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A simple shear strength model for interlayer shear weakness zone
Engineering Geology 147–148 (2012) 114–123
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A simple shear strength model for interlayer shear weakness zone Ding-Ping Xu a,⁎, Xia-Ting Feng a, Yu-Jun Cui b, c a b c
State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China Tongji University, Shanghai 200092, China UMR Navier/CERMES, Ecole des Ponts ParisTech, 6 et 8 av. Blaise Pascal, 77455 Marne-la-Vallée Cedex 2, France
a r t i c l e
i n f o
Article history: Received 19 April 2012 Received in revised form 17 July 2012 Accepted 24 July 2012 Available online 3 August 2012 Keywords: Interlayer soil Soil/rock interface Shear strength Combining mechanical effect
a b s t r a c t Interlayer shear weakness zone (ISWZ) is a widespread zonal weak geotechnical system with variable thickness in rock masses, representing a potential threat to the overall stability of structure constructed on or within the rock mass due to their relatively poor mechanical properties. Its shear behaviour depends on both the interlayer soil and the interlayer soil/host rock interface (soil/rock interface). In this study a dynamic approach is adopted by treating ISWZ as an unfilled joint (rock/rock interface) that is increasingly filled with interlayer soil of variable thickness. Based on the available experimental data, a simple shear strength model is developed, capable of describing both the shear behaviours of interlayer soil and soil/rock interface. Because the geometric factors (i.e., the thickness of interlayer soil and the morphology of interface) and the mechanical conditions (i.e., normal stress, uniaxial compressive strength of rock and shear strength of interlayer soil) are all taken into account, the combining mechanical effect of interlayer soil and soil/rock interface on the ISWZ is totally included in the model. This is partly confirmed by the good agreement between the model prediction and the experimental results from laboratory and field tests. Published by Elsevier B.V.
1. Introduction Interlayer shear weakness zones (ISWZs) are pre-existing soft layers in hard stratified rock masses in the area where geotectonic movement was active. When constructing in or on these rock masses, it is inevitable to face the stability problem induced by ISWZs because of their relatively poor mechanical properties. Fig. 1 shows a typical cross-section where two slightly ISWZs (No.4 and No.5) outcrop in the upper part of the high walls of underground powerhouses on the right bank of the future Baihetan hydropower station, Jinsha-river, Southwest China. The underground powerhouse is composed of a main powerhouse, a main transformer chamber, and three surge shafts. The dimensions of them are 438 m×34/31 m×86.7 m, 368 m×21 m×39.5 m, and about 49 m×100 m, respectively. The depths of the powerhouse on the left side and right side are 350 and 550 m respectively. The horizontal distances from the powerhouse to the toes of the Mountain slopes are 515 m on the left and 530 m on the right, to ensure that the powerhouse is far away from the zones with unloading induced by river erosion. The underground powerhouse is located in a rock mass of southeast tendency and monoclinal structure with a inclination of N30-55E, SE15-20. Rock masses surrounding the underground powerhouse on the left bank mainly include P2β23 (aphanitic basalt, amygdaloidal basalt and breccia lava) and P2β31 (aphanitic basalt, breccia lava with oblique basalt ⁎ Corresponding author. Tel.: +86 027 87198805; fax: +86 027 87197386. E-mail address: [email protected] (D.-P. Xu). 0013-7952/$ – see front matter. Published by Elsevier B.V. http://dx.doi.org/10.1016/j.enggeo.2012.07.016
and amygdaloidal basalt with oblique basalt) of Upper Ermei Mountain Group, Permian System. Those on the right bank are mainly P2β42 (amygdaloidal basalt and breccia lava) and P2β51 (aphanitic basalt and amygdaloidal basalt) of Upper Ermei Mountain Group, Permian System. These rock masses are generally rock mass class II according to the China National Standards GB 50218-94 (The Ministry of Water Resources of China, 1994), the strength of which is much higher than that of ISWZs with the same inclination. Through intensive site investigation and survey (ECIDI, 2006), it was found that the thickness of these interlayer soils vary from 50 to 300 mm and the soil/rock interfaces (or rock walls) are flat in most cases (see Figure 2). The grain size distribution curve shown in Fig. 3 indicates that these interlayer soils are a coarse material with a broad grain size ranging from 0.075 to 100 mm. As the shear strength of interlayer soil and soil/rock interface is expected to be much lower than the upper and lower rock stratum, shear failure could occur either in the soils or at the interface during excavation, posing stability problem to the construction. From the mechanical point of view, it means also that the ISWZ herein is composed of interlayer soil and soil/rock interfaces. Despite the importance of the ISWZ, to the authors’ knowledge, there are few models capable of appropriately predicting its shear behaviour. In this study, the shear behaviour of the ISWZ was analysed based on the existing laboratory test results (e.g., Sun et al., 1981; Guo, 1982; Xiao and Argelov, 1991; Xu et al., 2012), and a simple shear strength model accounting for the fabric effect of interlayer soil and soil/rock interface was proposed.
D.-P. Xu et al. / Engineering Geology 147–148 (2012) 114–123
115
ISWZ No.
ISWZ No.
1
ISWZ No.2
2
3 100
34
and
Fig. 1. Cross-section where two slightly ISWZ outcrop in the upper part of high walls at the future Baihetan hydropower station (1, main powerhouse; 2, main transformer chamber; 3, surge shaft). (1) P2β35: Oblique basalt, breccia lava; (2) P2β41: Columnar jointed basalt, amygdaloidal basalt, breccia lava and microcrystalline basalt; (3)P2β42: Amygdaloidal basalt, breccia lava; (4) P2β51: Aphanitic basalt and amygdaloidal basalt; (5) P2β61: Columnar jointed basalt and breccia lava (after ECIDI, 2006).
2. Conceptual model with the superposition of shear behaviour of interlayer soil and rock/rock interface It has been demonstrated by direct shear tests (e.g., Ladanyi and Archambault, 1977; Lama, 1978; Barla et al., 1987; Phien-wej et al., 1990; De Toledo and De Freitas, 1993; Papaliangas et al., 1993; Indraratna et al., 1999, 2005, 2008) that the shear strength of a filled joint is lower than that of unfilled joint. However, it has been common practice to assume that the shear strength of a filled joint is that of the filling material alone, regardless of its thickness (Oliveira et al., 2009). This assumption was also used for determining the shear strength of ISWZ. This is obviously not realistic. Indeed, Xiao and Argelov (1991) reported that there is a critical thickness hcr between 10 and 20 mm for the shear strength of some ISWZs. When the thickness of the interlayer soil h is less than hcr, reduction in the shear strength of ISWZ can be observed as h increases; when h is greater than hcr, its shear strength keeps nearly constant. In such a case, the shear behaviour of ISWZ is governed by either the shear strength of interlayer soil or that of soil/rock interface. Thereby, h is expected as a controlling factor for the shear strength of ISWZ.
10 c
Rock mass class II
As filled joint consists of soil/rock interfaces and filling material, it is commonly admitted that its shear strength is the superposition of that of soil/rock interface and filling material, as that was applied in the shear strength models elaborated by Indraratna et al. (1999, 2005, 2008, 2010). This can be seen as a static approach, and it is based on repeated tests on the joints with same profiles. However, it is difficult to be applied to ISWZ because of its variable thickness and the broad grain size distribution of interlayer soil. Common practice for ISWZs is to separately perform tests on interlayer soil and rock/rock interface (the interface between upper and lower rock walls). Therefore, a practical demand for understanding the shear behaviour of ISWZs is brought forward when the shear behaviours of interlayer soil and rock/rock interface are identified by laboratory and field testing. This practical demand can be satisfied by adopting a dynamic approach where ISWZ is treated as an unfilled joint (rock/rock interface) that is increasingly filled with interlayer soil. Its shear strength decreases with the increase of h. In other words, this decreasing process induced by the increase of interlayer soil thickness is a dynamic varying process during which the shear strength of rock/rock interface is decreasing and that of interlayer soil is increasing gradually. If the shear
Soil/rock interface (Upper rock wall)
Interlayer soil
Rock mass class II
Soil/rock interface (Lower rock wall) Fig. 2. Interlayer soil, soil/rock interface in testing tunnel No.62 with the buried depth of 550 m.
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a)
100
No.1 No.3 No.5
90 80
No.2 No.4
Finer (%)
70 60 50 40 30 20 10 0 100
10
1.0
0.1
0.01
0.001
Grain Diameter (mm)
b)
d<0.075 mm
0.075 d<0.25 mm
0.25 d<0.5 mm
d>10 mm
0.5 d<2.0 mm
2.0 d<5.0 mm 5.0 d<10 mm
Fig. 3. Grain distribution of interlayer soil at Baihetan Site: (a) grain size distribution curve, and (b) grain composition (the soil from ISWZ No.4).
behaviours of rock/rock interface and interlayer soil are known, the shear behaviour of ISWZ would be easily deduced. For rock/rock interface, its shear strength depends on the friction between the upper and lower rock walls, being controlled by the morphology and strength of rock walls. In general, rock/rock interface shows strain softening and dilatation during shearing owing to the interface asperities. For interlayer soil, its shear behaviour depends on its grain composition and stress history. According to the existing data reported by Xiao and Argelov (1991) and Xu et al. (2012), interlayer soil shows elastic perfect-plastic failure or strain softening failure without dilatation under high normal stresses during shearing. Based on the above analysis, the key role of h on the shear behaviour of ISWZ can be noted. By comparing h and hcr, a conceptual model for ISWZ on the superposition of shear behaviour of interlayer soil and rock/rock interface is derived from the dynamic approach (see Figure 4):
the behaviour of ISWZ is mainly governed by rock/rock interface and its shearing process is generally composed of three phases: firstly, most shear deformation and strength of ISWZ are undertaken by interlayer soil; then, interlayer soil yields and the asperity on rock walls may be in contact each other in some areas, leading to a higher shear strength of ISWZ; after wearing and rolling-over even squeezing among asperities, the shear process of ISWZ goes into the softening and residual deformation phase. (2) When h > hcr (see Figure 4b), upper and lower rock walls are prevented to be in contact by interlayer soil. In such a case, the mechanical effect induced by rock wall morphology disappears and the shear behaviour of ISWZ depends on interlayer soil or soil/rock interface. If the shear strength of soil/rock interface is greater than that of interlayer soil, the shear band occurs in interlayer soil, otherwise along the interface.
