INTRODUCTION
Regarding to the importance of coupling behavior, specially in civil engineering,
there has been a special attention to this subject in recent years, which proves
that future studies will be on the way of coupling problems solution. Many experimental
and in situ investigations in this field are good evidences for this statement
(Anderson and Hudson, 2003).
Hydromechanical behavior has been studied in this study with Regard to the bisotun epigraph case study (Fig. 1).
Of course, exactly understanding, characterization and modeling of the rock
mass properties, are unattainable. But coverage all geometrical details and
mechanical effects is not needed in practice.

Fig. 1: 
View of bisotun epigraph 
How comprehensively the coupled mechanisms have to be modeled should be related
to the objectives of the modeling. For many applications, existing understanding
and computer codes are sufficient; whereas for some other applications, development
of more sophisticated tools is required (Desai and Christian,
1997; Ewalds and Wanhill, 1984).
Regarding to complication of the hydromechanical coupling behavior and better
understanding of main factors, softwares of UDEC and 3DEC and Ansys have been
used. Usually, there are some limitations in most of softwares to model hydromechanical
behavior exactly, therefore some codes have been written to remove limitations
(ITASCA, 1999).
Analyses are based on following formulations:
The vertices of the triangular elements are gridpoints and the equations of motion for each gridpoint are formulated as follows:
where, s is the surface enclosing the mass m lumped at the gridpoint,
and F_{i}^{c} is the contact force along boundary.
The following effects are modeled in UDEC:
F_{i} 
= 
Pn_{i}l, 
q 
= 
k_{j}a^{3}Δp/l 
Δp 
= 
kw (ΣQΔtΔV)/V 
ΣQ 
= 
Flow into node 
ΔV 
= 
Mechanical volume change 
a 
= 
Joint aperture 
l 
= 
Joint length 
q 
= 
Domain flow rate 
F 
= 
Joint force 
p 
= 
Joint pressure 
k_{w} 
= 
Bulk modulus of the fluid 
k_{j} 
= 
Joint permeability factor 
Flow is governed by the pressure differential between adjacent domains. The flow rate per unit width can be expressed as q, which is based on the obtained mean velocity from the analytic solution for laminar viscous flow.
Darcy’s law for an anisotropic porous medium is:
where, V_{i} is the specific discharge vector, p is the pressure and _{kij} is the permeability tensor.
The specific discharge vector can be derived by gauss’ theorem:
Joint dilation is effective when the joint is at slip. The normal displacement increment, ΔU_{n}^{d} due to dilation is calculated as:
where, ΔU_{S} is shear displacement increment and dil is joint dilation angle.
Numerical analysis must be based on the proper comprehension of major factors,
therefore we need to an appropriate understanding of their coupling to get the
best results (Kanninen and Popelar, 1985).
GENERAL DESCRIPTION
This 18x3.2 m epigraph is located on a limestone rock mass which consist of
some discontinuities. These fractures are effective on the value of elasticity
modulus, rock mass strength, permeability, water flow direction and sedimentation
on epigraph surface. Therefore study on the fracture network and joint development
is essential. Epigraph has been subjected to HydroThermoMechanicalChemical
processes which have made karstic holes and surface erosion (Karimnia
and Shahkarami, 2006).
The following factors are the most significant factors on making damages:
• 
Surface and groundwater flow on epigraph surface 
• 
Weathering (consist of physicochemical processes) 
• 
Fatique due to temperature changing 
• 
Rock geometry alteration 
The rock mass contains many fractures. Regarding to the important effects of discontinuities on the rock mass behavior, we study on the properties of discontinuities in this part. This study shows that there are two major fracture sets, Two minor fracture sets and a bedding surface set.
