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Centrifuge modeling of reverse fault rupture propagation through single-layered and stratified soil
Engineering Geology 249 (2019) 273–289
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Centrifuge modeling of reverse fault rupture propagation through singlelayered and stratified soil
T
Naser Talia, Gholam Reza Lashkaripoura, , Naser Hafezi Moghadasa, Abbas Ghalandarzadehb ⁎
a b
Department of Geology, Faculty of Science, Ferdowsi University of Mashhad, Mashhad, Iran School of Civil Engineering, College of Engineering, University of Tehran, Tehran, Iran
ARTICLE INFO
ABSTRACT
Keywords: Fault rupture propagation Centrifuge modeling Surface rupture zone Reverse faulting
Many buildings have been built over active faults. Surface faulting as a main effect of earthquakes can cause damage such buildings. Properties of material over bedrock affect the pattern of rupture propagation through deposits and the width of the rupture zone on ground surface. Several researchers have primarily studied fault rupture propagation patterns on single-layered granular soil; however, natural geologic deposits are rarely homogeneous and uniform, but mostly consist of different layers. In this study, centrifuge model tests were conducted to investigate the patterns of reverse fault rupture propagation through single and double-layered soil stratum. It was observed that the soil type and sequence of layers affected the fault rupture propagation pattern as well as the surface rupture zone. The results show that the width of deformation zone tends to decrease in stiffer soil in compare to softer soil. These findings may help to produce a framework for predicting the occurrence and geometry of surface fault rupture zone that, can help us to define a setback zone, which is a major concern in building codes.
1. Introduction Before the 1999 earthquakes in Taiwan (Chi-Chi) and Turkey (Kocaeli and Duzce), no serious attention was paid to the soil-structurefault rupture interaction. However, because of the significant width of deformation and fault rupture zones in these three earthquakes and the extensive damages to structures and public utilities induced by faulting, they have become a turning point in the study of surface fault rupture hazard. In the Chi-Chi earthquake, at least 30% of the damages to buildings were caused by surface fault rupture (Yang and Beeson, 2001). It is obvious that the pattern of rupture propagation through alluvial deposit overlying bedrock fault must be investigated (Duffy et al., 2014). After the 1999 earthquakes, many researchers have studied the surface fault rupture hazard through (i) field observations (Faccioli et al., 2008; Lavine et al., 2003; Lin et al., 2012, 2003; Ma and Chiao, 2004; Qin et al., 2015; Wang et al., 2013), (ii) experimental modeling (Chang et al., 2015; Lin et al., 2007, 2005; Loli et al., 2011; Peng et al., 2013), (iii) numerical analysis (Anastasopoulos et al., 2008; Anastasopoulos and Gazetas, 2010; Dong et al., 2003; Hazeghian and Soroush, 2017; Loukidis et al., 2009; Oettle and Bray, 2013; Taniyama, 2011) and (iv) analytical approaches (Bray, 2001).
Previous researches concluded that the width of surface faulting depends on geological, tectonic and geotechnical parameters, which include but are not limited to the type, thickness, stiffness and strength of the surface layers and the focal mechanism of the main fault rupture. In addition, the performance of faulting in rocky outcrops differs from the case in which an alluvium layer is located on bedrock. In this regard, it is essential to determine the extent of the surface fault rupture zone and predict the region in which no construction should be allowed as an aspect of building codes and construction regulations. Increases in the price of urban land and a shortage of land for construction make optimal determination of this zone of special importance. Therefore, for effective usage of land, it is suggested that complementary studies (field investigation or laboratory model testing) be performed. 2. Previous physical model studies 2.1. Physical modeling under earth gravity conditions Many researchers have conducted experimental studies under earth gravity conditions (1 g) to understand failure mechanism of surface fault rupture. Cole and Lade (1984) undertook a series of comprehensive model test on cohesionless sand involving reverse and normal
Corresponding author. E-mail addresses: [email protected] (N. Tali), [email protected] (G.R. Lashkaripour), [email protected] (N. Hafezi Moghadas), [email protected] (A. Ghalandarzadeh). ⁎
https://doi.org/10.1016/j.enggeo.2018.12.021 Received 31 October 2017; Received in revised form 15 December 2018; Accepted 21 December 2018 Available online 02 January 2019 0013-7952/ © 2019 Elsevier B.V. All rights reserved.
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Fig. 1. Newly designed and manufactured split box: (a) longitudinal section of box model; (b) displacement mechanism of movable part; (c) overall view of box model and (d) manufactured split box.
faulting at different angles to determine the surface fault rupture location and the affected zone width on an alluvium deposit over a dipslip fault. They found that a maximum vertical displacement of approximately 4% of the total thickness of the soil was required for complete development of a failure surface. Larger vertical movements were required to develop failure surfaces in more compressible and looser sand. Lade et al. (1984) attempted to simulate multiple failure surfaces in sandy soil in a fault test box. Their results showed that the angle of dilation was the dominant soil property affecting the location of the failure surfaces and that the displacement fields were the same for different materials. Bray et al. (1993) showed that the thickness of the shear zone in the saturated clay layer overlying a bedrock fault was related to the magnitude of base movement and the failure strain of the soil. The range of the dip angle of the bedrock with respect to the horizontal plane was selected to vary between 60° and 90° for both normal and reverse faults. Taniyama and Watanabe (2001) found that shear failure propagates through sandy soil and breaks the ground surface when the vertical component of the bedrock fault slip reaches 3% to 5% of the thickness (ΔH/H) for 30 and 50 m deep alluvium. They reported that a vertical
slip of about 7% of the depth of the alluvium was needed for shear failure to propagate through 75-m deep alluvium. Lee and Hamada (2005) investigated the pattern of rupture propagation through sandy soil with particular concern for dip-slip faulting. Their 1 g model tests showed that the location of the surface fault rupture varied according to the model thickness due to the strongly dilatant behavior of the sand under low confinement. Johansson and Konagai (2007) performed experimental tests on both dry and wet cohesionless soil. They showed that the amount of uplift required for surface rupture is larger for wet soil. In general, the shear zone was wider for wet soil, especially for reverse faulting, where the incompressibility of the pore water prevents horizontal compression, resulting in increased shear strain. 2.2. Physical modeling under accelerated gravity conditions Some researchers have conducted experimental studies under accelerated gravity conditions (Ng) to understand failure phenomena. Roth et al. (1981) showed that the soil properties are significant factors in the formation of a failure pattern. Their tests were performed under Ng conditions for reverse faulting. Lee and Hamada (2005) showed that there was no significant variation in the location of surface fault rupture
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Max. horizontal displacement (mm)
24 Diameter of actuator shaft (mm) 50 42 Stroke of actuator (mm) 150
314 Min. static actuator force (kN) 85
when the thickness of the soil layer changed. Anastasopoulos et al. (2007) investigated the location of fault outcropping and found that vertical displacement profile of the ground surface and a minimal fault offset at bedrock were necessary for the rupture to reach the ground surface. Their analysis showed that dip-slip faults refract at the soil rock interface, initially increasing in dip angle. The dip angle may continue to increase in normal faults as they approach the ground surface. In contrast, reverse faults tend to decrease in dip angle as they emerge at the ground surface. For small values of base fault offset (ΔH) relative to soil thickness (H), a rupture cannot propagate all the way to the surface. The ΔH/H ratio required for outcropping is a function of soil ductility. Reverse faults require a significantly higher ΔH/H to outcrop than do normal faults. Cai et al. (2013, 2010) conducted two centrifuge tests to investigate the effects of rigid and flexible boundary conditions on normal fault propagation. They showed that, in the rigid boundary condition, a smaller differential settlement resulted on the ground surface in compare with the bedrock fault movement. On the other hand, for the flexible boundary condition the differential settlement on the ground surface was larger than the bedrock fault movement. Ng et al. (2012) provided experimental evidence and numerical explanations of the failure mechanisms of soil induced by normal faulting under three ground conditions (uncemented clay, cemented clay with and without a preexisting fracture). As stated above, most previous studies were conducted on homogeneous and uniform soil layers; however, in nature, soil is usually heterogenic and stratified. In this study, a series of centrifuge model tests were conducted on sandy and clayey-sandy soil to understand better soil behavior during fault rupture propagation towards the ground surface. These tests were performed on single and/or doublelayered soils and at a centrifugal acceleration of 60 g. In addition, the reverse fault rupture had a dip angle of 60° (at bedrock level). 3. Testing procedure The tests were performed at the centrifuge facility using Actidyn Systems C67-2 equipment. The device comprises a beam with a 7 m diameter that can accelerate a model package of up to 1.5 ton at 100 g of centrifugal acceleration (i.e. 150-g-t).
Peak acceleration (g)
60 Fixed part Footwall Reverse and normal Movable part Hanging wall
932*508*400 Dip angle of fault (°) 60
3.1. Split box
Type of faulting
Table 1 Specifications of split box.