(1) When h ≤ hcr (see Figure 4a), upper and lower rock walls are in contact in some area and interlayer soil reduces the friction between the rock walls by the effect of a lubricant. In such a case,
As the shear behaviour of ISWZ shown in Fig. 4b is similar to that of interlayer soil or soil/rock interface, in the following, emphasis will be put on the shear behaviour of ISWZ in the case shown in Fig. 4a.
D.-P. Xu et al. / Engineering Geology 147–148 (2012) 114–123
a)
I
σn
+
=
0
0
III
σn
0 ISWZ
un
Interlayer soil
un
un
Rock/rock interface
II
τs
τs
τs
σn
0
117
0
0
us
us
us
τs
τs
σn
τs
b) σn
=
+ 0
0
0
un
Interlayer soil
un
un
Rock/rock interface
0
σn
0
0
us
us
ISWZ
us
Fig. 4. Conceptual model for ISWZ with the superposition of shear behaviour of interlayer soil and rock/rock interface: (a) the case of h ≤ hcr, and (b) the case of h > hcr.
3. An interlayer soil thickness dependent shear strength model 3.1. Theoretical background The Mohr–Coulomb criterion is the most widely used strength criterion. It assumes that material failure mode is shear failure in which failure occurs once the shear stress on a plane within the material reaches the shear strength. As the assumption is well in accordance with the failure of the material with weak parts, this criterion is widely applied to predict the shear strength of discontinuity, soil/structure and soil/ rock interfaces. The Mohr–Coulomb criterion is expressed as: τs ¼ c þ σ n tanφ
ð1Þ
where c and φ are the cohesion and friction angle, respectively. Eq. (1) indicates that the shear strength of geo-materials is composed of cohesion and frictional strength, i.e., c and φ are the characteristic parameters of Mohr–Coulomb materials. Because there are many factors influencing the cohesion and frictional strength, c and φ in Eq. (1) are the functions of them. Thus the general form of Eq. (1) is: τs ¼ cðxi Þ þ σ n tanφ xj
ð2Þ
and φfill are the cohesion and friction angle of the filled soil, respectively; i is the climbing slope angle of the rock joint; a and b are empirical constants depending on normal stress, roughness of the joint surface; k is the ratio of h/asp to (h/asp)cr. The same approach is applied in this study to elaborate the shear strength model for ISWZ. As ISWZ can be seen as unfilled joint (rock/rock interface) filled interlayer soil with various thicknesses, the shear strength can be expressed by Eqs. (4) and (5) where c and φ are function of h to represent their interlayer soil thickness dependence, being different from that in Eq. (3) where tanφ is divided into two components:when h ≤ hcr, 8τ zone −czone > ¼ tanφzone < σn c ¼ c ð h > fill Þ : zone φzone ¼ φrock ðhÞ
ð4Þ
when h > hcr, 8τ zone −cfill > ¼ tanφfill τ fill ≤τinter < σn τ zone −cinter > : ¼ tanφinter τfill > τ inter σn
ð5Þ
where xi (i = 1,2,3……) and xj (j = 1,2,3……) are the influencing factors on the cohesion and frictional strength, respectively. Following this principle, Indraratna et al. (2005) developed a shear strength model in which the overall shear strength of a filled joint is controlled by both the filled joint soil and soil/rock interface. A linear addition of two functions describing the shear strength of the two mechanisms is adopted. When h/asp b (h/asp)cr,
where czone and φzone are the cohesion and the friction angle of ISWZ, respectively; cfill and φfill are the cohesion and friction angle of interlayer soil, respectively; cinter and φinter are the cohesion and friction angle of soil/rock interface, respectively.
b p τs −cfill 2 a ¼ A þ B ¼ tanðφb þ iÞ ð1 κ Þ þ tanφfill 1 þ 1=κ σn
The test results from literatures (e.g., Ladanyi and Archambault, 1977; Lama, 1978; Phien-wej et al., 1990; De Toledo and De Freitas, 1993; Papaliangas et al., 1993; Indraratna et al., 1999, 2005, 2008) showed that the shear strength of filled joint decreases nonlinearly as h increases. Accordingly, it can be deduced that the shear strength of ISWZ varies with h as shown in Fig. 5. To make the variable more general, h is replaced by a dimensionless variable h/hcr in the figure; thus, the tendency can be described as follows: when h/hcr ≤1, the shear strength of
ð3Þ where φb is the basic friction angle of the rock joint; aap is the height of the joint wall asperity; h/asp is the filling percentage; (h/asp)cr is the critical ratio of filling percentage (h/asp)cr; τsp is the peak shear strength; cfill
3.2. Description of the weakening effect of thickness of interlayer soil
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0.6
ISWZ decreases nonlinearly with increasing h/hcr; when h/hcr > 1, the shear strength of ISWZ is that of interlayer soil. As far as the relationship between φzone and h is concerned, Xiao and Argelov (1991) used a negative exponential equation to describe it and found that the fitting correlation coefficient is greater than 0.98 (see Figure 6). Observing the test results by Sun et al. (1981), Zhao et al. (1981) and Guo (1982), this type of equation can also well fit their experimental data. In this study the negative exponential equation and linear equation are combined to depict the relationship between φzone and h/hcr. The expression is given as:
φzone ¼ φrock expð−ξh=hcr Þ φzone ¼ φfill
0bh=hcr ≤1 h=hcr > 1
ð6Þ
where φrock is the friction angle of the rock/rock interface and is the same as that proposed by Barton (1973): φrock ¼ JRC logðJCS=σ n Þ þ φb
ð7Þ
where JRC is the field-scale joint roughness coefficient; JCS is the field-scale joint compressive strength; ξ is the decrease coefficient of thickness of φrock, which is obtained by fitting the experimental data. Although the quantitative description of the relationship between czone and h was not reported in the previous studies, many existing results (e.g., Sun et al., 1981; Zhao et al., 1981 and Guo, 1982) showed that this relationship is similar to that between φzone and h. According to the data by Sun et al. (1981), the negative exponential equation can also better fit the relationship between czone and h (see Figure 7, the fitting correlation coefficient is greater than 0.92):
czone ¼ cfill ð1− expð−ζ h=hcr ÞÞ czone ¼ cfill
0bh=hcr ≤1 h=hcr > 1
ð8Þ
where ζ is the growth coefficient of thickness of czone, obtained from fitting the experimental data. The physical interpretation of Eqs. (6) and (8) can be further depicted by Fig. 8: the point of h/hcr = 1 is the threshold to separate the constant phase from the decrease phase or increase phase on the curve of shear strength parameters versus h/hcr, and when h/hcr > 1 the shear strength parameters keep constant. The important role of
0.5
p tan ϕ zone = 0.634 exp ( −0.053h )
tan
0.4 0.3 0.2
tan ϕ rzone = 0.503exp ( −0.059h )
0.1
2
4
6
8
10
12
14
22
As described previously, in the case of h ≤ hcr the upper and lower rock walls may be in contact in some area during shearing, the asperities on flat rock walls wear down and rollover each other, leading to a decreasing frictional strength as the shear displacement us increases (see Figure 9a). Because the friction angle is the unique variable representing the frictional strength of material, its evolution law repp resents that for frictional strength as shown in Fig. 9b: φzone decreases r to φzone after us is beyond the shear displacement at peak shear strength up. This decreasing phase is no-linear and is also described by the negative exponential equation. In order to measure the degree of variation of φzone with the increase of us after the peak, a dimensionless softening factor D is defined as: D¼
us −up ur −up
ð9Þ
where ur is the shear displacement at the beginning of residual shear stress-shear displacement curve.
hcr h > hcr Interlayer soil
s (MPa)
22
3.3. Description of shear softening behaviour
ISWZ zone
fill
0 0.5
20
h/hcr = 1 to determine the parameters of shear strength model is highlighted later.
Rock/rock interface
h
18
Fig. 6. Frictional coefficient of ISWZ varies with h (after Xiao and Argelov, 1991) p r (φ zone and φ zone are the peak friction angle and residual friction angle, respectively).
h=0
rock
16
h(mm)
1.0
h/hcr Fig. 5. The shear strength of ISWZ varies with h/hcr.
1.5
2.0
D.-P. Xu et al. / Engineering Geology 147–148 (2012) 114–123
a)
c zone=77.6(1-exp(-0.318 h ))
80
τ
60
r τ zone
p zone
s
czone (kPa)
100
119
40
c zone =54(1-exp(-0.517 h )) Clay (data1) Sandy clay (data2)
20
0
0 0
3
6
9
12
15
18
h (mm)
p ϕ zone
b)
Fig. 7. Cohesion of ISWZ varies with h (modified after Sun et al., 1981). r ϕ zone
Then the evolution law of φzone during shearing can be expressed as: p
φzone ¼ φzone expð−βDÞ
ð10Þ
where β is the decrease coefficient of thickness of φzone, associated with the property of interlayer soil and the morphology of rock walls. Finally, the general form of the shear strength model can be obtained by integrating from Eqs. (4) to (10):when h ≤ hcr, 8 τzone −czone > > ¼ tanφzone > > σn > > <φ zone ¼ ðφb þ JRC logðJCS=σ n ÞÞ expð−ξh=hcr Þ expð−βDÞ cfill ð1− expð−ζ h=hcr ÞÞ > > czone u¼−u > > p >D ¼ s > : ur −up
ð11Þ
when h > hcr, the general form is the same as Eq. (5). 3.4. Model calibration From Eqs. (5) and (11), it can be seen that there are 11 parameters (φb, JRC, JCS, h, hcr, D, cfill, φfill, ξ, ζ and β) to be determined. Among them, φb, JCS, h, D, cfill and φfill are measured from physical and mechanical tests; hcr is estimated according to the grain size distribution curve of interlayer soil and JRC is back-calculated according to the experimental data. The other parameters are obtained on the basis of the continuity condition of the equations at critical point. The model parameters can be calibrated based on the following procedure: – Step 1: determine φb from residual shear tests on flat, unweathered rock surfaces which are normally prepared by sawing (Barton, 1976), or estimate it based on the empirical expression suggested by Stimpson (1981): φb ¼ atan ð1:155tanα Þ
ð12Þ
where α is the critical angle of sliding of cylindrical core surfaces in contact measured by tilt testing. φb can also be taken as an empirical
0
up
ur us
Fig. 9. Shear strength of ISWZ varies with shear displacement: (a) shear softening law, and (b) friction angle varies with shear displacement.
