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**Graduate school of Science and Technology, Nagasaki University**

ESTIMATING THE INFLUENCE OF SURFACE CHARACTERISTICS OF ROCK JOINTS ON SHEAR BEHAVIOR Y.Tasaku, Y.Jiang, Y.Tanahashi, B.Li My presentation is estimating the influence of surface characteristics of rock joints on shear behavior. Graduate school of Science and Technology, Nagasaki University

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**Introduction The development of deep underground**

space has received high attention The deformation behavior and stability of underground structures depend principally on the shear strength of discontinuities in rock masses. The shear strength is generally dominated by surface characteristics of rock joints. Direct shear test Measurement and evaluation of joint surface In recent years, the development of deep underground space has received high attention. And the deformation behavior and stability of underground structures depend principally on the shear strength of discontinuities in rock masses. Moreover, the shear strength is generally dominated by surface characteristics of rock joints, but the relationship has not been clarified. So, in this study, the dependency of mechanical behavior on boundary conditions and the relationship between the mechanical behavior and the surface characteristics are evaluated. ・ The dependency of mechanical behavior on boundary conditions. ・ The relationship between the mechanical behavior and the surface characteristics are evaluated.

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**Constant normal load condition**

Free σn＝Constant τ Constant normal load (CNL) condition Rock slope (non- reinforcement) The CNL condition is constant normal load condition. So, the CNL condition is fit for considering the field of non reinforcement such as rock slope.

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**Constant normal stiffness (CNS) condition**

σn≠Constant Joint τ Constant normal stiffness (CNS) condition Deep underground In deep underground, joint is constrain from rock masses. And the normal stress is change by shear. So, the shear test under CNS condition was carried out. Constraint from rock masses Change of normal stress

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** Digital-controlled shear test apparatus **

Vertical Jack Specimen Horizontal Jack In this study, a high performance Digital-controlled shear test apparatus was used. In this shear test apparatus, the specimen was set between lower box and upper box and rock joint is sheared by removing the lower box horizontally. Both normal and shear forces are applied by hydraulic cylinders through a hydraulic pump which is servo-controlled. Three digital load cells for measuring shear and normal loads are set with rods connected at two sides of the shear box. The loading capacity is 400kN in both the normal and shear direction.

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**Structure of surface measurement system**

Laser displacement meter This is the structure of surface measurement system, which is a three-dimensional laser scanning profilimeter. It composed of X-Y positioning table, laser displacement meter and computer for control and record. X-Y positioning table Computer for control and record

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**Specimen Natural surfaces ・Dimension (mm) 200×100×100**

・Mix ratio(weight ratio) plaster：water：retardant =1：0.2：0.005 In this study, specimen with natural surface like this picture was used. It is possible to analyze the substantial fractal dimension.The dimension of all specimens are 200mm in length, 100mm in width, and 100mm in height and are made of mixture of plaster, water and retardant with weight ratio of 1: 0.2: The unconfined compressive strength of specimen is 32MPa. It correspond middle hard rock. ・Unconfined compressive strength σn0=32.0MPa (middle hard rock) Possible to analyze the substantial fractal dimension

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**Test cases J2 J１ J3 (Large asperity in the center and smooth surface)**

(Many small asperities) These figures are the surfaces of test specimens. J1 has a large asperity in the center and smooth surface. J2 have many small asperities. J3 is the specimen of previous study with very smooth surface. J1 and J2 were used for direct shear test, and J3 was only used for evaluation of surface characteristics. J3 (Specimen of previous study with very smooth surface)

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**Each of J1 and J2 has 9 cases; 18 cases at all**

Test cases ・Control condition Constant normal load (CNL) condition and constant normal stiffness (CNS) condition ・Initial normal stress σn0: 1MPa, 2MPa (50～100ｍ), 5MPa (about 250ｍ) ・Normal stiffness: kn J1 is 1GPa/m and 7GPa/m J2 is 1GPa/m and 3GPa/m, Control conditions are constant normal load condition and constant normal stiffness condition, and the initial normal stresses are 1MPa, 2MPa and 5MPa. The normal stiffness of J1 are 1GPa/m and 7GPa/m, and J2 are 1GPa/m and 3GPa/m. 9 cases of shear tests were carried for each J1 and J2. The total test cases are eighteen cases. Each of J1 and J2 has 9 cases; 18 cases at all

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**Result of shear test (J1,σn0=2MPa)**

CNL condition CNS condition(kn=3GPa/m) CNS condition(kn=7GPa/m) This figure shows the result of shear test of J1 under initial stress of 2MPa. The left figure shows shear displacement versus shear stress, and the right figure shows shear displacement versus normal displacement. For all test, the largest shear stress occurs in very small shear displacement. In the CNS condition, the shear stress is close to that of CNL condition. The larger the normal stiffness is, the more normal strain would be strengthened and the residual strength will be lager.