Dimensions (L*W*H) (mm)
Max. vertical displacement (mm)
Weight of box (kg)
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A split box was designed and manufactured for this study to simulate reverse and normal faulting. It was composed with a fixed and movable part designed to simulate footwall and hanging wall, respectively. This type of split box is commonly used to simulate fault rupture propagation through soil layers in a centrifuge (Ashtiani et al., 2016; Bransby et al., 2008b, 2008a; Kiani et al., 2016a, 2016b; Lee and Hamada, 2005; Moradi et al., 2013; Ng et al., 2012; Rojhani et al., 2012). Fig. 1(a) shows the longitudinal section of the box and its 85 kN hydraulic actuator. Fig. 1(b) shows the displacement mechanism of the movable part that is pushed or pulled by the hydraulic actuator. The main parts of the box were made of high-resistance steel with a transparent sidewall made of a 30-mm thick Plexiglas plate that facilitated observation of rupture propagation during the tests. Fig. 1(c) shows an overall view of the split box. Fig. 1(d) shows the completed split box with hydraulic connections. This box can simulate both reverse and normal faulting at a dip angle of 60° with respect to the horizontal. It can be adjusted for dip angles of 15° to 80° by changing four parts. The maximum allowable vertical offset of the movable hanging wall is 42 mm (2.52 m at 60 g centrifugal acceleration). In compliance with the capacity of the centrifuge and design of the split box, the tests were conducted at a centrifugal acceleration of 60 g. Furthermore, the large dimensions of an actual prototype made it unfeasible to conduct a test on such a specimen in a centrifuge. It was necessary to scale down the dimensions of the specimen to fit into the centrifuge. Dimension analysis and scaling law require that, if the 275
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Fig. 2. Grain size distribution curves of Firoozkuh sand No. 161 and clayey-sand.
Fig. 3. Stress-strain curve of soils under different confining pressure: (a) Firoozkuh sand No. 161 and (b) Clayey-sand.
length is scaled down N times, the acceleration should be scaled up N times; thus, using the dimensions of the split box and the model, 60 g was calculated and adopted. Thus, “N” is the scaling factor. The maximum slip rate of the simulator was 30 mm/s. Table 1 presents the specifications of the different parts of the box.
friction angles were 35° and 33°, respectively, and the dilation angle was 5° for the stress at shallow depth of sandy soil layer (Ashtiani et al., 2016). To understand better the behavior of natural soil, the Firoozkuh sand was mixed with kaolinite to obtain cohesive soil. The mixture consisted of one portion of kaolinite and three portions of Firoozkuh sand by weight. The grain size distribution curve of the mixed soil is presented in Fig. 2. A series of direct shear tests were conducted on mixed soil having a relative density (Dr) of 140% and a moisture content of 10% (corresponding to a unit weight -wet- of 21.1 kN/m3). The peak and residual internal friction angles, angle of dilation and cohesion were measured to be φP = 25°, φres = 23°, ψP = 0° and C = 28 kPa, respectively. Additionally, in order to precisely identify the soil mechanical parameters, a series of triaxial tests (cd type) were conducted in this research. The confinement pressures were 50, 100 and 300 kPa, respectively. Fig. 3 illustrates the stress-strain curve for two selected soil
3.2. Soil properties Two different soil types were used in centrifuge model tests: clean sand (Firoozkuh sand No. 161) and mixed sand (clayey-sand). The Firoozkuh sand No. 161 with a relative density of Dr = 70% is uniformly-graded fine clean sand with a mean grain size (D50) of 0.3 mm, maximum void ratio (emax) of 0.943 and a minimum void ratio (emin) of 0.548. Its grain size distribution curve is shown in Fig. 2 (Farahmand et al., 2016). Direct shear tests were conducted on samples with a relative density of 70% and a moisture content of 5% (corresponding to a unit weight -wet- of 16.77 kN/m3). The peak and residual internal
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200 180
E0 Sand
160
E50 Sand
E(MPa)
140
Er Sand
120 100 80 60 40 20
a
0 0
5
10
15
20
√σ3(kPa) 200 E0 Clayey-sand
180
E50 Clayey-sand
160
Er Clayey-sand
E(MPa)
140 120 100 80 60 40 20 0
b
0
2
4
6
8
10
12
14
16
18
20
√σ3(kPa) Fig. 4. Comparison of different elasticity modulus (E0, E50 and Er) for the adopted soils in this research.
Fig. 5. (a) Colored sand layer for visual detection of shear planes; (b) spray-painted exposed surface that allows visual detection of shear and tension planes.
types under the specified confining pressure. It's concluded from the curves, that the sand is stiffer and has larger strength (higher yield point) than the clayey-sand. Furthermore, in order to compare the soils, the different elasticity modulus (E0, E50 and Er) are presented in Fig. 4. The results indicate that the stiffness of the sand is higher than the clayey-sand.
improve homogeneity, the surface of each layer was scratched before the next layer was laid (Cai et al., 2013, 2010). The layers were compacted using a calibrated steel hammer with a flat rectangular tamping face and a 1450 g sliding weight with a free fall of 25 cm (Ashtiani et al., 2016). After compaction of the two layers, a colored sand layer (navy-blue inked sand) was placed in close proximity to the Plexiglas side to facilitate visual detection of the shear planes during test procedure (Fig. 5(a)) and the subsequent digital image analysis (Bransby et al., 2008a, 2008b). After compaction of each layer, silicon oil was applied to both sides of the split box to reduce the frictional resistance between the soil and the sidewalls. The total thickness of the soil layers was
3.3. Model preparation As explained, clean sand and clayey-sand were used in the models. The moist tamping method was selected to produce homogeneous specimens. Soil layers of 15 mm in thickness were compacted. To
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Fig. 6. Layout of instrumental devices for centrifuge model of reverse faulting: (a) top view; (b) side view. Table 2 Lists of centrifuge model tests. Test No.
RV-01-S to 05-S
RV-06-S
RV-09-CS
RV-10-S/CS
RV-11-CS/S
Faulting type Soil type Dip angle of fault(°) Centrifugal acceleration (g) Model dimensions (L*W*H) (mm) Max. vertical displacement (mm)
Reverse Sand 60 60 932*508*300 42
Reverse Sand 60 60 932*508*300 42
Reverse Clayey-sand 60 60 932*508*300 42
Reverse Clayey-sand below sand layer 60 60 932*508*300 42
Reverse Clayey-sand above sand layer 60 60 932*508*300 42
30 cm. A grid of orthogonal blue lines was then spray-painted onto the exposed surface of the specimen to allow the visual detection of the shear and tension planes after testing (Fig. 5(b)). All models were initially prepared outside the centrifuge chamber and then transferred on a swinging platform into the centrifuge.
3.4. Model instrumentation The instrumentation layout for all four tests is shown in Fig. 6. Five linearly variable differential transformers (LVDTs), a digital camera and three digital video recorders were used during the tests. Four LVDTs were used to measure displacement on the model surface and another 278
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Fig. 7. Schematic diagrams of soil models for tests: (a) RV-06-S; (b) RV-09-CS; (c) RV-10-S/CS; (d) RV-11-CS/S.
3.5. Centrifuge test procedure After model preparation, the split box was transferred to the centrifuge. The instrumentation of the model was installed and the connections were fixed. The hydraulic inlet and outlet connections were joined to the centrifuge connections and the control panel was programmed to reach the desired centrifugal acceleration. After the model was subjected to centrifugal acceleration of 60 g in-flight, bedrock fault movement was applied. To improve the quality of the photos, the camera was programmed to capture one photo every 3 s. Accordingly, the average rate of fault movement was chosen to be approximately 1.4 mm/s (corresponding to 0.083 m/s at prototype scale) despite the higher capacity of the split box. The results were interpreted using the measured data accompanied by the photos and post-test observations. In these tests, the faulting velocity was not scaled. The experiment used a pseudo-static loading scheme and the dynamic effect of faulting was ignored. The soil in the current models was granular and was not saturated; thus, the shearing rate effect could have had a minor influence on the results. Kabir et al. (2010) reported that the compressive response of fine sand is not sensitive to the strain rate under loading conditions, but is significantly dependent on the moisture content, initial density and lateral confinement.
Fig. 8. Schematic illustration of the reverse faulting model and corresponding definitions.
was used to measure the bedrock fault movement. The digital camera was mounted in front of the Plexiglas side to photograph model deformation. One of the digital video recorders was used to monitor model surface deformation and the other two were employed to record bedrock fault movement. A data acquisition system automatically recorded these measurements.
3.6. Test cases Although 14 tests were conducted on reverse and normal faulting systems, only the results of nine reverse faulting tests are presented. The test conditions are summarized in Table 2. Five initial tests were done
Fig. 9. Measures for reducing sidewall friction: (a) double polyurethane sheets with silicon oil; (b) polyurethane sheet with silicon oil; (c) silicon oil alone. 279
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Fig. 10. Vertical displacement of ground surface and bedrock at prototype scale in tests: (a) RV-06-S; (b) RV-09-CS; (c) RV-10-S/CS; (d) RV-11-CS/S.
resistance (Fig. 9). Tests RV-06-S, RV-09-CS, RV-10-S/CS and RV-11CS/S were conducted using polyurethane sheets along with silicon oilcovered surfaces, which were determined to be the best solution (Fig. 9(b)).
to calibrate and improve the boundary conditions. Another four tests were performed to evaluate the soil type and stratified soil behavior during reverse fault rupture propagation through the soil. Test RV-06-S was performed in sandy soil. Test RV-09-CS was performed in clayeysand and tests RV-10-S/CS and RV-11-CS/S were performed in stratified soil. Fig. 7 shows the geometries of the models in tests RV-06-S, RV-09CS, RV-10-S/CS and RV-11-CS/S. Fig. 8 shows the 3D diagram of reverse faulting that describe the geometry and parameters used. In this figure, “flexure” denotes the width of the main ground surface distortion zone and “scarp” denotes the vertical offset between the initial ground surface and the distortion zone. : (ΔH) vertical movement of bedrock; (H) soil layer thickness; (d) induced vertical movement in soil layers; (1) bedrock; (2) stationary block (footwall); (3) moving block (hanging wall); (4) faulting plane; (5) straight extension of bedrock fault plane; (6) vertical projection of fault trace; (7) tension cracks; (8) faulting dip angle; (A) width of tension zone between vertical projection of fault trace in bedrock and boundary of fault deformation; (B) zone between fault trace outcrop and straight extension of bedrock fault place; (S) theoretical deformation zone between straight extension and vertical projection of fault to ground; (W) width of deformation zone.
