[[abstract]]The tension crack appears at the ground surface acompanied by excavations in soils. The 
development of tension crack is depended upon the horizontal earth pressure exerted on the soils. For a normally-consolidated level ground, the tension crack depth of a vertical cut can calculate according to Rankine’s active earth pressure theory. The critical height of a vertical cut can stand without lateral supports is twice as deep as the tension crack depth. However, in this paper a large tension crack depth observed for a vertical cut in fault zone. This tension crack depth and critical height of vertical cut are applied to estimate the in-situ horizontal earth pressure of fault zone at rest.[[sponsorship]]Japanese Comittee for Rock Mechanics (the ISRM NG Japan)[[conferencetype]]國際[[conferencedate]]20130820~20130822[[booktype]]電子版[[iscallforpapers]]Y[[conferencelocation]]Sendai, Japa

楊長義

The tension crack appears at the ground surface acompanied by excavations in soils. The 
development of tension crack is depended upon the horizontal earth pressure exerted on the soils. For a normally-consolidated level ground, the tension crack depth of a vertical cut can calculate according to Rankine’s active earth pressure theory. The critical height of a vertical cut can stand without lateral supports is twice as deep as the tension crack depth. However, in this paper a large tension crack depth observed for a vertical cut in fault zone. This tension crack depth and critical height of vertical cut are applied to estimate the in-situ horizontal earth pressure of fault zone at rest.Japanese Comittee for Rock Mechanics (the ISRM NG Japan)國際20130820~20130822電子版YSendai, Japa