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**Surface of specimen before and after shear (J1,σn0=2MPa)**

(mm) Before shear These figures show the surface of specimens before and after shear. The top figure is the surface before shear and left side is surface after shear on CNL condition, and right side is on CNS condition. Before shear, a large asperity could be found in the center of specimen. After shear on CNL condition, these larger asperities of all cases suffered damage, and the greater the normal stiffness is, the larger damaged area and depth happen. After shear on CNS condition ( kn=3GPa/m) After shear on CNL condition

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**Evaluation method of surface roughness by projective covering method**

Projective covering cell Fracture surface The fractal dimension of the surface of specimen was evaluated by the projective covering method. In this method, the fracture surface is divided into a large number of small squares by a selected scale. And the fractal dimension is calculated by substituting the total area to the apparent area as shown in such equation. AT(δ): Total area AT0(δ): Apparent area (2＜Ds＜3) δ : length of a mesh

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**Transition of fractal dimension**

CNL J2 CNS(kn=1GPa/m） CNS（kn=3GPa/m） Before shearing This figure is the transition of fractal dimension on J2. All cases, the fractal dimension have increased after shear compared with before shear. And the larger maximum normal stress causes larger fractal dimension. Moreover, the higher the normal stiffness is, the smaller fractal dimension increase.

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**Statistical parameter of two dimensions**

Z2 is the average slope of asperity N: Total number of measuring points along the profiles yi： ith value of height ⊿x：Minute distance to direction x Z2 which is the average slope of asperity given by under equation was also evaluated for the joint surfaces.

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**Transition of Z2 J2 CNL Before shearing CNS(kn=3GPa/m） CNS（kn=7GPa/m）**

This is the transition of Z2. The smaller maximum normal stress is, the smaller Z2 becomes. Because Z2 is evaluated only at the direction of shearing, it exhibits the smoothing process of joint surface at the direction of shearing.

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**Actual rock joint is three dimensional**

Maximum shear stress Maximum shear stress: (Barton、1977) τ：Maximum shear stress σn0：Initial normal stress JRC： Joint roughness coefficient JCS：Joint wall compressive strength φb：Inter friction of joint Two dimensional indicator Actual rock joint is three dimensional Suggestion equation The theoretical shear stress was calculated by Barton’s empirical equation, and compared the them with experimental shear stresses. JRC is joint roughness coefficient which is a two dimensional indicator. However, actual rock joint is three dimension. So I suggested under equation. ‘a’ and ‘b’ are obtained from the relationship between JRC and Ds on experience. ‘a’ and ‘b’ are obtained from the relationship between JRC and Ds on experience.

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**Comparison of the Barton’s empirical equation with proposed equation**

Base line σn0(MPa) 1 2 5 J1 J2 J3 Proposed equation σn0(MPa) 1 2 5 J1 J2 J3 This figure shows the result of the comparison of the theoretical shear stresses with experimental shear stresses. Upper legend is Barton’s empirical equation, and the under one is the proposed equation. The base line expresses that the theoretical value is equal to experimental value. The prediction values by using both kinds of methods agree well with the experiment ones. The validity of proposed equation is proved by these results. Proposed equation

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**Conclusion Influence Constraint from rock blocks**

Surface characteristics of joint The relation of Initial normal stress and surface roughness（about CNL） Shear behavior of rock joint As a result, the constraint from around rock blocks, surface characteristics of joint and the relation of initial normal stress and surface roughness affect the shear behavior of rock joint.Then, the validity of using 3-D fractal dimension to predict shear stress is confirmed. It is possible to predict the shear behavior by Ds. Proposed equation Confirmation of validity It is possible to predict the shear behavior by Ds

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END

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自然の岩石を供試体として用いる 圧裂試験 Dsを用いて、せん断特性を正確に予測 表面のケースの充実

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**Dsとピークせん断応力との関係 破線：理論値 表面2（Ds=2.0279) 表面1（Ds=2.0235） 表面3（Ds=2.008）**

次に、Bartonの式に基づいて、JRC値の代わりにフラクタル次元を用いたところ、表面1を除いてほぼ等しいという結果が得られました。フラクタル次元はこのようになっており、フラクタル次元が高いほどより高いピークせん断応力が生じる結果となりました。 表面3（Ds=2.008）

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JRC値とZ2 JRC値は以下の式(Tse、1979）

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**せん断応力の比較(σno=2MPa) 表面1 表面2 表面1 表面2 CNL制御 CNS制御(kn=3GPa/m)**

表面1と表面2のせん断応力のグラフを比較しました。左が表面1で右が表面2です。表面2は表面1ど同様にせん断初期にピークが見られ、最終的に残留強度に差が生じています。せん断応力の傾向はについて、表面1はせん断が進行するにつれ、せん断応力が増加していますが、表面2では、減少または一定であるという結果が得られました。これは、表面1の凹凸が大きく、乗り越しが大きいためであると考えられます。

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