4.1. Vertical ground surface displacement in flexure zone and footwall area One of the important factors that should be measured during the tests is the vertical ground surface displacement (Bransby et al., 2008b; Cai et al., 2010). Fig. 10 shows the vertical displacement of the ground surface and bedrock during the simulation of reverse faulting in tests RV-06-S, RV-09-CS, RV-10-S/CS and RV-11-CS/S. The moment that the reverse faulting was initiated was set as the origin of the time axis. It was found that vertical displacement of bedrock of 42 mm (equivalent to 2.52 m at prototype scale) occurred within an average of 30 s and resulted in a velocity of reverse faulting of approximately 1.4 mm/s (0.084 m/s at prototype scale). Consequently, the model surface at the hanging wall displaced 39, 33, 35 and 38 mm in tests RV-06-S, RV-09CS, RV-10-S/CS, and RV-11-CS/S, respectively (LVDT 1; Fig. 6). No obvious vertical displacement was observed at the ground surface on the footwall (LVDTs 3 and 4; Fig. 6) (Ahmed and Bransby, 2010; Cai et al., 2010; Lin et al., 2006).
4. Results of centrifuge tests
4.2. Appearance of faulting fractures on ground surface
The nature of the boundary conditions is an important factor that must be considered in physical modeling (Anastasopoulos et al., 2007; Cai et al., 2010; Stone and Wood, 1992). Therefore, five initial tests were conducted to improve the boundary conditions of the models. The sidewalls of a model could create undesirable friction that could affect the test results; thus, different solutions were examined for reducing friction. Polyurethane sheets, double polyurethane sheets and silicon oil were used on both sides of the split box to reduce the frictional
The required bedrock displacement for appearance of the rupture on ground surface is an important factor during faulting. A threshold earthquake magnitude of 5 to 5.5 (Richter scale) is required for the appearance of shear failure at the ground surface (Bonilla, 1988). The ratio ΔH/H is often used to assess the effect of soil thickness in surface faulting hazards. Lee and Hamada (2005) showed that this value varies from 5.77% to 10.1% of the soil thickness, depending on soil density.
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Fig. 11. Bedrock vertical displacement required the fault to outcrop and dip angle of fault rupture traces as they emerge on ground surface: (a) RV-06-S; (b) RV-09CS; (c) RV-10-S/CS; (d) RV-11-CS/S (Not to scale).
Propagation of shear failure through the soil models is shown in Fig. 11. In each test, the non-stationary half of the frame moved up and into the soil mass (reverse faulting) until the primary failure surface developed through the entire height of the soil. For the 30 cm soil thickness (18 m at prototype scale) in the four models with reverse faulting, a complete slip surface generally developed after 1.59 to 2.04 cm (95.4 cm to 122.04 cm at prototype scale) of vertical displacement of the bedrock. Thus, a maximum vertical displacement of approximately 6.8% of the total soil thickness was required for complete development
of a failure surface (Fig. 12). Comparing Fig. 11 a, b, c and d, it can be seen that the normalized vertical displacement required for the fault to outcrop (ΔH/H) increased with an increase in the percentage of clay content. These results agree with those of previous researchers (Ahmadi et al., 2018). 4.3. Angle of fault plane through soil layers Anastasopoulos et al. (2007) showed that the dip-slips of faults 281
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the fault dip angle at the surface. Furthermore, Fig. 13(c) and (d) indicate that in two-layered models, the change in material properties result refraction of dip angle of fault ruptures. According to Fig. 13, it can be concluded that when the fault rupture passes a stiffer soil layer (sand) to a softer soil (clayey-sand), the propagation dip angle will decrease. For instance, in Fig. 13(c) the propagation angle in the clayey–sand is 62°, however, after entering the sand layer, the dip angle increases to 67°. Similarly, by changing the layers' order, in Fig. 13(d), the propagation dip angle changes and decreases when the rupture passes a stiffer layer (sand) to a softer layer (clayey-sand), and it should be noted that the changes in the inclination is not obvious and large (refer to Fig. 4) as the differences in the stiffness is small. The relation between the rupture angle and the elasticity modulus is illustrated in Fig. 14. In the aforementioned Figure, the elasticity modulus of each layer is normalized with the amount of its below layer. In addition, the rupture angle in each layer is normalized with the amount of its below layer. The mentioned values compared to the normalized 45-Φ/2/60 and 45 + Φ/2/60 lines (respect to the fault rupture angle on the bedrock). As it could be concluded from Fig. 14, the curves of the rupture propagation in single-layered models are located on sides of the graph and the doubled-layer models are located between the two extreme (single-layered) curves. This has been observed in previous works (Cole and Lade, 1984) that the start of the fault rupture is assumed as an active condition, the slope of the rupture is complying with the 45 + Φ/ 2 and the emerged rupture on surface is complying with passive condition. Anastasopoulos et al. (2007) indicated that the initiation of the fault rupture is with an increase in dip angle and this increase alleviate along the soil depth and comply with the 45-Φ/2 on the surface. These findings are in accordance with those of Lee and Hamada (2005), who showed that fault rupture is mainly affected by the dip angle of the
Fig. 12. Propagation of shear failure in soil models related to bedrock displacement. The definitions of H, ΔH and h are indicated in the inset.
refract at the soil rock interface, initially increasing in dip, particularly in soil with a low angle of dilation. The dips of normal faults may continue to increase as they approach the ground surface. In contrast, reverse faults tend to decrease in dip as they emerge at the ground surface. Fig. 13 shows the surface angles of the fault planes and the refraction angles of the fault plane in boundary of two soil layers (Fig. 13c and d). In accordance to the previous studies, the results indicate that the rupture dip angle at the ground surface is decreased and it is smaller than the fault dip angle at the bedrock. As depicted in Fig. 13(a) and (b), the changing of soil type resulted in differences in
Fig. 13. Dip angle of fault rupture traces as they propagate through soil layers: (a) RV-06-S; (b) RV-09-CS; (c) RV-10-S/CS; (d) RV-11-CS/S.
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Fig. 14. The relations between the rupture dip angle and the elasticity modulus in different soil types (αi = dip angle of each three cm soil thickness rupture; α = dip angle of bedrock fault and Ei = elasticity modulus of each three cm soil thickness.
bedrock fault and the ductility of the soil rather than by model thickness. This was confirmed by Mortazavi Zanjani and Soroush (2014).
ground surface was recorded. The ratio of ground surface uplift to bedrock fault movement (d/h) was about 91%, 92%, 93% and 94% in tests RV-06-S, RV-11-CS/S, RV-10-S/CS and RV-09-CS, respectively. The decrease in ground surface uplift from bedrock uplift was accounted for and defined as the dissipated displacement ratio (DDR), in order to understand better the difference between the test results. A higher DDR value denotes decreased ground surface uplift so increased the dissipation of the ground surface displacement. Fig. 16 presents bedrock dislocation in relation to the ground surface as the DDR for different tests. The sand layer produced the highest DDR value and the clayey-sand deposit produced the lowest value. Fig. 16 shows that topsoil with 0.5 to 0.75 m of bedrock movement had the largest DDR.
4.4. Trishear model of deformation The shear deformation induced by reverse faulting could be explained by “Trishear model” that has been proposed and developed by Allmendinger, 1998; Cardozo, 2005; Cardozo et al., 2003; Champion et al., 2001; Erslev, 1991; Hardy and Ford, 1997; Jin and Groshong, 2006; Zehnder and Allmendinger, 2000). In the trishear model, a single fault in bedrock expands outward into a triangular zone of distributed shear zone. According to Allmendinger et al. (2004), the present fault rupture propagation could be classified as reactivation a preexisting fault or generating a new one. Fig. 15 illustrated the fault displacement and trishear formation. As reported by Lin et al. (2006); Ahmed and Bransby (2010) and Lee et al. (2000) a bifurcation of the fault zone into two branches can be observed in sand models (tests RV-06-S and RV-10S/CS), and it is going to form in two other models as shown in Fig. 15 (b) and (d). This phenomenon has been observed with progressive fault uplift after emergence of fault fracture at surface, developed and reported in previous works (Bray, 2001; Cole and Lade, 1984; Lin et al., 2006) (denoted as numbers 1 and 2 in Fig. 15 (a), (b), (c) and (d)). When the fault tip propagation continued, the slip trace divided into two branches. The resulting of this mechanism is that the fault rupture zone formed a stepped shape and the sand models show a steeper slope than did the clayey-sand models. Therefore, this phenomenon resulted in a wider fault rupture zone in the clayey-sand model. This indicates that the sandy deposit without cohesive particles created a steeper scarp, which generated a narrower deformation of the fault rupture zone, and the clayey-sand created a gentler slope with wider deformation of the fault rupture zone. These differences can have a strong effect on the level of damages to buildings.