Bisotun rock mass is formed by Bisotun limestone and located on a tectonic zone with many faults and fractures. Faults show the historical stress conditions in this area.
Water originates from a near minor fault which is located on intersection between two faults. Thus it can be concluded that this site has been subjected to tectonic stresses.
Because of steep slope and high mountains, it can be concluded that the rock mass strength is high.
The epigraph is divided to upper and lower parts by a bedding surface which it’s slopecause water flow toward epigraph. Surface erosion of the upper part is more than the lower part.
GEOTECHNICAL INVESTIGATIONS AND MICROSCOPIC TEST RESULTS
To study the rock specifications, some tests have been done on some samples.
Results of this study show that regarding the voids which are full of calcite, increasing of the void ratio is unavoidable, because of calcite erosion.
Rock mass is under climatic condition and water influences through it and dissolves
CO_{2} of the soil, air and plants thus change to acid water and can
dissolve calcium carbonate. Therefore lime dissolution due to this water is
unavoidable. In addition, fracture development in this limestone and in the
upstream of the epigraph make a karstic zone in Bisotun limestone (Mehdi
Abadi, 2000).
Tectonic study shows that according to seismic zoning of iran, Bisotun mountain is located on the high risk zone. During the last 100 years, most of earthquakes have happened around 3 points which are around Bisotun mountain, kashmar and Bandar abbas.
More than 6 earthquakes have happened during 4.5 years in Bisotun. Bisotun
bedding layer system and fracture network are unique in geological science.
Sedimentary layers are nearly horizontal, fractures and faults networks are
parallel to each other and vertical to bedding planes. Therefore damages happen
due to landslide and slide happens along the surface.
The following items are major properties of Bisotun epigraph rock mass discontinuities:
Fracture orientation
The first major fracture set: This set is very important. That is
parallel to the epigraph surface and is developed into the limestone deeply.
Therefore it has a main role in water flow specially around epigraph.
The second major fracture set: This set is nearly vertical to the first one and intersects epigraph surface. This set is important to rock mass hydraulic conductivity .Where this set intersects epigraph, water flow and karstic holes are visible. Number of fractures in this set are less than the first one. Intersection of this set with bedding surface has made a flow channel to water conduction toward epigraph surface.
Minor fracture set: This fracture set is not developed very much into the rock mass, therefore it does not have an important role in ground water conduction, however, that is important to dissolution and development of karstic holes into the limestone.
Bedding planes: That is known as a main factor in water conduction toward epigraph surface.
Fracture spacing: Fracture spacing is 12 m in the first major fracture set and 35 m in the second major fracture set. Although bedding plane spacing is 1m, only two layers with 40 m distance are visible, thus bedding plane spacing is considered 40 m. Random fracture set spacing is variable.
Fracture length: Major and minor fracture sets consist of very long fractures and some of them are longer than 40 m. Bedding planes are developed very much but random fracture sets consist of short fractures (at most 5 m). Therefore major and minor fracture sets and bedding plane are important in water conduction.
Surface roughness: The most important fracture sets are rough, thus jrc 100 and jr are considered 9 and 3, respectively. This parameter value is considered 2.3 for bedding plane. Fracture surfaces are weathered and without filling material so ja is considered 1.5. Thus we can obtain the value of internal friction angle which is determined equal to 45. These fractures are developed into the rock mass deeply.