value directly according to the existing data. For instance, Barton and Choubey (1977) suggested that φb of basalt rock wall ranges from 35 to 38° in dry conditions and from 31 to 36° in wet conditions. – Step 2: obtain JCS from the uniaxial compression test on the rock wall and the shear failure point (τs, σn) from shear test on the rock/rock interface, then back calculate JRC according to the following expression proposed by Barton and Choubey (1977): JRC ¼
arctanðτs =σ n Þ−φb logðJCS=σ n Þ
ð13Þ
– Step 3: i) conduct in-situ direct shear test on interlayer soil to obtain cfill and φfill on the typical spot where h > hcr; ii) perform a set of in-situ direct shear test on ISWZ (more than four samples) in the areas where h ≤ hcr to obtain the shear failure p r p r point (σn, τzone and τzone ), φzone and φzone ; iii) measure h of interlayer soil; iv) substitute the data into Eq. (14) rearranged from Eqs. (6) and (7) to back calculate ξ according to the continuity condition at the point of h/hcr = 1 shown in Fig. 8, JCS ξ ¼ ln φb þ JRC log =φfill σn
ð14Þ
v) substitute ξ from Eq. (14) into Eq. (6) to calculate φzone in the case of the given h, as that shown in Eq. (15): JCS φzone ¼ φrock exp −h=hcr ⋅ ln φb þ JRC log =φfill ð15Þ σn
rock
c
cfill
vi) substitute φzone from Eq. (15) into Eq. (4) to back calculate czone in the case of the given h and then substitute it into Eq. (8) to back calculate ζ, as that shown in Eq. (16):
fill
ζ ¼−
0
0.5
1.0
1.5
2.0
h/hcr Fig. 8. Shear strength parameters of ISWZ varies with h/hcr.
hcr c ln 1− zone h cfill
ð16Þ
– Step 5: repeat Step 4 more than 4 times to obtain a set of ξ and ζ, and calculate their mean values;
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p r – Step 6: substitute φzone and φzone into Eq. (10) to back calculate β when D = 1 as that shown in Eq. (17):
r p β ¼ − ln φzone =φzone
ð17Þ
When h > hcr, whether cinter and φinter are needed to be determined by performing direct shear test on soil/rock interface depends on the situation. In the case where the failure cannot occur along soil/ rock interface, these determinations are not necessary. 3.5. Estimation of the critical thickness of interlayer soil hcr is treated as a constant in the proposed model. It is related to the roughness of rock walls and the grain size of filling material. De Toledo and De Freitas (1993) pointed out that rock walls as the solid boundaries for the filling material can prevent the grain to slide or roll along filling material/rock interfaces, and the magnitude of the influence of their roughness depends on the grain size of filling material itself. From the mechanical point of view, the effect of the rock wall boundaries on filling material is similar to the scale effect of over-size grains on shear test samples as shown in Fig. 10. In order to avoid scale effect on the shear strength of sample, ASTM standard D3080-98 (2003) recommends that the maximum grain size dmax in a shear test must be no larger than 1/10 of the shear box width and 1/6 of the box height. Cerato and Lutenegger (2006) also suggested that dmax in a shear test should be less than 1/6 of the box height. Nevertheless, Fakhimi and Hosseinpour (2011) stated that the ratio of dmax to box width may be increased to 1/5. Although there has not been consensus on the value of dmax, it can be admitted that the shear box size may be determined according to the dmax of the soil tested. Accounting for the similarity of the stress environment between filled joint and shear test sample, it is logical to estimate hcr of interlayer soil according to its grain size distribution curve, as follows: d max =hcr ¼ R
ð18Þ
where R is the ratio of dmax to hcr. Table 1 lists R of filling materials between flat rock walls from the existing laboratory test results (e.g., Sun et al., 1981; Zhao et al., 1981;
a)
Overburden load
Rock wall
Push force Free face Large gravel
Filling material
b)
Counter-force
Rock wall
Guo, 1982; Wang et al., 1983; Xiao and Argelov, 1991). It can be seen that R is generally between 1/40 and 1/2. Fig. 11 shows the relationship between hcr and dmax with the data in Table 1. From the figure, a negative exponential growth trend of hcr with the increase of dmax can be observed (see fitting line) and the calculated R is 3.32 at the end point of fitting line. Thus, with more data of greater dmax and hcr, it can be expected that the variation tendency between dmax and hcr follows the trend line shown in the figure and a smaller R could be obtained. Interlayer soils at Baihetan site were compacted heavily under overburden load, leading to a high dry density between 1.86 and 2.17 Mg/m 3 and shear contraction during shearing (ECIDI, 2006), indicating that their hcr is less than that of filling materials listed in Table 1. Hence R for these interlayer soils is between 2.0 an 3.0 based on the analysis above. 4. Verification of the proposed model 4.1. Verification with laboratory test results Guo (1982) combined undulating sandstone rock walls and leaching deposition heavy clay to model ISWZ for studying the mechanical effect of the thickness of the weak intercalated layers. The filled clay has a water content (w) of 39%, a liquid limit (wL) of 37.9%, and a plastic limit (wP) of 20%. The critical thickness hcr is 4.0 mm according to the tan φ–h curve. cfill and φfill are 24 kPa and 3°, respectively. JCS of the given sandstone rock wall in wet condition is 238.3 MPa. The shear strength of interlayer soil with various h is listed in Table 2. The basic friction angle of rock wall in wet condition is selected as φb = 31° referring to the range of that suggested by Barton and Choubey (1977). The calculated JRC is equal to 6.35 according to the experimental data when h = 0. Following the steps detailed in the section of model calibration, the mean values of ξ and ζ computed based on the data provided above are respectively 2.86 and 0.67. Substituting ξ and ζ obtained into Eq. (11), the model prediction can be achieved. They are listed with the test results together in Table 3. Fig. 12 shows the comparison between laboratory test results and model prediction. A good agreement between them can be observed. 4.2. Verification with in-situ test results In order to evaluate the shear strength of ISWZ at future Baihetan hydropower station, some in-situ direct tests were performed (ECIDI, 2006). Here the test results of sample No.57 with relatively complete information (see Table 4) are used to compare to the model predictions. JCS of the given rock wall in wet condition is 65.3 MPa and JRC is 6.0 though comparing rock wall surface to standard roughness contour line. φb is 31° according to the range of basalt rock wall in wet condition suggested by Barton and Choubey (1977). According to the step and data mentioned above, the calculated mean value of ξ and ζ are 0.91 and 1.82, respectively. The model
Normal load Matrix Shear force Over-size grain
Counter force
Shear box
Counter-force Fig. 10. The stress environment of filled joint and shear test sample with over-size grains: (a) filling material with large gravels, and (b) shear sample with over-size grains.
Table 1 The ratio of dmax to hcr of filling materials between flat rock walls. Author
Year
Fillings
dmax (mm)
hcr (mm)
dmax/ hcr
Wang et al.; Xiao and Argelov
1983; 1991
Zhao et al.; Guo
1981; 1982
Clastic clay Clay Silty clay Leaching deposition clay Dissolution deposition clay Sandy clay Clayey sand
5 5 5 >0.1
20 10 20 4
1/4 1/2 1/4 >1/40
b0.1
4
b1/40
0.5 0.5
5 7
1/10 1/14
Sun et al.
1981
D.-P. Xu et al. / Engineering Geology 147–148 (2012) 114–123 Table 3 Laboratory test results and model prediction.
25 Fitting line (based on existing data)
20
hcr (mm)
121
(5, 16.6) (end point)
15
σn (kPa)
h(mm)
Trend line (with more data)
10 Test data
5
0 1.0 1.5 3.0 7.0
ξ
100
2.86
ζ
p τzone (kPa)
p' τzone (kPa)
0.67
130 56 35 20 12
130 51.7 37.7 20.2 12
p' τzone : peak shear strength predicted by the proposed model.
0 0
2
4
6
8
10
dmax (mm)
Consulting Group, 2005) can be adopted: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
Fig. 11. The variation tendency between dmax and hcr of filling materials.
prediction based on the given ξ and ζ is listed in Table 5 with the in-situ test results. Fig. 13 shows the comparison between the in-situ test results and model prediction. It can be seen that the predictions are well in accordance with the in-situ test results on the whole.
D¼
s Δκ j
¼
2 Δεp3′ 3′
2
þ Δε p1′ 3′
2
þ Δεp2′ 3′
2
ð19Þ
3
p p p where Δε3′3′ , Δε1′3′ and Δε2′3′ are equivalent plastic shear strain increment components under local coordinate.
6. Conclusions 5. Discussion The proposed model is only for ISWZ because it is established based on the experimental data from the direct shear test on ISWZ with flat soil/rock interfaces under constant normal stress. Even so, the fabric effect of interlayer soil and soil/rock interface on ISWZ is reflected comprehensively through the geometric factors (i.e., JRC and h). The mechanical conditions (i.e., σn, JCS, cfill and φfill) are also taken into account. However, for the practical convenience, advisable simplicities are adopted in the model. For instance, the negative exponent expression with less control parameters is selected to describe the relationship between the shear strength and influence factors. hcr is taken as a constant though it depends on the grain composition of interlayer soil, which varies with locations and is difficult to be determined from shear tests in most cases. Thus, when the model is applied in practice, the following suggestions may be of concern:
(1) When h > hcr, the shear behaviour of ISWZ is the same as that of interlayer soil or soil/rock interface. (2) When h ≤ hcr, the shear behaviour of ISWZ is governed by the combining mechanical effect of interlayer soil and soil/rock interface: the smaller the value of h, the more obvious the characteristic of rock/rock interface; the greater the value of h, the more obvious the characteristic of interlayer soil. Although the simple model adopts the negative exponent expression to depict h dependence of shear strength of ISWZ and treats hcr as constant, it reflects the combining mechanical effect between interlayer soil and soil/rock interface on ISWZ totally because it takes their geometric factors and mechanical conditions into account. Comparison with the laboratory and in-situ test results showed that the model can reasonably predict the shear strength of ISWZ.