4.6. Development of deformation area The width of a surface rupture must be considered when determining a safe distance from the rupture for construction sites (Zhang et al., 2013). Estimation of this zone is very important for the seismic safety of buildings near an active fault. To do this during testing, photographs were taken of the surface of the models before and after each test (Fig. 17). The progression of the fault rupture zone on the footwall is shown in Fig. 18. In this figure, line 5 shows the position of the straight extension of the fault plane and line 6 shows the vertical projection of the fault plane. The zone between lines 5 and 6 is the theoretical fault rupture zone. Fig. 18 reveals that the real deformation area is wider than the theoretical zone. During the initial stage of fault rupture propagation in the sand model, a fracture formed a large dip angle. As faulting continued, the fracture formed two branches, of which the second had a smaller dip angle. This created a deformation area with a stepped form and resulted in a limited fault rupture zone. The clayey-sand and the stratified model with clayey-sand on top show a gentle slope flexure. This indicates that the type of soil in the layer on top of the bedrock defines the width of the fault rupture zone and the upper layer defines its exposed shape. In Fig. 17, the ground surface has been divided into three parts by orthogonal grid lines showing deformation. The diameters of some squares are fixed, of some are stretched and of others have decreased. These cases indicate the no change, tension and compression stress conditions, respectively. The tension and compression areas are shown in Fig. 17. The areas outside of the fault rupture zone (W) experienced no change. The zone located between the vertical projection of the fault
4.5. Ground surface uplift Previous earthquake experience has shown that thick sediment layers can prevent fault rupture from reaching the ground surface. An increase in bedrock vertical displacement will increase the probability of the appearance of a fault trace at the ground surface. In fact, ground surface uplift is a hanging wall translation for which the displacement ratio depends on the physical and mechanical properties of the soil. During testing, the displacement of the bedrock in relation to the
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Fig. 15. Trishear model of deformation and generation of a bifurcation of the fault zone in different models (a) RV-06-S; (b) RV-09-CS; (c) RV-10-S/CS; (d) RV-11-CS/ S.
trace and the border of the extension area on the hanging wall side is denoted as A, and the zone between the straight projection of the fault trace and fault rupture line is denoted as B. Finally, zone S is located between the straight extension and vertical projection of the fault to the ground surface that forms theoretical fault rupture zone. The compression and tension zones across W were different in all tests (Fig. 18) such that W-CS > W-S/CS > W-CS/S > W-S in which W-CS, W-S/CS, W-CS/S and W-S are the width of the fault rupture zones in RV-09-CS, RV-10-S/CS, RV-11-CS/S and RV-06-S tests, respectively. It appears that the clay content of the soil affected W. Table 3
summarizes the values for S, A, B, W and W/H. Fig. 19 illustrated the development of ground surface deformation zone related to vertical displacement of bedrock. According to this Figure, the clayey-sand has the widest deformation zone and sand layer has the narrowest one. The Stratified models have an average reaction. The deformation zones on both sides of the fault are asymmetric and the proportion between the hanging wall side and the footwall side ranges from 4.3:1 to 2.5:1. This indicates that the avoidance zone is not simply half of the deformation zone. The above mentioned results agree with those of previous researchers (Lee et al., 2000). 284
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phenomena and they are relatively inexpensive. Therefore, the results of current study may offer some insight into the fault rupture problem. Specially, the width of deformation zone is a key parameter in determination of avoidance zone, which is very well measurable in model tests. As shown in Table 4 the values of avoidance zone proposed by New Zealand building code and the abovementioned studies are larger than those observed in tests RV-06-S; RV-09-CS; RV-10-S/CS and RV-11-CS/ S. The thickness and type of sediment layer and dip angle of bedrock fault are not reported by building codes and field studies and they do not take into account these parameters for measuring and calculating avoidance zone. That could be the reason for differences between values of Table 4. Fig. 20 (b to e) illustrates the results of avoidance zone according to the test results (RV-06-S; RV-09-CS; RV-10-S/CS and RV-11-CS/S) compare to the proposed avoidance zone in New Zealand building code (Fig. 20 a). It seems that a further studies and observation are necessary for better understanding of this issue. Therefore, for effective usage of land, it is suggested that complementary studies (field investigation or laboratory model testing) could be performed.
18
Dissipated displacement ratio (%)
RV-06-S 16
RV-09-CS RV-11-CS/S
14
RV-10-S/CS 12 10 8 6 4 2 0 0.0
0.5
1.0
1.5
2.0
2.5
Vertical bedrock displacement (m) Fig. 16. Ground surface uplift dissipation in soil models at prototype scale.
4.7. Comparison of findings and building codes Some building codes and construction regulations state that an avoidance zone should be determined around an active fault (Kerr et al., 2003). A common misconception regarding setbacks is that they should always be 15 m from both side of the active fault trace. According to studies on 1999 Chi-Chi earthquake hanging wall deformation and its effect to buildings and structures conducted by Lee et al. (2000), they proposed a setback zone about 15 m wide on both side of the fault trace for common buildings. Moreover, field studies of Lin et al. (2003) showed that the deformation fault zone of the Chelungpu fault varied between 10 and 65 m. Furthermore the research results of Kelson et al. (2001) indicated that, the deformation width of an individual scarp is about 10 to 20 times the net vertical displacement. The field observations and measurements of Zhang et al. (2013) were used to calculate the width of deformation zone as 41.72 m. Accurate determination of avoidance zone requires observation of real fault ruptures (previous earthquakes) or conducting model tests. Centrifuge model tests provide more or less similar conditions to real
5. Conclusions In this research, a series of centrifuge model tests were conducted to study the effects of soil type and stratification on fault rupture propagation and development of a fault rupture zone caused by reverse faulting. The following findings were determined in relation to model parameters such as fault dip angle, soil type and soil thickness. These observations are obviously limited to the test conditions and may not be applicable for different types of soil, sequences of stratification, thickness of deposits, fault dip angles and mechanisms.
• Vertical movement of the ground surface in the rupture zone in the sand (stiffer soil) model was larger than for the clayey-sand model. • The rupture zone showed a gentler slope in the clayey-sand model, while the sand model (stiffer soil) showed a stepped slope. • The curves of the rupture propagation in single-layered models are located on sides of the graph and the doubled-layer models are
Fig. 17. Top view of ground surface deformation induced by reverse fault movement. 285
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Fig. 18. Development of fault rupture zone induced by reverse fault movement in different models. Table 3 Values of S, A, B, and W in test models for fault throw ΔH = 2.4 m. Test No.
Soil type
S (m)
A (m)
B (m)
W (m)
W/H
RV-06-S RV-09-CS RV-10-S/CS RV-11-CS/S
Sand Clayey-sand Sand/Clayey-sand Clayey-sand/Sand
10.4 10.4 10.4 10.4
2.9 9.0 4.6 4.2
4.0 5.8 6.1 3.4
17.3 25.2 21.1 18.0
0.96 1.40 1.17 1.00
located between the two extreme (single-layered) curves.
• The sand layer had the highest dissipated displacement ratio of bedrock displacement and clayey-sand had the lowest DDR. • The highest DDR occurred during the initial movement of the bedrock (0.5–0.75 m). • Vertical displacement of 5.3% to 6.8% of the total thickness of the • • •
soil was required for complete development of a failure surface. The minimum required displacement occurred in test RV-10-S/CS and the maximum in the clayey-sand model (RV-09-CS). The failure surface approached the ground surface at a smaller dip angle than the fault dip angle at bedrock. This decrease was more pronounced when the soil layer was clayey-sand. The model with a sand layer demonstrated the smallest decrease. Clayey-sand had the widest fault rupture zone, followed by the stratified S/CS, CS/S, and sand models. The width of the fault rupture zones could be affected by soil type, thickness and stratification in addition to the other parameters, which were investigated in the previous researches. The measured widths under the conditions of the present study ranged from 17.3
Fig. 19. Development of deformation zone induced by reverse fault movement in different models. The definitions of H, ΔH, and W are indicated in the inset.
to 25.2 m at prototype scale. The setback zones in the California and New Zealand building codes are proposed regardless of soil type, thickness and fault dip angle and usually are based on the vulnerability of structures. Under the conditions of the current tests, the measured widths of the rupture zones were smaller than the minimum setback zone values in the above-mentioned codes.
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Table 4 Comparison of width of Avoidance zone values in different studies. Code or study
New Zealand building code
Lee et al. (2000)
Lin et al. (2003)
Kelson et al. (2001)
Zhang et al. (2013)
RV-06-S
RV-09CS
RV-10-S/ CS
RV-11-CS/ S
Avoidance zone (m)
40
30
10–65
25–50
41.72
17.3
25.2
21.1
18
Fig. 20. Proposed avoidance zone according to results of different tests (Fig. 20 b to e) compare to the New Zealand building code (Fig. 20 a) (adapted from Kerr et al., 2003).