Fig. 2: 
Water flow into rock mass 
Fracture’s wall strength: According to the results of in situ tests, fracture’s wall strength is obtained about 24 mpa.
Joint aperture: The maximum value of joint aperture, 12 mm, is related to two bedding surfaces, 40 m distant from each other. This joint aperture is only visible on the surface and there is no information about it’s development into rock mass. This aperture is made due to water dissolution. Two major fracture sets aperture values are not greater than .1 mm and minor fracture sets aperture are nearly closed. Therefore we conclude that the major fracture sets conduct raining water toward the bedding surfaces and then conduct it toward rock mass surface.
Filling materials: Only random fracture sets and small fractures are filled with calcite but another fracture sets does not have any filling materials. It is considerable that water flow into the rock mass, has made rock mass fractures (Fig. 2).
EFFECTIVE FACTORS IN NUMERICAL ANALYSIS
Stability of Bisotun epigraph is changing in some aspects (Fig.
3):
• 
Tectonic loading which can be explained by weight and changing
boundary conditions 
• 
Thermal loading 
• 
Loading and erosion due to water suspended solids 
• 
Dissolution due to ground water 
• 
Microstructural changes, weathering and degradation 

Fig. 3: 
Main fractures in bisotun epigraph 
This research intend to explain a methodology using fracture and fatique. To
study on stability analysis, critical points of the Bisotun epigraph and the
physical comprehension about the reason of inclined crack in the right side
of the epigraph, numerical modeling is used by ansys software, which is a powerful
software.
Regarding the geotechnical investigations and analysis of the test results, rock mass mechanical properties are mentioned below:
MODELING AND NUMERICAL ANALYSIS OF HYDROMECHANICAL COUPLING
To study on the rock mass hydromechanical behavior, Ansys, 3Dec and Udec softwares
have been used. These softwares are among the most powerful softwares for:
• 
Intact rock rock mass 
• 
Compressive strength 30 4 
• 
Tensile strength 4.5 .53 
• 
Elasticity modulus 5.7 2 
• 
Poisson ratio .31 .3 
• 
Cohesion 8.5 1.5 Internal friction angle 30 25 
M 4.86 0.22 S 1 0.012 geotechnical modeling but have some limitations to hydromechanical
modeling.

Fig. 4: 
Modeling of bisotun epigraph domain 

Fig. 5: 
Vertical stress state around epigraph 
Therefore these limitations have been removed with programming (Sato
and Hiragawa, 2003).
Rock mass initial conditions have been studied and blocks stability analysis have been done in this paper. In this modeling, joint geometrical and mechanical properties, rock mass mechanical properties, boundary conditions and loading have been considered exactly (Fig. 4), then hydraulic properties sensitivity to mechanical properties, stress variation, mechanical boundary conditions, initial mechanical aperture and geometrical fracture net have been studied.
Study has been done on the behavior of rock mass and stressstrain state around
epigraph. Rock mass consists of various joint sets and bedding surfaces which
are introduced with more details in this part (Wilson, 1997;
Zienkiewicz and Taylor, 1989).
According to the analysis results, stress and strain distribution have been
evaluated. Maximum vertical stress and maximum shear stress are equal to 1.9*10e2
(KP) and 0.9*10e2 (KP), respectively. Stress and strain distribution show that,
rock mass around epigraph has been subjected to significant stresses (Fig.
5, 6).
Induced stresses on epigraph rock mass due to water pressure, has been considered.
This pressure value is 18 (KP) which is a significant value.

Fig. 6: 
Shear stress state around epigraph 

Fig. 7: 
Hydraulic pressure around epigraph 
Obtained results show that, hydraulic pressure has had a significant role on
epigraph behavior (Fig. 7).
Analyses which have been done to assign blocks stability safety factor around the epigraph, show that the most critical value of the safety factor is limited to 2 which can be considered as an appropriate safety (Fig. 8).
To study on the joints density effects on the seepage condition, various analyses have been done. Firstly, j1 and j2 joint sets with 1(M) and 2(M) spacing then j3 random joint set have been considered (Fig. 9).
Obtained results show that, increasing fracture density cause increasing the seepage value. Also seepage in random fractures is more than organized fractures in order that there are more connected fractures in this case.
Regarding to the importance of stresses on seepage value, some models have been analysed to study on this subject. According to the results, increasing of the lateral stresses from 20 to 80 KP cause about 40% decrease in seepage value (Fig. 10).
Regarding to significant effects of stress state on seepage value, proportion
of the joint shear stress to joint normal stress has been considered as a main
factor.

Fig. 8: 
Blocks stability safety factor around epigraph 

Fig. 9: 
Joint density effects on seepage 

Fig. 10: 
Effect of stresses on seepage 
If this factor remains constant and sliding does not happen in the fracture,
normal stress increase makes seepage reduction.
If the mentioned factor changes but joint slip does not happen, increasing of this factor cause seepage value reduction (Fig. 11).
If increasing the mentioned factor causes joint slip, seepage value will increase
(Fig. 12, 13).

Fig. 11: 
Stress state effects on seepage 

Fig. 12: 
Proportion of joint shear stress to joint normal stress effect
on seepage 

Fig. 13: 
Stress state effects on seepage 
Joint length effects on seepage value has been studied. Obtained results show that, seepage value has been increased with joint length increase.
Two significant factors in rock mass seepage value are elasticity modulus of
the rock mass and joint normal stiffness. Reduction of the rock mass elasticity
modulus cause seepage increasing because of joint aperture increasing due to
deformability increasing. Also joint normal stiffness decreasing cause seepage
increasing (Fig. 14, 15).