150 120
τs (kPa)
(1) Because the strength mainly depends on frictional strength, the cohesion of interlayer soil should be taken into account when the overburden load is lower, but not when the overburden load is higher. (2) The parameters such as JRC, h, cfill and φfill can be treated as stochastic variables in case of large data scatter. (3) For the softening phenomenon of shear strength, D can vary according to the actual situation. When implementing it into joint element, it is suitable to adopt the expression of Eq. (9) because ur and up are easy to be determined and the displacements of key points are easy to be traced during modeling. When it is implemented into constitutive models for ISWZ, it is difficult to do that for calculating D. Thus, equivalent plastic shear strain increment on the shear failure plane Δκjs (Itasca
A dynamic approach for treating ISWZ as an unfilled joint increasingly filled interlayer soil with variable h was proposed. From this approach, a conceptual model with superposition of shear behaviours of interlayer soil and rock/rock interface was developed and a simple model derived from Mohr–Coulomb strength criterion was suggested to predict the shear strength of ISWZ based on existing shear test results. According to the conceptual model, it is easy to deduce the shear behaviour of ISWZ when the shear behaviours of interlayer soil and rock/rock interface are known. By adopting the critical thickness hcr as the threshold, the shear behaviour of ISWZ with different h was distinguished:
Table 2 The shear strength of modeling ISWZ with various h (after Guo, 1982). No.
h(mm)
hcr (mm)
σn (kPa)
p τzone (kPa)
1 2 3 4 5
0 1.0 1.5 3.0 7.0
4.0 4.0 4.0 4.0 4.0
100 100 100 100 100
130 56 35 20 12
Laboratory test results
90
Model prediction
60 30 0 0
2
4
6
8
h (mm) Fig. 12. The comparison between laboratory test results and model prediction.
122
D.-P. Xu et al. / Engineering Geology 147–148 (2012) 114–123
1.0
Table 4 In-situ test results of sample No.57 at Baihetan site (after ECIDI, 2006). cfill (MPa)
φfill (°)
σn (MPa)
p τzone (MPa)
7 8 15 15 15
0.06 0.06 0.06 0.06 0.06
17 17 17 17 17
1.51 1.20 0.60 0.90 0.61
0.92 0.71 0.28 0.36 0.25
In-situ test results 0.8
τs (Mpa)
h(cm)
( n=1.5 MPa)
Model prediction
( n=1.2 MPa)
0.6
( n=0.9 MPa)
0.4 Nomenclature a and b empirical constants in cumulative shear strength model asp asperity height on rock wall cfill cohesion of interlayer soil (filling) cinter cohesion of soil/rock interface czone cohesion of ISWZ dmax maximum grain diameter of filling D softening factor h thickness of interlayer soil (filling material) hcr critical thickness of interlayer soil (filling material) i climbing slope angle of the rock joint JRC roughness coefficient of rock wall JCS compressive strength of rock wall k ratio of filling percentage to critical filling percentage R ratio of dmax to hcr up shear displacement at peak shear strength ur shear displacement at the beginning of residual shear stress-shear displacement curve us horizontal displacement un vertical displacement w water content wL liquid limit wP plastic limit α critical angle of sliding of cylindrical core surfaces in contact measured by tilt testing β scale coefficient for describing the softening process σn normal stress τfill shear strength of interlayer soil (filling material) τinter shear strength of soil/rock interface τs shear strength τzone shear strength of ISWZ p τzone peak shear strength of ISWZ p' τzone peak shear strength predicted by the proposed model p p p Δε3′3′ , Δε1′3′ and Δε2′3′ equivalent plastic shear strain increment components under local coordinate ξ and ζ empirical coefficients of proposed shear strength model φb basic friction angle of rock/rock interface φfill friction angle of interlayer soil (filling material) φinter friction angle of soil/rock interface φrock friction angle of rock/rock interface φzone friction angle of ISWZ p φzone peak friction angle of ISWZ r φzone residual friction angle of ISWZ Δκjs equivalent plastic shear strain increment on the shear failure plane
Table 5 In-situ test results and model prediction. h(cm)
hcr (cm)
σn (MPa)
p τzone (MPa)
p' τzone (MPa)
7 8 15 15 15
20 20 20 20 20
1.51 1.20 0.60 0.90 0.61
0.92 0.71 0.28 0.36 0.25
0.89 0.69 0.29 0.40 0.29
( n=0.6 MPa)
( n=0.61 MPa)
0.2 7
8
15
15
15
h (cm) Fig. 13. The comparison between in-situ test results and model prediction.
Acknowledgements The authors gratefully acknowledge the financial support from the National Special Funds of China for Major State Basic Research Project under Grant No. 2010CB732006 and the National Natural Science Foundation of China under Grant No. 51178187. The work is also supported by the Chinese Academy of Sciences and State Administration of Foreign Experts Affairs, P.R of China, for the CAS/SAFEA International Partnership Program for Creative Research Teams under Grant No. KZCX2‐ YW‐T12. The first author also wishes to thank Dr. Jie Zhang of Tongji University for helpful discussions on the work presented.
References ASTM D 3080-98, 2003. Standard test method for direct shear test of soils under consolidated drained conditions. Annual Book of ASTM Standards. American Society For Testing and Materials, West Conshohocken, PA, pp. 347–352 (04.08). Barla, G., Forlati, F., Bertacchi, P., Zaninetti, A., 1987. Shear behaviour of natural filled joints. Proceedings of the 6th congress of the international society for rock mechanics, pp. 291–300. Barton, N., 1973. Review of a new shear strength criterion for rock joints. Engineering Geology 7 (4), 287–332. Barton, N., 1976. The shear strength of rock and rock joints. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 13 (9), 255–279. Barton, N., Choubey, V., 1977. The shear strength of rock joints in theory and practice. Rock Mechanics and Rock Engineering 10 (1–2), 1–54. Cerato, A.B., Lutenegger, A.J., 2006. Specimen size and scale effects of direct shear box tests of sands. Geotechnical Testing Journal 29 (6), 507–516. De Toledo, P.E.C., De Freitas, M.H., 1993. Laboratory testing and parameters controlling the shear strength of filled rock joints. Geotechnique 43 (1), 1–19. East China Investigation and Design Institute, 2006. Engineering geology report for dam site selection of Baihetan hydropower station at feasibility study stage. (Hangzhou, in Chinese). Fakhimi, A., Hosseinpour, H., 2011. Experimental and numerical study of the effect of an oversize particle on the shear strength of mined-rock pile material. Geotechnical Testing Journal 34 (2), 131–138. Guo, Z., 1982. The mechanical effect of the thickness of the weak intercalated layers within undulated weak structural plane. Hydrogeology & Engineering Geology 9 (1), 33–39 (in Chinese). Indraratna, B., Jayanathan, M., Brown, E.T., 2008. Shear strength model for overconsolidated clay-filled idealised rock joints. Geotechnique 58 (1), 55–65. Indraratna, B., Haque, A., Aziz, N., 1999. Shear behaviour of idealized filled joints under constant normal stiffness. Geotechnique 49 (3), 331–355. Indraratna, B., Oliveira, D.A.F., Brown, E.T., 2010. A shear-displacement criterion for soil-filled rock discontinuities. Géotechnique 60 (8), 623–633. Indraratna, B., Welideniya, H.S., Brown, E.T., 2005. A shear strength model for idealised filled joints under constant normal stiffness. Geotechnique 55 (3), 215–226. Itasca Consulting Group, 2005. FLAC3D Manual, Version 3.1. Itasca, Minneapolis. Ladanyi, B., Archambault, G., 1977. Shear strength and deformability of filled indented joints. Proceedings of the 1st international symposium on geotechnics of structurally complex formations, pp. 317–326. Lama, R.D., 1978. Influence of clay fillings on shear behaviour of joints. Proceedings of the 3rd congress on international association of engineers and geologists, 2, pp. 27–34. Oliveira, D.A.F., Indraratna, B., Nemcika, J., 2009. Critical review on shear strength models for soil-filled joints. Geomechanics and Geoengineering: An International Journal 4 (3), 237–244.
D.-P. Xu et al. / Engineering Geology 147–148 (2012) 114–123 Papaliangas, T., Hencher, S.R., Lumsden, A.C., Manolopoulou, S., 1993. The effect of frictional fill thickness on the shear strength of rock discontinuities. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 30 (2), 81–91. Phien-wej, N., Shrestha, U.B., Rantucci, G., 1990. Effect of infill thickness on shear behaviour of rock joints. In: Barton, Stephansson (Eds.), Rock jonits: Proceedings of the international conference on rock joints. Balkema, Rotterdam, pp. 289–294. Stimpson, B., 1981. A suggested technique for determining the basic friction angle of rock surfaces using core. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 18 (3), 63–65. Sun, W.H., Zhen, T.M., Li, M.Y., 1981. The mechanical effect of the thickness of the weak intercalary layers. Proceedings of international symposium on weak rock. Balkema, Rotterdam, pp. 49–54.
123
The Ministry of Water Resources of China, 1994. China National Standards GB5021894: Standard for Engineering Classification of Rock Masses. China Planning Press, Beijing. (in Chinese). Wang, X.F., Liu, W., Er, L., 1983. Fabric types and microstructure of clay partings. Journal of Jilin University (Earth Science Edition) 13 (4), 73–84 (in Chinese). Xiao, S.F., Argelov, K., 1991. Structures of inter-layer shear zones and their creeping behaviour. Jilin Science Press, Changchun. (in Chinese). Xu, D.P., Feng, X.T., Cui, Y.J., 2012. A comparative study on the shear ehaviour of an interlayer material based on laboratory and in situ shear tests. Geotechnical Testing Journal 35 (3), 375–386. Zhao, R.H., Zhou, R.G., Sun, G.Z., 1981. Engineering mechanical effect of weak structural plane. Geotechnical Investigation & Surveying (6), 56–59 (in Chinese).