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Acknowledgments
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Centrifuge modeling of reverse fault rupture propagation through singlelayered and stratified soil
T
Naser Talia, Gholam Reza Lashkaripoura, , Naser Hafezi Moghadasa, Abbas Ghalandarzadehb ⁎
a b
Department of Geology, Faculty of Science, Ferdowsi University of Mashhad, Mashhad, Iran School of Civil Engineering, College of Engineering, University of Tehran, Tehran, Iran
ARTICLE INFO
ABSTRACT
Keywords: Fault rupture propagation Centrifuge modeling Surface rupture zone Reverse faulting
Many buildings have been built over active faults. Surface faulting as a main effect of earthquakes can cause damage such buildings. Properties of material over bedrock affect the pattern of rupture propagation through deposits and the width of the rupture zone on ground surface. Several researchers have primarily studied fault rupture propagation patterns on single-layered granular soil; however, natural geologic deposits are rarely homogeneous and uniform, but mostly consist of different layers. In this study, centrifuge model tests were conducted to investigate the patterns of reverse fault rupture propagation through single and double-layered soil stratum. It was observed that the soil type and sequence of layers affected the fault rupture propagation pattern as well as the surface rupture zone. The results show that the width of deformation zone tends to decrease in stiffer soil in compare to softer soil. These findings may help to produce a framework for predicting the occurrence and geometry of surface fault rupture zone that, can help us to define a setback zone, which is a major concern in building codes.
1. Introduction Before the 1999 earthquakes in Taiwan (Chi-Chi) and Turkey (Kocaeli and Duzce), no serious attention was paid to the soil-structurefault rupture interaction. However, because of the significant width of deformation and fault rupture zones in these three earthquakes and the extensive damages to structures and public utilities induced by faulting, they have become a turning point in the study of surface fault rupture hazard. In the Chi-Chi earthquake, at least 30% of the damages to buildings were caused by surface fault rupture (Yang and Beeson, 2001). It is obvious that the pattern of rupture propagation through alluvial deposit overlying bedrock fault must be investigated (Duffy et al., 2014). After the 1999 earthquakes, many researchers have studied the surface fault rupture hazard through (i) field observations (Faccioli et al., 2008; Lavine et al., 2003; Lin et al., 2012, 2003; Ma and Chiao, 2004; Qin et al., 2015; Wang et al., 2013), (ii) experimental modeling (Chang et al., 2015; Lin et al., 2007, 2005; Loli et al., 2011; Peng et al., 2013), (iii) numerical analysis (Anastasopoulos et al., 2008; Anastasopoulos and Gazetas, 2010; Dong et al., 2003; Hazeghian and Soroush, 2017; Loukidis et al., 2009; Oettle and Bray, 2013; Taniyama, 2011) and (iv) analytical approaches (Bray, 2001).
Previous researches concluded that the width of surface faulting depends on geological, tectonic and geotechnical parameters, which include but are not limited to the type, thickness, stiffness and strength of the surface layers and the focal mechanism of the main fault rupture. In addition, the performance of faulting in rocky outcrops differs from the case in which an alluvium layer is located on bedrock. In this regard, it is essential to determine the extent of the surface fault rupture zone and predict the region in which no construction should be allowed as an aspect of building codes and construction regulations. Increases in the price of urban land and a shortage of land for construction make optimal determination of this zone of special importance. Therefore, for effective usage of land, it is suggested that complementary studies (field investigation or laboratory model testing) be performed. 2. Previous physical model studies 2.1. Physical modeling under earth gravity conditions Many researchers have conducted experimental studies under earth gravity conditions (1 g) to understand failure mechanism of surface fault rupture. Cole and Lade (1984) undertook a series of comprehensive model test on cohesionless sand involving reverse and normal
Corresponding author. E-mail addresses: [email protected] (N. Tali), [email protected] (G.R. Lashkaripour), [email protected] (N. Hafezi Moghadas), [email protected] (A. Ghalandarzadeh). ⁎
https://doi.org/10.1016/j.enggeo.2018.12.021 Received 31 October 2017; Received in revised form 15 December 2018; Accepted 21 December 2018 Available online 02 January 2019 0013-7952/ © 2019 Elsevier B.V. All rights reserved.
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Fig. 1. Newly designed and manufactured split box: (a) longitudinal section of box model; (b) displacement mechanism of movable part; (c) overall view of box model and (d) manufactured split box.
faulting at different angles to determine the surface fault rupture location and the affected zone width on an alluvium deposit over a dipslip fault. They found that a maximum vertical displacement of approximately 4% of the total thickness of the soil was required for complete development of a failure surface. Larger vertical movements were required to develop failure surfaces in more compressible and looser sand. Lade et al. (1984) attempted to simulate multiple failure surfaces in sandy soil in a fault test box. Their results showed that the angle of dilation was the dominant soil property affecting the location of the failure surfaces and that the displacement fields were the same for different materials. Bray et al. (1993) showed that the thickness of the shear zone in the saturated clay layer overlying a bedrock fault was related to the magnitude of base movement and the failure strain of the soil. The range of the dip angle of the bedrock with respect to the horizontal plane was selected to vary between 60° and 90° for both normal and reverse faults. Taniyama and Watanabe (2001) found that shear failure propagates through sandy soil and breaks the ground surface when the vertical component of the bedrock fault slip reaches 3% to 5% of the thickness (ΔH/H) for 30 and 50 m deep alluvium. They reported that a vertical
slip of about 7% of the depth of the alluvium was needed for shear failure to propagate through 75-m deep alluvium. Lee and Hamada (2005) investigated the pattern of rupture propagation through sandy soil with particular concern for dip-slip faulting. Their 1 g model tests showed that the location of the surface fault rupture varied according to the model thickness due to the strongly dilatant behavior of the sand under low confinement. Johansson and Konagai (2007) performed experimental tests on both dry and wet cohesionless soil. They showed that the amount of uplift required for surface rupture is larger for wet soil. In general, the shear zone was wider for wet soil, especially for reverse faulting, where the incompressibility of the pore water prevents horizontal compression, resulting in increased shear strain. 2.2. Physical modeling under accelerated gravity conditions Some researchers have conducted experimental studies under accelerated gravity conditions (Ng) to understand failure phenomena. Roth et al. (1981) showed that the soil properties are significant factors in the formation of a failure pattern. Their tests were performed under Ng conditions for reverse faulting. Lee and Hamada (2005) showed that there was no significant variation in the location of surface fault rupture
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Max. horizontal displacement (mm)
24 Diameter of actuator shaft (mm) 50 42 Stroke of actuator (mm) 150
314 Min. static actuator force (kN) 85
when the thickness of the soil layer changed. Anastasopoulos et al. (2007) investigated the location of fault outcropping and found that vertical displacement profile of the ground surface and a minimal fault offset at bedrock were necessary for the rupture to reach the ground surface. Their analysis showed that dip-slip faults refract at the soil rock interface, initially increasing in dip angle. The dip angle may continue to increase in normal faults as they approach the ground surface. In contrast, reverse faults tend to decrease in dip angle as they emerge at the ground surface. For small values of base fault offset (ΔH) relative to soil thickness (H), a rupture cannot propagate all the way to the surface. The ΔH/H ratio required for outcropping is a function of soil ductility. Reverse faults require a significantly higher ΔH/H to outcrop than do normal faults. Cai et al. (2013, 2010) conducted two centrifuge tests to investigate the effects of rigid and flexible boundary conditions on normal fault propagation. They showed that, in the rigid boundary condition, a smaller differential settlement resulted on the ground surface in compare with the bedrock fault movement. On the other hand, for the flexible boundary condition the differential settlement on the ground surface was larger than the bedrock fault movement. Ng et al. (2012) provided experimental evidence and numerical explanations of the failure mechanisms of soil induced by normal faulting under three ground conditions (uncemented clay, cemented clay with and without a preexisting fracture). As stated above, most previous studies were conducted on homogeneous and uniform soil layers; however, in nature, soil is usually heterogenic and stratified. In this study, a series of centrifuge model tests were conducted on sandy and clayey-sandy soil to understand better soil behavior during fault rupture propagation towards the ground surface. These tests were performed on single and/or doublelayered soils and at a centrifugal acceleration of 60 g. In addition, the reverse fault rupture had a dip angle of 60° (at bedrock level). 3. Testing procedure The tests were performed at the centrifuge facility using Actidyn Systems C67-2 equipment. The device comprises a beam with a 7 m diameter that can accelerate a model package of up to 1.5 ton at 100 g of centrifugal acceleration (i.e. 150-g-t).
Peak acceleration (g)
60 Fixed part Footwall Reverse and normal Movable part Hanging wall
932*508*400 Dip angle of fault (°) 60
3.1. Split box
Type of faulting
Table 1 Specifications of split box.