Fig. 14: 
Elasticity of rock mass effects on seepage 

Fig. 15: 
Joint normal stiffness effects on seepage 
How to solve fractures problem: The best solution to correct cracks and joints and fractures around the epigraph is the use of injections. Because of that, from the inside of boreholes with approximate diameter of 10 cm must inject into the rock mass around the epigraph. Considering the importance and sensitivity of the project and its historical value, Injection operation must be done carefully and with high quality. One of the most important parameters in this project is injection pressure, which should be fully controlled and its value must be assigned using numerical analysis.
Therefore the numerical analysis are performed on the result and specifications and limitations of injection pressure has been analysed.
Model and analysis scheme are shown in the model in Fig. 16. Analysis results show that in order to improve joint and cracks in rock mass should have a maximum injection pressure about five bar.
Results of the analysis are shown in Fig. 1719.
In fact, if the injection pressure to reach more than five bar, hydraulic fractures
will actually begin, It means that five bar pressure is hydraulic fracture initiation
value, Therefore injection pressure should never be more than five bar.

Fig. 16:

Meshing of the injection model 

Fig. 17: 
Stress state around borehole in the model 

Fig. 18: 
Stress state vectors around the model 

Fig. 19: 
Displacements around the model 
DISCUSSION
The following items are the main results of this study:
• 
Obtained results show that the fracture density is a very
effective factor in hydromechanical behavior of fractured rock mass, because
of the significant effect of the fracture as a localized path to fluid flow 
• 
Regarding to heterogeneity of rock mass, mechanical loading can cause
opening and closure of joints. This can induce changes in rock structure
and fluid properties 
• 
If the stress state in the model changes and proportion of the joint shear
and normal stresses remains constant, increasing the normal stress cause
decreasing the joint permeability. The reason of this result can be explained
by the joint closure due to normal stress increase which results permeability
decrease 
• 
If the stress state in the model changes in a manner that joint shear
and normal stresses proportion increase but joint does not slip, then hydromechanical
behavior will be same as previous item 
• 
If stress state changing causes joint slip, then joint dilation will happen
which cause normal displacement and joint permeability increase 
• 
Joint dilation will not continue after critical shear stress, therefore
in a certain proportion of shear stress to normal stress, the permeability
value will be constant 
• 
Joint aperture changes with joint length variation and block size change,
but aperture sensitivity to these factors is much less than to mechanical
properties and stress conditions 
• 
Joint and rock mass mechanical properties are important factors on fluid
flow through rock mass. It can be explained with this reality that joint
and rock matrix stiffness are directly related to deformability of joints
and rock matrix therefore they will be effective on joint aperture and fluid
flow (Khak Payeh Consulting Engineers, 2002) 
• 
Confining pressure increasing, cause permeability reduction which can
be explained with joint closure due to confining pressure increase 
CONCLUSION
Bisotun epigraph which is located on a limestone rock mass, has been subjected to different damaging factors which water flow has been the most important one among them. Therefore, rock mass hydromechanical coupling behavior has been studied in this paper to evaluate the effects of these factors on the rock mass hydraulic and mechanical behavior. Results show that the main geometrical effect on hydraulic behavior is fracture density. Also, sensitivity investigations show that hydromechanical coupling effects is significantly related to the rock mass and joints mechanical properties. Therefore understanding of the mechanical properties of joints and rock mass and fracture densities is a key factor to better understanding of the rock mass hydromechanical behavior. Joint and rock matrix stiffness and their properties are significant factors in rock mass permeability.
Furthermore, if induced stresses cause normal stress increase then joint closure happens and permeability reduces, but if they make joint slip then permeability increases.
Regarding to the rock mass strength gradually reduction during the long time due to the mentioned factors, possibility of current fracture development and new fracture initiation and propagation will increase. Therefore finding appropriate methods such as rock pressure reduction and water flow prevention is needed to prevent development of epigraph damages.