Contents lists available at SciVerse ScienceDirect
Engineering Geology journal homepage: www.elsevier.com/locate/enggeo
A simple shear strength model for interlayer shear weakness zone Ding-Ping Xu a,⁎, Xia-Ting Feng a, Yu-Jun Cui b, c a b c
State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China Tongji University, Shanghai 200092, China UMR Navier/CERMES, Ecole des Ponts ParisTech, 6 et 8 av. Blaise Pascal, 77455 Marne-la-Vallée Cedex 2, France
a r t i c l e
i n f o
Article history: Received 19 April 2012 Received in revised form 17 July 2012 Accepted 24 July 2012 Available online 3 August 2012 Keywords: Interlayer soil Soil/rock interface Shear strength Combining mechanical effect
a b s t r a c t Interlayer shear weakness zone (ISWZ) is a widespread zonal weak geotechnical system with variable thickness in rock masses, representing a potential threat to the overall stability of structure constructed on or within the rock mass due to their relatively poor mechanical properties. Its shear behaviour depends on both the interlayer soil and the interlayer soil/host rock interface (soil/rock interface). In this study a dynamic approach is adopted by treating ISWZ as an unfilled joint (rock/rock interface) that is increasingly filled with interlayer soil of variable thickness. Based on the available experimental data, a simple shear strength model is developed, capable of describing both the shear behaviours of interlayer soil and soil/rock interface. Because the geometric factors (i.e., the thickness of interlayer soil and the morphology of interface) and the mechanical conditions (i.e., normal stress, uniaxial compressive strength of rock and shear strength of interlayer soil) are all taken into account, the combining mechanical effect of interlayer soil and soil/rock interface on the ISWZ is totally included in the model. This is partly confirmed by the good agreement between the model prediction and the experimental results from laboratory and field tests. Published by Elsevier B.V.
1. Introduction Interlayer shear weakness zones (ISWZs) are pre-existing soft layers in hard stratified rock masses in the area where geotectonic movement was active. When constructing in or on these rock masses, it is inevitable to face the stability problem induced by ISWZs because of their relatively poor mechanical properties. Fig. 1 shows a typical cross-section where two slightly ISWZs (No.4 and No.5) outcrop in the upper part of the high walls of underground powerhouses on the right bank of the future Baihetan hydropower station, Jinsha-river, Southwest China. The underground powerhouse is composed of a main powerhouse, a main transformer chamber, and three surge shafts. The dimensions of them are 438 m×34/31 m×86.7 m, 368 m×21 m×39.5 m, and about 49 m×100 m, respectively. The depths of the powerhouse on the left side and right side are 350 and 550 m respectively. The horizontal distances from the powerhouse to the toes of the Mountain slopes are 515 m on the left and 530 m on the right, to ensure that the powerhouse is far away from the zones with unloading induced by river erosion. The underground powerhouse is located in a rock mass of southeast tendency and monoclinal structure with a inclination of N30-55E, SE15-20. Rock masses surrounding the underground powerhouse on the left bank mainly include P2β23 (aphanitic basalt, amygdaloidal basalt and breccia lava) and P2β31 (aphanitic basalt, breccia lava with oblique basalt ⁎ Corresponding author. Tel.: +86 027 87198805; fax: +86 027 87197386. E-mail address: [email protected] (D.-P. Xu). 0013-7952/$ – see front matter. Published by Elsevier B.V. http://dx.doi.org/10.1016/j.enggeo.2012.07.016
and amygdaloidal basalt with oblique basalt) of Upper Ermei Mountain Group, Permian System. Those on the right bank are mainly P2β42 (amygdaloidal basalt and breccia lava) and P2β51 (aphanitic basalt and amygdaloidal basalt) of Upper Ermei Mountain Group, Permian System. These rock masses are generally rock mass class II according to the China National Standards GB 50218-94 (The Ministry of Water Resources of China, 1994), the strength of which is much higher than that of ISWZs with the same inclination. Through intensive site investigation and survey (ECIDI, 2006), it was found that the thickness of these interlayer soils vary from 50 to 300 mm and the soil/rock interfaces (or rock walls) are flat in most cases (see Figure 2). The grain size distribution curve shown in Fig. 3 indicates that these interlayer soils are a coarse material with a broad grain size ranging from 0.075 to 100 mm. As the shear strength of interlayer soil and soil/rock interface is expected to be much lower than the upper and lower rock stratum, shear failure could occur either in the soils or at the interface during excavation, posing stability problem to the construction. From the mechanical point of view, it means also that the ISWZ herein is composed of interlayer soil and soil/rock interfaces. Despite the importance of the ISWZ, to the authors’ knowledge, there are few models capable of appropriately predicting its shear behaviour. In this study, the shear behaviour of the ISWZ was analysed based on the existing laboratory test results (e.g., Sun et al., 1981; Guo, 1982; Xiao and Argelov, 1991; Xu et al., 2012), and a simple shear strength model accounting for the fabric effect of interlayer soil and soil/rock interface was proposed.
D.-P. Xu et al. / Engineering Geology 147–148 (2012) 114–123
115
ISWZ No.
ISWZ No.
1
ISWZ No.2
2
3 100
34
and
Fig. 1. Cross-section where two slightly ISWZ outcrop in the upper part of high walls at the future Baihetan hydropower station (1, main powerhouse; 2, main transformer chamber; 3, surge shaft). (1) P2β35: Oblique basalt, breccia lava; (2) P2β41: Columnar jointed basalt, amygdaloidal basalt, breccia lava and microcrystalline basalt; (3)P2β42: Amygdaloidal basalt, breccia lava; (4) P2β51: Aphanitic basalt and amygdaloidal basalt; (5) P2β61: Columnar jointed basalt and breccia lava (after ECIDI, 2006).
2. Conceptual model with the superposition of shear behaviour of interlayer soil and rock/rock interface It has been demonstrated by direct shear tests (e.g., Ladanyi and Archambault, 1977; Lama, 1978; Barla et al., 1987; Phien-wej et al., 1990; De Toledo and De Freitas, 1993; Papaliangas et al., 1993; Indraratna et al., 1999, 2005, 2008) that the shear strength of a filled joint is lower than that of unfilled joint. However, it has been common practice to assume that the shear strength of a filled joint is that of the filling material alone, regardless of its thickness (Oliveira et al., 2009). This assumption was also used for determining the shear strength of ISWZ. This is obviously not realistic. Indeed, Xiao and Argelov (1991) reported that there is a critical thickness hcr between 10 and 20 mm for the shear strength of some ISWZs. When the thickness of the interlayer soil h is less than hcr, reduction in the shear strength of ISWZ can be observed as h increases; when h is greater than hcr, its shear strength keeps nearly constant. In such a case, the shear behaviour of ISWZ is governed by either the shear strength of interlayer soil or that of soil/rock interface. Thereby, h is expected as a controlling factor for the shear strength of ISWZ.
10 c
Rock mass class II
As filled joint consists of soil/rock interfaces and filling material, it is commonly admitted that its shear strength is the superposition of that of soil/rock interface and filling material, as that was applied in the shear strength models elaborated by Indraratna et al. (1999, 2005, 2008, 2010). This can be seen as a static approach, and it is based on repeated tests on the joints with same profiles. However, it is difficult to be applied to ISWZ because of its variable thickness and the broad grain size distribution of interlayer soil. Common practice for ISWZs is to separately perform tests on interlayer soil and rock/rock interface (the interface between upper and lower rock walls). Therefore, a practical demand for understanding the shear behaviour of ISWZs is brought forward when the shear behaviours of interlayer soil and rock/rock interface are identified by laboratory and field testing. This practical demand can be satisfied by adopting a dynamic approach where ISWZ is treated as an unfilled joint (rock/rock interface) that is increasingly filled with interlayer soil. Its shear strength decreases with the increase of h. In other words, this decreasing process induced by the increase of interlayer soil thickness is a dynamic varying process during which the shear strength of rock/rock interface is decreasing and that of interlayer soil is increasing gradually. If the shear
Soil/rock interface (Upper rock wall)
Interlayer soil
Rock mass class II
Soil/rock interface (Lower rock wall) Fig. 2. Interlayer soil, soil/rock interface in testing tunnel No.62 with the buried depth of 550 m.
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a)
100
No.1 No.3 No.5
90 80
No.2 No.4
Finer (%)
70 60 50 40 30 20 10 0 100
10
1.0
0.1
0.01
0.001
Grain Diameter (mm)
b)
d<0.075 mm
0.075 d<0.25 mm
0.25 d<0.5 mm
d>10 mm
0.5 d<2.0 mm
2.0 d<5.0 mm 5.0 d<10 mm
Fig. 3. Grain distribution of interlayer soil at Baihetan Site: (a) grain size distribution curve, and (b) grain composition (the soil from ISWZ No.4).
behaviours of rock/rock interface and interlayer soil are known, the shear behaviour of ISWZ would be easily deduced. For rock/rock interface, its shear strength depends on the friction between the upper and lower rock walls, being controlled by the morphology and strength of rock walls. In general, rock/rock interface shows strain softening and dilatation during shearing owing to the interface asperities. For interlayer soil, its shear behaviour depends on its grain composition and stress history. According to the existing data reported by Xiao and Argelov (1991) and Xu et al. (2012), interlayer soil shows elastic perfect-plastic failure or strain softening failure without dilatation under high normal stresses during shearing. Based on the above analysis, the key role of h on the shear behaviour of ISWZ can be noted. By comparing h and hcr, a conceptual model for ISWZ on the superposition of shear behaviour of interlayer soil and rock/rock interface is derived from the dynamic approach (see Figure 4):
the behaviour of ISWZ is mainly governed by rock/rock interface and its shearing process is generally composed of three phases: firstly, most shear deformation and strength of ISWZ are undertaken by interlayer soil; then, interlayer soil yields and the asperity on rock walls may be in contact each other in some areas, leading to a higher shear strength of ISWZ; after wearing and rolling-over even squeezing among asperities, the shear process of ISWZ goes into the softening and residual deformation phase. (2) When h > hcr (see Figure 4b), upper and lower rock walls are prevented to be in contact by interlayer soil. In such a case, the mechanical effect induced by rock wall morphology disappears and the shear behaviour of ISWZ depends on interlayer soil or soil/rock interface. If the shear strength of soil/rock interface is greater than that of interlayer soil, the shear band occurs in interlayer soil, otherwise along the interface.