Dimensions (L*W*H) (mm)
Max. vertical displacement (mm)
Weight of box (kg)
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A split box was designed and manufactured for this study to simulate reverse and normal faulting. It was composed with a fixed and movable part designed to simulate footwall and hanging wall, respectively. This type of split box is commonly used to simulate fault rupture propagation through soil layers in a centrifuge (Ashtiani et al., 2016; Bransby et al., 2008b, 2008a; Kiani et al., 2016a, 2016b; Lee and Hamada, 2005; Moradi et al., 2013; Ng et al., 2012; Rojhani et al., 2012). Fig. 1(a) shows the longitudinal section of the box and its 85 kN hydraulic actuator. Fig. 1(b) shows the displacement mechanism of the movable part that is pushed or pulled by the hydraulic actuator. The main parts of the box were made of high-resistance steel with a transparent sidewall made of a 30-mm thick Plexiglas plate that facilitated observation of rupture propagation during the tests. Fig. 1(c) shows an overall view of the split box. Fig. 1(d) shows the completed split box with hydraulic connections. This box can simulate both reverse and normal faulting at a dip angle of 60° with respect to the horizontal. It can be adjusted for dip angles of 15° to 80° by changing four parts. The maximum allowable vertical offset of the movable hanging wall is 42 mm (2.52 m at 60 g centrifugal acceleration). In compliance with the capacity of the centrifuge and design of the split box, the tests were conducted at a centrifugal acceleration of 60 g. Furthermore, the large dimensions of an actual prototype made it unfeasible to conduct a test on such a specimen in a centrifuge. It was necessary to scale down the dimensions of the specimen to fit into the centrifuge. Dimension analysis and scaling law require that, if the 275
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Fig. 2. Grain size distribution curves of Firoozkuh sand No. 161 and clayey-sand.
Fig. 3. Stress-strain curve of soils under different confining pressure: (a) Firoozkuh sand No. 161 and (b) Clayey-sand.
length is scaled down N times, the acceleration should be scaled up N times; thus, using the dimensions of the split box and the model, 60 g was calculated and adopted. Thus, “N” is the scaling factor. The maximum slip rate of the simulator was 30 mm/s. Table 1 presents the specifications of the different parts of the box.
friction angles were 35° and 33°, respectively, and the dilation angle was 5° for the stress at shallow depth of sandy soil layer (Ashtiani et al., 2016). To understand better the behavior of natural soil, the Firoozkuh sand was mixed with kaolinite to obtain cohesive soil. The mixture consisted of one portion of kaolinite and three portions of Firoozkuh sand by weight. The grain size distribution curve of the mixed soil is presented in Fig. 2. A series of direct shear tests were conducted on mixed soil having a relative density (Dr) of 140% and a moisture content of 10% (corresponding to a unit weight -wet- of 21.1 kN/m3). The peak and residual internal friction angles, angle of dilation and cohesion were measured to be φP = 25°, φres = 23°, ψP = 0° and C = 28 kPa, respectively. Additionally, in order to precisely identify the soil mechanical parameters, a series of triaxial tests (cd type) were conducted in this research. The confinement pressures were 50, 100 and 300 kPa, respectively. Fig. 3 illustrates the stress-strain curve for two selected soil
3.2. Soil properties Two different soil types were used in centrifuge model tests: clean sand (Firoozkuh sand No. 161) and mixed sand (clayey-sand). The Firoozkuh sand No. 161 with a relative density of Dr = 70% is uniformly-graded fine clean sand with a mean grain size (D50) of 0.3 mm, maximum void ratio (emax) of 0.943 and a minimum void ratio (emin) of 0.548. Its grain size distribution curve is shown in Fig. 2 (Farahmand et al., 2016). Direct shear tests were conducted on samples with a relative density of 70% and a moisture content of 5% (corresponding to a unit weight -wet- of 16.77 kN/m3). The peak and residual internal
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200 180
E0 Sand
160
E50 Sand
E(MPa)
140
Er Sand
120 100 80 60 40 20
a
0 0
5
10
15
20
√σ3(kPa) 200 E0 Clayey-sand
180
E50 Clayey-sand
160
Er Clayey-sand
E(MPa)
140 120 100 80 60 40 20 0
b
0
2
4
6
8
10
12
14
16
18
20
√σ3(kPa) Fig. 4. Comparison of different elasticity modulus (E0, E50 and Er) for the adopted soils in this research.
Fig. 5. (a) Colored sand layer for visual detection of shear planes; (b) spray-painted exposed surface that allows visual detection of shear and tension planes.
types under the specified confining pressure. It's concluded from the curves, that the sand is stiffer and has larger strength (higher yield point) than the clayey-sand. Furthermore, in order to compare the soils, the different elasticity modulus (E0, E50 and Er) are presented in Fig. 4. The results indicate that the stiffness of the sand is higher than the clayey-sand.
improve homogeneity, the surface of each layer was scratched before the next layer was laid (Cai et al., 2013, 2010). The layers were compacted using a calibrated steel hammer with a flat rectangular tamping face and a 1450 g sliding weight with a free fall of 25 cm (Ashtiani et al., 2016). After compaction of the two layers, a colored sand layer (navy-blue inked sand) was placed in close proximity to the Plexiglas side to facilitate visual detection of the shear planes during test procedure (Fig. 5(a)) and the subsequent digital image analysis (Bransby et al., 2008a, 2008b). After compaction of each layer, silicon oil was applied to both sides of the split box to reduce the frictional resistance between the soil and the sidewalls. The total thickness of the soil layers was
3.3. Model preparation As explained, clean sand and clayey-sand were used in the models. The moist tamping method was selected to produce homogeneous specimens. Soil layers of 15 mm in thickness were compacted. To
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Fig. 6. Layout of instrumental devices for centrifuge model of reverse faulting: (a) top view; (b) side view. Table 2 Lists of centrifuge model tests. Test No.
RV-01-S to 05-S
RV-06-S
RV-09-CS
RV-10-S/CS
RV-11-CS/S
Faulting type Soil type Dip angle of fault(°) Centrifugal acceleration (g) Model dimensions (L*W*H) (mm) Max. vertical displacement (mm)
Reverse Sand 60 60 932*508*300 42
Reverse Sand 60 60 932*508*300 42
Reverse Clayey-sand 60 60 932*508*300 42
Reverse Clayey-sand below sand layer 60 60 932*508*300 42
Reverse Clayey-sand above sand layer 60 60 932*508*300 42
30 cm. A grid of orthogonal blue lines was then spray-painted onto the exposed surface of the specimen to allow the visual detection of the shear and tension planes after testing (Fig. 5(b)). All models were initially prepared outside the centrifuge chamber and then transferred on a swinging platform into the centrifuge.
3.4. Model instrumentation The instrumentation layout for all four tests is shown in Fig. 6. Five linearly variable differential transformers (LVDTs), a digital camera and three digital video recorders were used during the tests. Four LVDTs were used to measure displacement on the model surface and another 278
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Fig. 7. Schematic diagrams of soil models for tests: (a) RV-06-S; (b) RV-09-CS; (c) RV-10-S/CS; (d) RV-11-CS/S.
3.5. Centrifuge test procedure After model preparation, the split box was transferred to the centrifuge. The instrumentation of the model was installed and the connections were fixed. The hydraulic inlet and outlet connections were joined to the centrifuge connections and the control panel was programmed to reach the desired centrifugal acceleration. After the model was subjected to centrifugal acceleration of 60 g in-flight, bedrock fault movement was applied. To improve the quality of the photos, the camera was programmed to capture one photo every 3 s. Accordingly, the average rate of fault movement was chosen to be approximately 1.4 mm/s (corresponding to 0.083 m/s at prototype scale) despite the higher capacity of the split box. The results were interpreted using the measured data accompanied by the photos and post-test observations. In these tests, the faulting velocity was not scaled. The experiment used a pseudo-static loading scheme and the dynamic effect of faulting was ignored. The soil in the current models was granular and was not saturated; thus, the shearing rate effect could have had a minor influence on the results. Kabir et al. (2010) reported that the compressive response of fine sand is not sensitive to the strain rate under loading conditions, but is significantly dependent on the moisture content, initial density and lateral confinement.
Fig. 8. Schematic illustration of the reverse faulting model and corresponding definitions.
was used to measure the bedrock fault movement. The digital camera was mounted in front of the Plexiglas side to photograph model deformation. One of the digital video recorders was used to monitor model surface deformation and the other two were employed to record bedrock fault movement. A data acquisition system automatically recorded these measurements.
3.6. Test cases Although 14 tests were conducted on reverse and normal faulting systems, only the results of nine reverse faulting tests are presented. The test conditions are summarized in Table 2. Five initial tests were done
Fig. 9. Measures for reducing sidewall friction: (a) double polyurethane sheets with silicon oil; (b) polyurethane sheet with silicon oil; (c) silicon oil alone. 279
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Fig. 10. Vertical displacement of ground surface and bedrock at prototype scale in tests: (a) RV-06-S; (b) RV-09-CS; (c) RV-10-S/CS; (d) RV-11-CS/S.
resistance (Fig. 9). Tests RV-06-S, RV-09-CS, RV-10-S/CS and RV-11CS/S were conducted using polyurethane sheets along with silicon oilcovered surfaces, which were determined to be the best solution (Fig. 9(b)).
to calibrate and improve the boundary conditions. Another four tests were performed to evaluate the soil type and stratified soil behavior during reverse fault rupture propagation through the soil. Test RV-06-S was performed in sandy soil. Test RV-09-CS was performed in clayeysand and tests RV-10-S/CS and RV-11-CS/S were performed in stratified soil. Fig. 7 shows the geometries of the models in tests RV-06-S, RV-09CS, RV-10-S/CS and RV-11-CS/S. Fig. 8 shows the 3D diagram of reverse faulting that describe the geometry and parameters used. In this figure, “flexure” denotes the width of the main ground surface distortion zone and “scarp” denotes the vertical offset between the initial ground surface and the distortion zone. : (ΔH) vertical movement of bedrock; (H) soil layer thickness; (d) induced vertical movement in soil layers; (1) bedrock; (2) stationary block (footwall); (3) moving block (hanging wall); (4) faulting plane; (5) straight extension of bedrock fault plane; (6) vertical projection of fault trace; (7) tension cracks; (8) faulting dip angle; (A) width of tension zone between vertical projection of fault trace in bedrock and boundary of fault deformation; (B) zone between fault trace outcrop and straight extension of bedrock fault place; (S) theoretical deformation zone between straight extension and vertical projection of fault to ground; (W) width of deformation zone.
