip becomes steeper, but some fractures with shallower dip exist in the fold core and near the mudstone interlayers, oblique to the fold trend due to widely bed-parallel slip. Lithology as an innate factor influencing the mechanical properties of rock and possibility of fracturing, has non-linear relationship with fracture linear density. In terms of microcosmic, along with the grain size of minerals becoming coarser and the sorting getting better, the fracture density increases although most fractures in glutenite and conglomeratic siltstone belong to inner-grain fractures and grain boundary fractures. Therefore, these geomechanical factors altogether control and influence the development and distribution of tectonic fractures during evolutionary stages of the fault-propagation fold, and the relative height of fold uplift has the largest slope value among all the factors, which implies that the fold uplift in the most important factor for fractures. The second geomechanical factor influencing the development and distribution of fractures in high thrust fault-propagation fold is slip displacement along fault, and the third is lithology, the last is distance to fault plane. Here it must be emphasized that crosscutting relationships lie among these geomechanical factors, such as the derived stress factors are the outcome of fold contraction and uplift.

Finally, this evolutionary model of the structures present to us is a distinct and intuitive top-graben fold with high amplitude and high-density factures in the top, has experienced strong folding and uplift process. From early to late, in profiles both high-density and high-angle areas of fractures migrated from south to north, from deep to shallow and from the limb to the top, and fractures begin to generate in the sandstones, then gradually extend into the mudstones rather than unboundedly clustering in sandstones. Moreover, when the uplift height of fold along with corresponding slip displacement exceeded approximately 55 percent of the total height the early fractures on top parallel to the axis of fold were reactivated until developed into normal faults, which undoubtedly reduced the later density of tensile fractures at present.

This research was financially supported by the National Oil and Gas Major Project (2016ZX05047-003,2016ZX05014002-006), the National Natural Science Foundation of China (41572124) and the Fundamental Research Funds for the Central Universities (17CX05010). The authors wish to thank master student Naser lovely for the meticulous review of the manuscript. We also thank Prof. Jusheng Dai, Prof. Shaochun Yang for their insightful reviews and comments.

Feng, J.W. and Gu, K.K. (2017) Geomechanical Modeling of Stress and Fracture Distribution during Contractional Fault-Related Folding. Journal of Geoscience and Environment Protection, 5, 61-93. https://doi.org/10.4236/gep.2017.511006