(1) When h ≤ hcr (see Figure 4a), upper and lower rock walls are in contact in some area and interlayer soil reduces the friction between the rock walls by the effect of a lubricant. In such a case,
As the shear behaviour of ISWZ shown in Fig. 4b is similar to that of interlayer soil or soil/rock interface, in the following, emphasis will be put on the shear behaviour of ISWZ in the case shown in Fig. 4a.
D.-P. Xu et al. / Engineering Geology 147–148 (2012) 114–123
a)
I
σn
+
=
0
0
III
σn
0 ISWZ
un
Interlayer soil
un
un
Rock/rock interface
II
τs
τs
τs
σn
0
117
0
0
us
us
us
τs
τs
σn
τs
b) σn
=
+ 0
0
0
un
Interlayer soil
un
un
Rock/rock interface
0
σn
0
0
us
us
ISWZ
us
Fig. 4. Conceptual model for ISWZ with the superposition of shear behaviour of interlayer soil and rock/rock interface: (a) the case of h ≤ hcr, and (b) the case of h > hcr.
3. An interlayer soil thickness dependent shear strength model 3.1. Theoretical background The Mohr–Coulomb criterion is the most widely used strength criterion. It assumes that material failure mode is shear failure in which failure occurs once the shear stress on a plane within the material reaches the shear strength. As the assumption is well in accordance with the failure of the material with weak parts, this criterion is widely applied to predict the shear strength of discontinuity, soil/structure and soil/ rock interfaces. The Mohr–Coulomb criterion is expressed as: τs ¼ c þ σ n tanφ
ð1Þ
where c and φ are the cohesion and friction angle, respectively. Eq. (1) indicates that the shear strength of geo-materials is composed of cohesion and frictional strength, i.e., c and φ are the characteristic parameters of Mohr–Coulomb materials. Because there are many factors influencing the cohesion and frictional strength, c and φ in Eq. (1) are the functions of them. Thus the general form of Eq. (1) is: τs ¼ cðxi Þ þ σ n tanφ xj
ð2Þ
and φfill are the cohesion and friction angle of the filled soil, respectively; i is the climbing slope angle of the rock joint; a and b are empirical constants depending on normal stress, roughness of the joint surface; k is the ratio of h/asp to (h/asp)cr. The same approach is applied in this study to elaborate the shear strength model for ISWZ. As ISWZ can be seen as unfilled joint (rock/rock interface) filled interlayer soil with various thicknesses, the shear strength can be expressed by Eqs. (4) and (5) where c and φ are function of h to represent their interlayer soil thickness dependence, being different from that in Eq. (3) where tanφ is divided into two components:when h ≤ hcr, 8τ zone −czone > ¼ tanφzone < σn c ¼ c ð h > fill Þ : zone φzone ¼ φrock ðhÞ
ð4Þ
when h > hcr, 8τ zone −cfill > ¼ tanφfill τ fill ≤τinter < σn τ zone −cinter > : ¼ tanφinter τfill > τ inter σn
ð5Þ
where xi (i = 1,2,3……) and xj (j = 1,2,3……) are the influencing factors on the cohesion and frictional strength, respectively. Following this principle, Indraratna et al. (2005) developed a shear strength model in which the overall shear strength of a filled joint is controlled by both the filled joint soil and soil/rock interface. A linear addition of two functions describing the shear strength of the two mechanisms is adopted. When h/asp b (h/asp)cr,
where czone and φzone are the cohesion and the friction angle of ISWZ, respectively; cfill and φfill are the cohesion and friction angle of interlayer soil, respectively; cinter and φinter are the cohesion and friction angle of soil/rock interface, respectively.
b p τs −cfill 2 a ¼ A þ B ¼ tanðφb þ iÞ ð1 κ Þ þ tanφfill 1 þ 1=κ σn
The test results from literatures (e.g., Ladanyi and Archambault, 1977; Lama, 1978; Phien-wej et al., 1990; De Toledo and De Freitas, 1993; Papaliangas et al., 1993; Indraratna et al., 1999, 2005, 2008) showed that the shear strength of filled joint decreases nonlinearly as h increases. Accordingly, it can be deduced that the shear strength of ISWZ varies with h as shown in Fig. 5. To make the variable more general, h is replaced by a dimensionless variable h/hcr in the figure; thus, the tendency can be described as follows: when h/hcr ≤1, the shear strength of
ð3Þ where φb is the basic friction angle of the rock joint; aap is the height of the joint wall asperity; h/asp is the filling percentage; (h/asp)cr is the critical ratio of filling percentage (h/asp)cr; τsp is the peak shear strength; cfill
3.2. Description of the weakening effect of thickness of interlayer soil
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0.6
ISWZ decreases nonlinearly with increasing h/hcr; when h/hcr > 1, the shear strength of ISWZ is that of interlayer soil. As far as the relationship between φzone and h is concerned, Xiao and Argelov (1991) used a negative exponential equation to describe it and found that the fitting correlation coefficient is greater than 0.98 (see Figure 6). Observing the test results by Sun et al. (1981), Zhao et al. (1981) and Guo (1982), this type of equation can also well fit their experimental data. In this study the negative exponential equation and linear equation are combined to depict the relationship between φzone and h/hcr. The expression is given as:
φzone ¼ φrock expð−ξh=hcr Þ φzone ¼ φfill
0bh=hcr ≤1 h=hcr > 1
ð6Þ
where φrock is the friction angle of the rock/rock interface and is the same as that proposed by Barton (1973): φrock ¼ JRC logðJCS=σ n Þ þ φb
ð7Þ
where JRC is the field-scale joint roughness coefficient; JCS is the field-scale joint compressive strength; ξ is the decrease coefficient of thickness of φrock, which is obtained by fitting the experimental data. Although the quantitative description of the relationship between czone and h was not reported in the previous studies, many existing results (e.g., Sun et al., 1981; Zhao et al., 1981 and Guo, 1982) showed that this relationship is similar to that between φzone and h. According to the data by Sun et al. (1981), the negative exponential equation can also better fit the relationship between czone and h (see Figure 7, the fitting correlation coefficient is greater than 0.92):
czone ¼ cfill ð1− expð−ζ h=hcr ÞÞ czone ¼ cfill
0bh=hcr ≤1 h=hcr > 1
ð8Þ
where ζ is the growth coefficient of thickness of czone, obtained from fitting the experimental data. The physical interpretation of Eqs. (6) and (8) can be further depicted by Fig. 8: the point of h/hcr = 1 is the threshold to separate the constant phase from the decrease phase or increase phase on the curve of shear strength parameters versus h/hcr, and when h/hcr > 1 the shear strength parameters keep constant. The important role of
0.5
p tan ϕ zone = 0.634 exp ( −0.053h )
tan
0.4 0.3 0.2
tan ϕ rzone = 0.503exp ( −0.059h )
0.1
2
4
6
8
10
12
14
22
As described previously, in the case of h ≤ hcr the upper and lower rock walls may be in contact in some area during shearing, the asperities on flat rock walls wear down and rollover each other, leading to a decreasing frictional strength as the shear displacement us increases (see Figure 9a). Because the friction angle is the unique variable representing the frictional strength of material, its evolution law repp resents that for frictional strength as shown in Fig. 9b: φzone decreases r to φzone after us is beyond the shear displacement at peak shear strength up. This decreasing phase is no-linear and is also described by the negative exponential equation. In order to measure the degree of variation of φzone with the increase of us after the peak, a dimensionless softening factor D is defined as: D¼
us −up ur −up
ð9Þ
where ur is the shear displacement at the beginning of residual shear stress-shear displacement curve.
hcr h > hcr Interlayer soil
s (MPa)
22
3.3. Description of shear softening behaviour
ISWZ zone
fill
0 0.5
20
h/hcr = 1 to determine the parameters of shear strength model is highlighted later.
Rock/rock interface
h
18
Fig. 6. Frictional coefficient of ISWZ varies with h (after Xiao and Argelov, 1991) p r (φ zone and φ zone are the peak friction angle and residual friction angle, respectively).
h=0
rock
16
h(mm)
1.0
h/hcr Fig. 5. The shear strength of ISWZ varies with h/hcr.
1.5
2.0
D.-P. Xu et al. / Engineering Geology 147–148 (2012) 114–123
a)
c zone=77.6(1-exp(-0.318 h ))
80
τ
60
r τ zone
p zone
s
czone (kPa)
100
119
40
c zone =54(1-exp(-0.517 h )) Clay (data1) Sandy clay (data2)
20
0
0 0
3
6
9
12
15
18
h (mm)
p ϕ zone
b)
Fig. 7. Cohesion of ISWZ varies with h (modified after Sun et al., 1981). r ϕ zone
Then the evolution law of φzone during shearing can be expressed as: p
φzone ¼ φzone expð−βDÞ
ð10Þ
where β is the decrease coefficient of thickness of φzone, associated with the property of interlayer soil and the morphology of rock walls. Finally, the general form of the shear strength model can be obtained by integrating from Eqs. (4) to (10):when h ≤ hcr, 8 τzone −czone > > ¼ tanφzone > > σn > > <φ zone ¼ ðφb þ JRC logðJCS=σ n ÞÞ expð−ξh=hcr Þ expð−βDÞ cfill ð1− expð−ζ h=hcr ÞÞ > > czone u¼−u > > p >D ¼ s > : ur −up
ð11Þ
when h > hcr, the general form is the same as Eq. (5). 3.4. Model calibration From Eqs. (5) and (11), it can be seen that there are 11 parameters (φb, JRC, JCS, h, hcr, D, cfill, φfill, ξ, ζ and β) to be determined. Among them, φb, JCS, h, D, cfill and φfill are measured from physical and mechanical tests; hcr is estimated according to the grain size distribution curve of interlayer soil and JRC is back-calculated according to the experimental data. The other parameters are obtained on the basis of the continuity condition of the equations at critical point. The model parameters can be calibrated based on the following procedure: – Step 1: determine φb from residual shear tests on flat, unweathered rock surfaces which are normally prepared by sawing (Barton, 1976), or estimate it based on the empirical expression suggested by Stimpson (1981): φb ¼ atan ð1:155tanα Þ
ð12Þ
where α is the critical angle of sliding of cylindrical core surfaces in contact measured by tilt testing. φb can also be taken as an empirical
0
up
ur us
Fig. 9. Shear strength of ISWZ varies with shear displacement: (a) shear softening law, and (b) friction angle varies with shear displacement.