4.1. Vertical ground surface displacement in flexure zone and footwall area One of the important factors that should be measured during the tests is the vertical ground surface displacement (Bransby et al., 2008b; Cai et al., 2010). Fig. 10 shows the vertical displacement of the ground surface and bedrock during the simulation of reverse faulting in tests RV-06-S, RV-09-CS, RV-10-S/CS and RV-11-CS/S. The moment that the reverse faulting was initiated was set as the origin of the time axis. It was found that vertical displacement of bedrock of 42 mm (equivalent to 2.52 m at prototype scale) occurred within an average of 30 s and resulted in a velocity of reverse faulting of approximately 1.4 mm/s (0.084 m/s at prototype scale). Consequently, the model surface at the hanging wall displaced 39, 33, 35 and 38 mm in tests RV-06-S, RV-09CS, RV-10-S/CS, and RV-11-CS/S, respectively (LVDT 1; Fig. 6). No obvious vertical displacement was observed at the ground surface on the footwall (LVDTs 3 and 4; Fig. 6) (Ahmed and Bransby, 2010; Cai et al., 2010; Lin et al., 2006).
4. Results of centrifuge tests
4.2. Appearance of faulting fractures on ground surface
The nature of the boundary conditions is an important factor that must be considered in physical modeling (Anastasopoulos et al., 2007; Cai et al., 2010; Stone and Wood, 1992). Therefore, five initial tests were conducted to improve the boundary conditions of the models. The sidewalls of a model could create undesirable friction that could affect the test results; thus, different solutions were examined for reducing friction. Polyurethane sheets, double polyurethane sheets and silicon oil were used on both sides of the split box to reduce the frictional
The required bedrock displacement for appearance of the rupture on ground surface is an important factor during faulting. A threshold earthquake magnitude of 5 to 5.5 (Richter scale) is required for the appearance of shear failure at the ground surface (Bonilla, 1988). The ratio ΔH/H is often used to assess the effect of soil thickness in surface faulting hazards. Lee and Hamada (2005) showed that this value varies from 5.77% to 10.1% of the soil thickness, depending on soil density.
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Fig. 11. Bedrock vertical displacement required the fault to outcrop and dip angle of fault rupture traces as they emerge on ground surface: (a) RV-06-S; (b) RV-09CS; (c) RV-10-S/CS; (d) RV-11-CS/S (Not to scale).
Propagation of shear failure through the soil models is shown in Fig. 11. In each test, the non-stationary half of the frame moved up and into the soil mass (reverse faulting) until the primary failure surface developed through the entire height of the soil. For the 30 cm soil thickness (18 m at prototype scale) in the four models with reverse faulting, a complete slip surface generally developed after 1.59 to 2.04 cm (95.4 cm to 122.04 cm at prototype scale) of vertical displacement of the bedrock. Thus, a maximum vertical displacement of approximately 6.8% of the total soil thickness was required for complete development
of a failure surface (Fig. 12). Comparing Fig. 11 a, b, c and d, it can be seen that the normalized vertical displacement required for the fault to outcrop (ΔH/H) increased with an increase in the percentage of clay content. These results agree with those of previous researchers (Ahmadi et al., 2018). 4.3. Angle of fault plane through soil layers Anastasopoulos et al. (2007) showed that the dip-slips of faults 281
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the fault dip angle at the surface. Furthermore, Fig. 13(c) and (d) indicate that in two-layered models, the change in material properties result refraction of dip angle of fault ruptures. According to Fig. 13, it can be concluded that when the fault rupture passes a stiffer soil layer (sand) to a softer soil (clayey-sand), the propagation dip angle will decrease. For instance, in Fig. 13(c) the propagation angle in the clayey–sand is 62°, however, after entering the sand layer, the dip angle increases to 67°. Similarly, by changing the layers' order, in Fig. 13(d), the propagation dip angle changes and decreases when the rupture passes a stiffer layer (sand) to a softer layer (clayey-sand), and it should be noted that the changes in the inclination is not obvious and large (refer to Fig. 4) as the differences in the stiffness is small. The relation between the rupture angle and the elasticity modulus is illustrated in Fig. 14. In the aforementioned Figure, the elasticity modulus of each layer is normalized with the amount of its below layer. In addition, the rupture angle in each layer is normalized with the amount of its below layer. The mentioned values compared to the normalized 45-Φ/2/60 and 45 + Φ/2/60 lines (respect to the fault rupture angle on the bedrock). As it could be concluded from Fig. 14, the curves of the rupture propagation in single-layered models are located on sides of the graph and the doubled-layer models are located between the two extreme (single-layered) curves. This has been observed in previous works (Cole and Lade, 1984) that the start of the fault rupture is assumed as an active condition, the slope of the rupture is complying with the 45 + Φ/ 2 and the emerged rupture on surface is complying with passive condition. Anastasopoulos et al. (2007) indicated that the initiation of the fault rupture is with an increase in dip angle and this increase alleviate along the soil depth and comply with the 45-Φ/2 on the surface. These findings are in accordance with those of Lee and Hamada (2005), who showed that fault rupture is mainly affected by the dip angle of the
Fig. 12. Propagation of shear failure in soil models related to bedrock displacement. The definitions of H, ΔH and h are indicated in the inset.
refract at the soil rock interface, initially increasing in dip, particularly in soil with a low angle of dilation. The dips of normal faults may continue to increase as they approach the ground surface. In contrast, reverse faults tend to decrease in dip as they emerge at the ground surface. Fig. 13 shows the surface angles of the fault planes and the refraction angles of the fault plane in boundary of two soil layers (Fig. 13c and d). In accordance to the previous studies, the results indicate that the rupture dip angle at the ground surface is decreased and it is smaller than the fault dip angle at the bedrock. As depicted in Fig. 13(a) and (b), the changing of soil type resulted in differences in
Fig. 13. Dip angle of fault rupture traces as they propagate through soil layers: (a) RV-06-S; (b) RV-09-CS; (c) RV-10-S/CS; (d) RV-11-CS/S.
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Fig. 14. The relations between the rupture dip angle and the elasticity modulus in different soil types (αi = dip angle of each three cm soil thickness rupture; α = dip angle of bedrock fault and Ei = elasticity modulus of each three cm soil thickness.
bedrock fault and the ductility of the soil rather than by model thickness. This was confirmed by Mortazavi Zanjani and Soroush (2014).
ground surface was recorded. The ratio of ground surface uplift to bedrock fault movement (d/h) was about 91%, 92%, 93% and 94% in tests RV-06-S, RV-11-CS/S, RV-10-S/CS and RV-09-CS, respectively. The decrease in ground surface uplift from bedrock uplift was accounted for and defined as the dissipated displacement ratio (DDR), in order to understand better the difference between the test results. A higher DDR value denotes decreased ground surface uplift so increased the dissipation of the ground surface displacement. Fig. 16 presents bedrock dislocation in relation to the ground surface as the DDR for different tests. The sand layer produced the highest DDR value and the clayey-sand deposit produced the lowest value. Fig. 16 shows that topsoil with 0.5 to 0.75 m of bedrock movement had the largest DDR.
4.4. Trishear model of deformation The shear deformation induced by reverse faulting could be explained by “Trishear model” that has been proposed and developed by Allmendinger, 1998; Cardozo, 2005; Cardozo et al., 2003; Champion et al., 2001; Erslev, 1991; Hardy and Ford, 1997; Jin and Groshong, 2006; Zehnder and Allmendinger, 2000). In the trishear model, a single fault in bedrock expands outward into a triangular zone of distributed shear zone. According to Allmendinger et al. (2004), the present fault rupture propagation could be classified as reactivation a preexisting fault or generating a new one. Fig. 15 illustrated the fault displacement and trishear formation. As reported by Lin et al. (2006); Ahmed and Bransby (2010) and Lee et al. (2000) a bifurcation of the fault zone into two branches can be observed in sand models (tests RV-06-S and RV-10S/CS), and it is going to form in two other models as shown in Fig. 15 (b) and (d). This phenomenon has been observed with progressive fault uplift after emergence of fault fracture at surface, developed and reported in previous works (Bray, 2001; Cole and Lade, 1984; Lin et al., 2006) (denoted as numbers 1 and 2 in Fig. 15 (a), (b), (c) and (d)). When the fault tip propagation continued, the slip trace divided into two branches. The resulting of this mechanism is that the fault rupture zone formed a stepped shape and the sand models show a steeper slope than did the clayey-sand models. Therefore, this phenomenon resulted in a wider fault rupture zone in the clayey-sand model. This indicates that the sandy deposit without cohesive particles created a steeper scarp, which generated a narrower deformation of the fault rupture zone, and the clayey-sand created a gentler slope with wider deformation of the fault rupture zone. These differences can have a strong effect on the level of damages to buildings.