value directly according to the existing data. For instance, Barton and Choubey (1977) suggested that φb of basalt rock wall ranges from 35 to 38° in dry conditions and from 31 to 36° in wet conditions. – Step 2: obtain JCS from the uniaxial compression test on the rock wall and the shear failure point (τs, σn) from shear test on the rock/rock interface, then back calculate JRC according to the following expression proposed by Barton and Choubey (1977): JRC ¼
arctanðτs =σ n Þ−φb logðJCS=σ n Þ
ð13Þ
– Step 3: i) conduct in-situ direct shear test on interlayer soil to obtain cfill and φfill on the typical spot where h > hcr; ii) perform a set of in-situ direct shear test on ISWZ (more than four samples) in the areas where h ≤ hcr to obtain the shear failure p r p r point (σn, τzone and τzone ), φzone and φzone ; iii) measure h of interlayer soil; iv) substitute the data into Eq. (14) rearranged from Eqs. (6) and (7) to back calculate ξ according to the continuity condition at the point of h/hcr = 1 shown in Fig. 8, JCS ξ ¼ ln φb þ JRC log =φfill σn
ð14Þ
v) substitute ξ from Eq. (14) into Eq. (6) to calculate φzone in the case of the given h, as that shown in Eq. (15): JCS φzone ¼ φrock exp −h=hcr ⋅ ln φb þ JRC log =φfill ð15Þ σn
rock
c
cfill
vi) substitute φzone from Eq. (15) into Eq. (4) to back calculate czone in the case of the given h and then substitute it into Eq. (8) to back calculate ζ, as that shown in Eq. (16):
fill
ζ ¼−
0
0.5
1.0
1.5
2.0
h/hcr Fig. 8. Shear strength parameters of ISWZ varies with h/hcr.
hcr c ln 1− zone h cfill
ð16Þ
– Step 5: repeat Step 4 more than 4 times to obtain a set of ξ and ζ, and calculate their mean values;
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D.-P. Xu et al. / Engineering Geology 147–148 (2012) 114–123
p r – Step 6: substitute φzone and φzone into Eq. (10) to back calculate β when D = 1 as that shown in Eq. (17):
r p β ¼ − ln φzone =φzone
ð17Þ
When h > hcr, whether cinter and φinter are needed to be determined by performing direct shear test on soil/rock interface depends on the situation. In the case where the failure cannot occur along soil/ rock interface, these determinations are not necessary. 3.5. Estimation of the critical thickness of interlayer soil hcr is treated as a constant in the proposed model. It is related to the roughness of rock walls and the grain size of filling material. De Toledo and De Freitas (1993) pointed out that rock walls as the solid boundaries for the filling material can prevent the grain to slide or roll along filling material/rock interfaces, and the magnitude of the influence of their roughness depends on the grain size of filling material itself. From the mechanical point of view, the effect of the rock wall boundaries on filling material is similar to the scale effect of over-size grains on shear test samples as shown in Fig. 10. In order to avoid scale effect on the shear strength of sample, ASTM standard D3080-98 (2003) recommends that the maximum grain size dmax in a shear test must be no larger than 1/10 of the shear box width and 1/6 of the box height. Cerato and Lutenegger (2006) also suggested that dmax in a shear test should be less than 1/6 of the box height. Nevertheless, Fakhimi and Hosseinpour (2011) stated that the ratio of dmax to box width may be increased to 1/5. Although there has not been consensus on the value of dmax, it can be admitted that the shear box size may be determined according to the dmax of the soil tested. Accounting for the similarity of the stress environment between filled joint and shear test sample, it is logical to estimate hcr of interlayer soil according to its grain size distribution curve, as follows: d max =hcr ¼ R
ð18Þ
where R is the ratio of dmax to hcr. Table 1 lists R of filling materials between flat rock walls from the existing laboratory test results (e.g., Sun et al., 1981; Zhao et al., 1981;
a)
Overburden load
Rock wall
Push force Free face Large gravel
Filling material
b)
Counter-force
Rock wall
Guo, 1982; Wang et al., 1983; Xiao and Argelov, 1991). It can be seen that R is generally between 1/40 and 1/2. Fig. 11 shows the relationship between hcr and dmax with the data in Table 1. From the figure, a negative exponential growth trend of hcr with the increase of dmax can be observed (see fitting line) and the calculated R is 3.32 at the end point of fitting line. Thus, with more data of greater dmax and hcr, it can be expected that the variation tendency between dmax and hcr follows the trend line shown in the figure and a smaller R could be obtained. Interlayer soils at Baihetan site were compacted heavily under overburden load, leading to a high dry density between 1.86 and 2.17 Mg/m 3 and shear contraction during shearing (ECIDI, 2006), indicating that their hcr is less than that of filling materials listed in Table 1. Hence R for these interlayer soils is between 2.0 an 3.0 based on the analysis above. 4. Verification of the proposed model 4.1. Verification with laboratory test results Guo (1982) combined undulating sandstone rock walls and leaching deposition heavy clay to model ISWZ for studying the mechanical effect of the thickness of the weak intercalated layers. The filled clay has a water content (w) of 39%, a liquid limit (wL) of 37.9%, and a plastic limit (wP) of 20%. The critical thickness hcr is 4.0 mm according to the tan φ–h curve. cfill and φfill are 24 kPa and 3°, respectively. JCS of the given sandstone rock wall in wet condition is 238.3 MPa. The shear strength of interlayer soil with various h is listed in Table 2. The basic friction angle of rock wall in wet condition is selected as φb = 31° referring to the range of that suggested by Barton and Choubey (1977). The calculated JRC is equal to 6.35 according to the experimental data when h = 0. Following the steps detailed in the section of model calibration, the mean values of ξ and ζ computed based on the data provided above are respectively 2.86 and 0.67. Substituting ξ and ζ obtained into Eq. (11), the model prediction can be achieved. They are listed with the test results together in Table 3. Fig. 12 shows the comparison between laboratory test results and model prediction. A good agreement between them can be observed. 4.2. Verification with in-situ test results In order to evaluate the shear strength of ISWZ at future Baihetan hydropower station, some in-situ direct tests were performed (ECIDI, 2006). Here the test results of sample No.57 with relatively complete information (see Table 4) are used to compare to the model predictions. JCS of the given rock wall in wet condition is 65.3 MPa and JRC is 6.0 though comparing rock wall surface to standard roughness contour line. φb is 31° according to the range of basalt rock wall in wet condition suggested by Barton and Choubey (1977). According to the step and data mentioned above, the calculated mean value of ξ and ζ are 0.91 and 1.82, respectively. The model
Normal load Matrix Shear force Over-size grain
Counter force
Shear box
Counter-force Fig. 10. The stress environment of filled joint and shear test sample with over-size grains: (a) filling material with large gravels, and (b) shear sample with over-size grains.
Table 1 The ratio of dmax to hcr of filling materials between flat rock walls. Author
Year
Fillings
dmax (mm)
hcr (mm)
dmax/ hcr
Wang et al.; Xiao and Argelov
1983; 1991
Zhao et al.; Guo
1981; 1982
Clastic clay Clay Silty clay Leaching deposition clay Dissolution deposition clay Sandy clay Clayey sand
5 5 5 >0.1
20 10 20 4
1/4 1/2 1/4 >1/40
b0.1
4
b1/40
0.5 0.5
5 7
1/10 1/14
Sun et al.
1981
D.-P. Xu et al. / Engineering Geology 147–148 (2012) 114–123 Table 3 Laboratory test results and model prediction.
25 Fitting line (based on existing data)
20
hcr (mm)
121
(5, 16.6) (end point)
15
σn (kPa)
h(mm)
Trend line (with more data)
10 Test data
5
0 1.0 1.5 3.0 7.0
ξ
100
2.86
ζ
p τzone (kPa)
p' τzone (kPa)
0.67
130 56 35 20 12
130 51.7 37.7 20.2 12
p' τzone : peak shear strength predicted by the proposed model.
0 0
2
4
6
8
10
dmax (mm)
Consulting Group, 2005) can be adopted: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
Fig. 11. The variation tendency between dmax and hcr of filling materials.
prediction based on the given ξ and ζ is listed in Table 5 with the in-situ test results. Fig. 13 shows the comparison between the in-situ test results and model prediction. It can be seen that the predictions are well in accordance with the in-situ test results on the whole.
D¼
s Δκ j
¼
2 Δεp3′ 3′
2
þ Δε p1′ 3′
2
þ Δεp2′ 3′
2
ð19Þ
3
p p p where Δε3′3′ , Δε1′3′ and Δε2′3′ are equivalent plastic shear strain increment components under local coordinate.
6. Conclusions 5. Discussion The proposed model is only for ISWZ because it is established based on the experimental data from the direct shear test on ISWZ with flat soil/rock interfaces under constant normal stress. Even so, the fabric effect of interlayer soil and soil/rock interface on ISWZ is reflected comprehensively through the geometric factors (i.e., JRC and h). The mechanical conditions (i.e., σn, JCS, cfill and φfill) are also taken into account. However, for the practical convenience, advisable simplicities are adopted in the model. For instance, the negative exponent expression with less control parameters is selected to describe the relationship between the shear strength and influence factors. hcr is taken as a constant though it depends on the grain composition of interlayer soil, which varies with locations and is difficult to be determined from shear tests in most cases. Thus, when the model is applied in practice, the following suggestions may be of concern:
(1) When h > hcr, the shear behaviour of ISWZ is the same as that of interlayer soil or soil/rock interface. (2) When h ≤ hcr, the shear behaviour of ISWZ is governed by the combining mechanical effect of interlayer soil and soil/rock interface: the smaller the value of h, the more obvious the characteristic of rock/rock interface; the greater the value of h, the more obvious the characteristic of interlayer soil. Although the simple model adopts the negative exponent expression to depict h dependence of shear strength of ISWZ and treats hcr as constant, it reflects the combining mechanical effect between interlayer soil and soil/rock interface on ISWZ totally because it takes their geometric factors and mechanical conditions into account. Comparison with the laboratory and in-situ test results showed that the model can reasonably predict the shear strength of ISWZ.
150 120
τs (kPa)
(1) Because the strength mainly depends on frictional strength, the cohesion of interlayer soil should be taken into account when the overburden load is lower, but not when the overburden load is higher. (2) The parameters such as JRC, h, cfill and φfill can be treated as stochastic variables in case of large data scatter. (3) For the softening phenomenon of shear strength, D can vary according to the actual situation. When implementing it into joint element, it is suitable to adopt the expression of Eq. (9) because ur and up are easy to be determined and the displacements of key points are easy to be traced during modeling. When it is implemented into constitutive models for ISWZ, it is difficult to do that for calculating D. Thus, equivalent plastic shear strain increment on the shear failure plane Δκjs (Itasca
A dynamic approach for treating ISWZ as an unfilled joint increasingly filled interlayer soil with variable h was proposed. From this approach, a conceptual model with superposition of shear behaviours of interlayer soil and rock/rock interface was developed and a simple model derived from Mohr–Coulomb strength criterion was suggested to predict the shear strength of ISWZ based on existing shear test results. According to the conceptual model, it is easy to deduce the shear behaviour of ISWZ when the shear behaviours of interlayer soil and rock/rock interface are known. By adopting the critical thickness hcr as the threshold, the shear behaviour of ISWZ with different h was distinguished:
Table 2 The shear strength of modeling ISWZ with various h (after Guo, 1982). No.
h(mm)
hcr (mm)
σn (kPa)
p τzone (kPa)
1 2 3 4 5
0 1.0 1.5 3.0 7.0
4.0 4.0 4.0 4.0 4.0
100 100 100 100 100
130 56 35 20 12
Laboratory test results
90
Model prediction
60 30 0 0
2
4
6
8
h (mm) Fig. 12. The comparison between laboratory test results and model prediction.
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D.-P. Xu et al. / Engineering Geology 147–148 (2012) 114–123
1.0
Table 4 In-situ test results of sample No.57 at Baihetan site (after ECIDI, 2006). cfill (MPa)
φfill (°)
σn (MPa)
p τzone (MPa)
7 8 15 15 15
0.06 0.06 0.06 0.06 0.06
17 17 17 17 17
1.51 1.20 0.60 0.90 0.61
0.92 0.71 0.28 0.36 0.25
In-situ test results 0.8
τs (Mpa)
h(cm)
( n=1.5 MPa)
Model prediction
( n=1.2 MPa)
0.6
( n=0.9 MPa)
0.4 Nomenclature a and b empirical constants in cumulative shear strength model asp asperity height on rock wall cfill cohesion of interlayer soil (filling) cinter cohesion of soil/rock interface czone cohesion of ISWZ dmax maximum grain diameter of filling D softening factor h thickness of interlayer soil (filling material) hcr critical thickness of interlayer soil (filling material) i climbing slope angle of the rock joint JRC roughness coefficient of rock wall JCS compressive strength of rock wall k ratio of filling percentage to critical filling percentage R ratio of dmax to hcr up shear displacement at peak shear strength ur shear displacement at the beginning of residual shear stress-shear displacement curve us horizontal displacement un vertical displacement w water content wL liquid limit wP plastic limit α critical angle of sliding of cylindrical core surfaces in contact measured by tilt testing β scale coefficient for describing the softening process σn normal stress τfill shear strength of interlayer soil (filling material) τinter shear strength of soil/rock interface τs shear strength τzone shear strength of ISWZ p τzone peak shear strength of ISWZ p' τzone peak shear strength predicted by the proposed model p p p Δε3′3′ , Δε1′3′ and Δε2′3′ equivalent plastic shear strain increment components under local coordinate ξ and ζ empirical coefficients of proposed shear strength model φb basic friction angle of rock/rock interface φfill friction angle of interlayer soil (filling material) φinter friction angle of soil/rock interface φrock friction angle of rock/rock interface φzone friction angle of ISWZ p φzone peak friction angle of ISWZ r φzone residual friction angle of ISWZ Δκjs equivalent plastic shear strain increment on the shear failure plane
Table 5 In-situ test results and model prediction. h(cm)
hcr (cm)
σn (MPa)
p τzone (MPa)
p' τzone (MPa)
7 8 15 15 15
20 20 20 20 20
1.51 1.20 0.60 0.90 0.61
0.92 0.71 0.28 0.36 0.25
0.89 0.69 0.29 0.40 0.29
( n=0.6 MPa)
( n=0.61 MPa)
0.2 7
8
15
15
15
h (cm) Fig. 13. The comparison between in-situ test results and model prediction.
Acknowledgements The authors gratefully acknowledge the financial support from the National Special Funds of China for Major State Basic Research Project under Grant No. 2010CB732006 and the National Natural Science Foundation of China under Grant No. 51178187. The work is also supported by the Chinese Academy of Sciences and State Administration of Foreign Experts Affairs, P.R of China, for the CAS/SAFEA International Partnership Program for Creative Research Teams under Grant No. KZCX2‐ YW‐T12. The first author also wishes to thank Dr. Jie Zhang of Tongji University for helpful discussions on the work presented.
References ASTM D 3080-98, 2003. Standard test method for direct shear test of soils under consolidated drained conditions. Annual Book of ASTM Standards. American Society For Testing and Materials, West Conshohocken, PA, pp. 347–352 (04.08). Barla, G., Forlati, F., Bertacchi, P., Zaninetti, A., 1987. Shear behaviour of natural filled joints. Proceedings of the 6th congress of the international society for rock mechanics, pp. 291–300. Barton, N., 1973. Review of a new shear strength criterion for rock joints. Engineering Geology 7 (4), 287–332. Barton, N., 1976. The shear strength of rock and rock joints. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 13 (9), 255–279. Barton, N., Choubey, V., 1977. The shear strength of rock joints in theory and practice. Rock Mechanics and Rock Engineering 10 (1–2), 1–54. Cerato, A.B., Lutenegger, A.J., 2006. Specimen size and scale effects of direct shear box tests of sands. Geotechnical Testing Journal 29 (6), 507–516. De Toledo, P.E.C., De Freitas, M.H., 1993. Laboratory testing and parameters controlling the shear strength of filled rock joints. Geotechnique 43 (1), 1–19. East China Investigation and Design Institute, 2006. Engineering geology report for dam site selection of Baihetan hydropower station at feasibility study stage. (Hangzhou, in Chinese). Fakhimi, A., Hosseinpour, H., 2011. Experimental and numerical study of the effect of an oversize particle on the shear strength of mined-rock pile material. Geotechnical Testing Journal 34 (2), 131–138. Guo, Z., 1982. The mechanical effect of the thickness of the weak intercalated layers within undulated weak structural plane. Hydrogeology & Engineering Geology 9 (1), 33–39 (in Chinese). Indraratna, B., Jayanathan, M., Brown, E.T., 2008. Shear strength model for overconsolidated clay-filled idealised rock joints. Geotechnique 58 (1), 55–65. Indraratna, B., Haque, A., Aziz, N., 1999. Shear behaviour of idealized filled joints under constant normal stiffness. Geotechnique 49 (3), 331–355. Indraratna, B., Oliveira, D.A.F., Brown, E.T., 2010. A shear-displacement criterion for soil-filled rock discontinuities. Géotechnique 60 (8), 623–633. Indraratna, B., Welideniya, H.S., Brown, E.T., 2005. A shear strength model for idealised filled joints under constant normal stiffness. Geotechnique 55 (3), 215–226. Itasca Consulting Group, 2005. FLAC3D Manual, Version 3.1. Itasca, Minneapolis. Ladanyi, B., Archambault, G., 1977. Shear strength and deformability of filled indented joints. Proceedings of the 1st international symposium on geotechnics of structurally complex formations, pp. 317–326. Lama, R.D., 1978. Influence of clay fillings on shear behaviour of joints. Proceedings of the 3rd congress on international association of engineers and geologists, 2, pp. 27–34. Oliveira, D.A.F., Indraratna, B., Nemcika, J., 2009. Critical review on shear strength models for soil-filled joints. Geomechanics and Geoengineering: An International Journal 4 (3), 237–244.
D.-P. Xu et al. / Engineering Geology 147–148 (2012) 114–123 Papaliangas, T., Hencher, S.R., Lumsden, A.C., Manolopoulou, S., 1993. The effect of frictional fill thickness on the shear strength of rock discontinuities. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 30 (2), 81–91. Phien-wej, N., Shrestha, U.B., Rantucci, G., 1990. Effect of infill thickness on shear behaviour of rock joints. In: Barton, Stephansson (Eds.), Rock jonits: Proceedings of the international conference on rock joints. Balkema, Rotterdam, pp. 289–294. Stimpson, B., 1981. A suggested technique for determining the basic friction angle of rock surfaces using core. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 18 (3), 63–65. Sun, W.H., Zhen, T.M., Li, M.Y., 1981. The mechanical effect of the thickness of the weak intercalary layers. Proceedings of international symposium on weak rock. Balkema, Rotterdam, pp. 49–54.
123
The Ministry of Water Resources of China, 1994. China National Standards GB5021894: Standard for Engineering Classification of Rock Masses. China Planning Press, Beijing. (in Chinese). Wang, X.F., Liu, W., Er, L., 1983. Fabric types and microstructure of clay partings. Journal of Jilin University (Earth Science Edition) 13 (4), 73–84 (in Chinese). Xiao, S.F., Argelov, K., 1991. Structures of inter-layer shear zones and their creeping behaviour. Jilin Science Press, Changchun. (in Chinese). Xu, D.P., Feng, X.T., Cui, Y.J., 2012. A comparative study on the shear ehaviour of an interlayer material based on laboratory and in situ shear tests. Geotechnical Testing Journal 35 (3), 375–386. Zhao, R.H., Zhou, R.G., Sun, G.Z., 1981. Engineering mechanical effect of weak structural plane. Geotechnical Investigation & Surveying (6), 56–59 (in Chinese).