4.6. Development of deformation area The width of a surface rupture must be considered when determining a safe distance from the rupture for construction sites (Zhang et al., 2013). Estimation of this zone is very important for the seismic safety of buildings near an active fault. To do this during testing, photographs were taken of the surface of the models before and after each test (Fig. 17). The progression of the fault rupture zone on the footwall is shown in Fig. 18. In this figure, line 5 shows the position of the straight extension of the fault plane and line 6 shows the vertical projection of the fault plane. The zone between lines 5 and 6 is the theoretical fault rupture zone. Fig. 18 reveals that the real deformation area is wider than the theoretical zone. During the initial stage of fault rupture propagation in the sand model, a fracture formed a large dip angle. As faulting continued, the fracture formed two branches, of which the second had a smaller dip angle. This created a deformation area with a stepped form and resulted in a limited fault rupture zone. The clayey-sand and the stratified model with clayey-sand on top show a gentle slope flexure. This indicates that the type of soil in the layer on top of the bedrock defines the width of the fault rupture zone and the upper layer defines its exposed shape. In Fig. 17, the ground surface has been divided into three parts by orthogonal grid lines showing deformation. The diameters of some squares are fixed, of some are stretched and of others have decreased. These cases indicate the no change, tension and compression stress conditions, respectively. The tension and compression areas are shown in Fig. 17. The areas outside of the fault rupture zone (W) experienced no change. The zone located between the vertical projection of the fault
4.5. Ground surface uplift Previous earthquake experience has shown that thick sediment layers can prevent fault rupture from reaching the ground surface. An increase in bedrock vertical displacement will increase the probability of the appearance of a fault trace at the ground surface. In fact, ground surface uplift is a hanging wall translation for which the displacement ratio depends on the physical and mechanical properties of the soil. During testing, the displacement of the bedrock in relation to the
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Fig. 15. Trishear model of deformation and generation of a bifurcation of the fault zone in different models (a) RV-06-S; (b) RV-09-CS; (c) RV-10-S/CS; (d) RV-11-CS/ S.
trace and the border of the extension area on the hanging wall side is denoted as A, and the zone between the straight projection of the fault trace and fault rupture line is denoted as B. Finally, zone S is located between the straight extension and vertical projection of the fault to the ground surface that forms theoretical fault rupture zone. The compression and tension zones across W were different in all tests (Fig. 18) such that W-CS > W-S/CS > W-CS/S > W-S in which W-CS, W-S/CS, W-CS/S and W-S are the width of the fault rupture zones in RV-09-CS, RV-10-S/CS, RV-11-CS/S and RV-06-S tests, respectively. It appears that the clay content of the soil affected W. Table 3
summarizes the values for S, A, B, W and W/H. Fig. 19 illustrated the development of ground surface deformation zone related to vertical displacement of bedrock. According to this Figure, the clayey-sand has the widest deformation zone and sand layer has the narrowest one. The Stratified models have an average reaction. The deformation zones on both sides of the fault are asymmetric and the proportion between the hanging wall side and the footwall side ranges from 4.3:1 to 2.5:1. This indicates that the avoidance zone is not simply half of the deformation zone. The above mentioned results agree with those of previous researchers (Lee et al., 2000). 284
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phenomena and they are relatively inexpensive. Therefore, the results of current study may offer some insight into the fault rupture problem. Specially, the width of deformation zone is a key parameter in determination of avoidance zone, which is very well measurable in model tests. As shown in Table 4 the values of avoidance zone proposed by New Zealand building code and the abovementioned studies are larger than those observed in tests RV-06-S; RV-09-CS; RV-10-S/CS and RV-11-CS/ S. The thickness and type of sediment layer and dip angle of bedrock fault are not reported by building codes and field studies and they do not take into account these parameters for measuring and calculating avoidance zone. That could be the reason for differences between values of Table 4. Fig. 20 (b to e) illustrates the results of avoidance zone according to the test results (RV-06-S; RV-09-CS; RV-10-S/CS and RV-11-CS/S) compare to the proposed avoidance zone in New Zealand building code (Fig. 20 a). It seems that a further studies and observation are necessary for better understanding of this issue. Therefore, for effective usage of land, it is suggested that complementary studies (field investigation or laboratory model testing) could be performed.
18
Dissipated displacement ratio (%)
RV-06-S 16
RV-09-CS RV-11-CS/S
14
RV-10-S/CS 12 10 8 6 4 2 0 0.0
0.5
1.0
1.5
2.0
2.5
Vertical bedrock displacement (m) Fig. 16. Ground surface uplift dissipation in soil models at prototype scale.
4.7. Comparison of findings and building codes Some building codes and construction regulations state that an avoidance zone should be determined around an active fault (Kerr et al., 2003). A common misconception regarding setbacks is that they should always be 15 m from both side of the active fault trace. According to studies on 1999 Chi-Chi earthquake hanging wall deformation and its effect to buildings and structures conducted by Lee et al. (2000), they proposed a setback zone about 15 m wide on both side of the fault trace for common buildings. Moreover, field studies of Lin et al. (2003) showed that the deformation fault zone of the Chelungpu fault varied between 10 and 65 m. Furthermore the research results of Kelson et al. (2001) indicated that, the deformation width of an individual scarp is about 10 to 20 times the net vertical displacement. The field observations and measurements of Zhang et al. (2013) were used to calculate the width of deformation zone as 41.72 m. Accurate determination of avoidance zone requires observation of real fault ruptures (previous earthquakes) or conducting model tests. Centrifuge model tests provide more or less similar conditions to real
5. Conclusions In this research, a series of centrifuge model tests were conducted to study the effects of soil type and stratification on fault rupture propagation and development of a fault rupture zone caused by reverse faulting. The following findings were determined in relation to model parameters such as fault dip angle, soil type and soil thickness. These observations are obviously limited to the test conditions and may not be applicable for different types of soil, sequences of stratification, thickness of deposits, fault dip angles and mechanisms.
• Vertical movement of the ground surface in the rupture zone in the sand (stiffer soil) model was larger than for the clayey-sand model. • The rupture zone showed a gentler slope in the clayey-sand model, while the sand model (stiffer soil) showed a stepped slope. • The curves of the rupture propagation in single-layered models are located on sides of the graph and the doubled-layer models are
Fig. 17. Top view of ground surface deformation induced by reverse fault movement. 285
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Fig. 18. Development of fault rupture zone induced by reverse fault movement in different models. Table 3 Values of S, A, B, and W in test models for fault throw ΔH = 2.4 m. Test No.
Soil type
S (m)
A (m)
B (m)
W (m)
W/H
RV-06-S RV-09-CS RV-10-S/CS RV-11-CS/S
Sand Clayey-sand Sand/Clayey-sand Clayey-sand/Sand
10.4 10.4 10.4 10.4
2.9 9.0 4.6 4.2
4.0 5.8 6.1 3.4
17.3 25.2 21.1 18.0
0.96 1.40 1.17 1.00
located between the two extreme (single-layered) curves.
• The sand layer had the highest dissipated displacement ratio of bedrock displacement and clayey-sand had the lowest DDR. • The highest DDR occurred during the initial movement of the bedrock (0.5–0.75 m). • Vertical displacement of 5.3% to 6.8% of the total thickness of the • • •
soil was required for complete development of a failure surface. The minimum required displacement occurred in test RV-10-S/CS and the maximum in the clayey-sand model (RV-09-CS). The failure surface approached the ground surface at a smaller dip angle than the fault dip angle at bedrock. This decrease was more pronounced when the soil layer was clayey-sand. The model with a sand layer demonstrated the smallest decrease. Clayey-sand had the widest fault rupture zone, followed by the stratified S/CS, CS/S, and sand models. The width of the fault rupture zones could be affected by soil type, thickness and stratification in addition to the other parameters, which were investigated in the previous researches. The measured widths under the conditions of the present study ranged from 17.3
Fig. 19. Development of deformation zone induced by reverse fault movement in different models. The definitions of H, ΔH, and W are indicated in the inset.
to 25.2 m at prototype scale. The setback zones in the California and New Zealand building codes are proposed regardless of soil type, thickness and fault dip angle and usually are based on the vulnerability of structures. Under the conditions of the current tests, the measured widths of the rupture zones were smaller than the minimum setback zone values in the above-mentioned codes.
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Table 4 Comparison of width of Avoidance zone values in different studies. Code or study
New Zealand building code
Lee et al. (2000)
Lin et al. (2003)
Kelson et al. (2001)
Zhang et al. (2013)
RV-06-S
RV-09CS
RV-10-S/ CS
RV-11-CS/ S
Avoidance zone (m)
40
30
10–65
25–50
41.72
17.3
25.2
21.1
18
Fig. 20. Proposed avoidance zone according to results of different tests (Fig. 20 b to e) compare to the New Zealand building code (Fig. 20 a) (adapted from Kerr et al., 2003).
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Acknowledgments
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