Tamkang University Institutional Repository

6th Int. Symp. on In-Situ Rock Stress  RS2013   20-22 August 2013, Sendai, Japan  Estimate the In-situ Earth Pressure in a Thrust Fault Zone by Vertical Cut  Z.Y. Yanga*, J.Q. Hsiaob and J.K. Yanga   aTamkang University, Tamsui, Taipei, Taiwan  bHJQ Geotechnical Consultant, Taoyuan, Taiwan * yang@mail.tku.edu.tw   Abstract  The tension crack appears at the ground surface acompanied by excavations in soils. The development of tension crack is depended upon the horizontal earth pressure exerted on the soils. For a normally-consolidated level ground, the tension crack depth of a vertical cut can calculate according to Rankine’s active earth pressure theory. The critical height of a vertical cut can stand without lateral supports is twice as deep as the tension crack depth. However, in this paper a large tension crack depth observed for a vertical cut in fault zone. This tension crack depth and critical height of vertical cut are applied to estimate the in-situ horizontal earth pressure of fault zone at rest.   Keywords: In-situ earth pressure, Fault zone, Vertical cut, Tension crack, Critical height   1. Introduction For the normally consolidated deposit soils, the vertical overburden pressure 0v is the maximum pressure that the soil mass in its history. The in-situ horizontal earth pressure at rest that no deformation in the lateral direction is 000 vh K    as shown in Fig.1(a). The coefficient of at-rest earth pressure (see Fig.2) at a depth z in the level ground is defined as 000 / vhK  . The coefficient of 0K  is depended upon the stress history of the soils, such as soil deposition process and geological history. For a vertical cut in an infinite half deposited space, the in-situ horizontal stress at rest is decreasing  due to the soils expand in lateral direction (McCarthy, 1993). At the state of shear failure, the at-rest horizontal stress decreases to reach the so-called ‘active’ stress state (see Fig.2). The active horizontal pressure at failure that remained in soils based on Rankine’s active earth pressure theory for cohesive granular ( c ) soils is expressed as, )245tan(2)245(tan2   czA                          (1) The magnitude of the horizontal pressure A  is the minimum and will exert on a retaining structure. During the vertical cut, the released horizontal pressure that acts on soil mass from at-rest stable state to active failure state (see Fig.2 and Fig.3) is, zKzK Ah   0                                         (2) The coefficient of active earth pressure is designed as, for example in cohesionless soils )2/45(tan2 AK  and sin10 K .  From the variation of )( Ah    with depth z in Eq.(1) shown in Fig.1(b), it shows that at the ground surface the tension stress is a maximum. The negative lateral earth pressure takes place within the depth of )2/45tan(/2  c  due to the soil cohesion. If the tensile strength of soils is very close to zero, it remains customary to estimate the maximum depth of tension crack zc expresses as, )245tan(2  czc                                        (3) 6th Int. Symp. on In-Situ Rock Stress  RS2013   20-22 August 2013, Sendai, Japan  Terzaghi (1943) suggested the tension crack depth does not exceed one-half the critical height Hc of a vertical cut that may stand without lateral supports (Kutschke and Vallejo, 2011). This indicates that the horizontal tension force and compression force acting on the cut wall is in force equilibrium (see Fig.1). This suggestion indicates that the critical self-stand height of a vertical cut without supports is cc zH 2                                             (4) Thorne and Abt (1993) also supported that if no specific data for the depth of tension crack are available, 0.5 may be used as the default value of tension crack ratio zc/Hc. The above statement is supposed that the horizontal stress only caused by soil gravity effect. This does not consider for a faulting process that the in-situ horizontal stress can be much greater than that caused by gravity effect of soil mass. ߛݖܭ஺ െ 2cඥܭ஺ 2cߛ tan ቀ45 ൅߮2ቁ Tension crack  Z σ௛ σ௩H Open cut െ2cඥܭ஺ ࡷ࡭ ൌ ܜ܉ܖ૛ ቀ૝૞ െ ࣐૛ቁ   Figure 1. The development of lateral earth pressures and tension crack due to vertical cut. Mohr‐Coulomb shear envelope  passive active σσ஺ ൌ ܭ஺σ௏೚ σ௛೚ ൌ ܭ௢σ௏೚  σ௩೚ ൌ ݎݖ σ௣ ൌ ܭ௣σ௩ At restτ failure  Figure 2. The in-situ horizontal earth pressure decreases from at-rest state to active shear failure due to ground movement. 6th Int. Symp. on In-Situ Rock Stress  RS2013   20-22 August 2013, Sendai, Japan   Original positionof wall Towards soil mass  Wall movement  Away fromsoil mass Kp (passive) Ko (at‐rest) KA (active) Kp  ؆ 3 to 6 for cohesionless ؆ 2 for cohesive Ko  ؆ 0.5 for cohesionless ؆ 1.0 for cohesive  KA  ؆ 0.25 to 0.50 for cohesionless ؆ 0.5 for cohessionless  Figure 3. The coefficient of earth pressure decreases from K0 to KA due to ground movement.  A shallow excavation to 5m depth in fault zone in Taiwan causes a rapidly lateral slope movement. Several tensile cracks appeared in the upper slope surface extend to 80m far away from the slope cut (Yang et al., 2006). The field displacement measurements of inclinometers show that the possible shear slip surface is limited within a certain distance, but not a circular failure surface. This indicates that the in-situ stresses in fault zone is different to the sedimention deposite. This paper aims to estimate the in-situ stresses by the observation of critical excavation height in fault zone related to the developed tension crack depth.  2. Site condition and material property A vertical cut in 3m depth with no lateral support will be carried out to observe the tension crack development in a 40m-thick fault zone (see Fig.4). The test site in Taiwan is located in a slope land with the inclination less than 6 degree. Actually, this site of open cut is within the hanging wall of a thrust fault. The fractured material in faulted zone mainly is the mudstone/siltstone occasionally with sandstone interlayers. The foot wall material with a high pressured groundwater from measurement mainly is the gravelly formation. Before the test of open cut, a 5m-depth slope cut in the field was done and a retaining wall with anchorage installed.    Figure 4. The profile of open cut and previous slope cut in the fault zone.  The unit weight of faulted mudstone/siltstone with natural water content of 8%~12% in the fault zone is 23 kN/m3. The Atterberg limits of mudstone are obtained as: Liquid Limit LL=24, Plastic Limit PL=13, and Plastic Index PI=11. It is noticed that the natural water content of 8% is less than PL. This property makes this mudstone like the stiff clay by air dried. Several conjugate micro-fractures, such as the Reidel shear fractures are observed in the mudstone/siltstone sample (see Fig.5) cored from the fault zone. The clay-sized material in the shear fractures reveals the high water absorbability. 6th Int. Symp. on In-Situ Rock Stress  RS2013   20-22 August 2013, Sendai, Japan      (a)micro-fractures in mudstone sample            (b)case of excavation with supports Figure 5. The appearance of faulted mudstone block and excavation cases in the fault zone.  The uniaxial compression strength of mudstone samples with natural water content ranges from 2.8 kg/cm2  to 5.5 kg/cm2. The deformation modulus is 120 kg/cm2 (120~960 kg/cm2). The fracture pattern after peak strength is split fracture or fracture (see Fig.6).  The shear strength parameters by direct shear tests are: the average frictional angle = 25o(8.5) and cohesion C=0.4 kg/cm2. The ratio of E/Su used in clayey soil analysis is roughly estimated as 300~2400. It is noticed that the residual frictional angle for remolded samples of mudstone (siltstone/shale) with 20% water content is seriously decreasing to 7.2 degree (see Fig.7). The behavior at natural water content  =10% shows more brittle in shear failure than that at  =20%.         Figure 6. The typical stress-strain behavior of mudstone and fracture mode under compressive test. 6th Int. Symp. on In-Situ Rock Stress  RS2013   20-22 August 2013, Sendai, Japan  0 4 8 12 16 20Shear strain (%)00.20.40.60.81Shear stress (kg/cm2 )mudstone- Normal stress  (kg/cm2) 0.5   ,   w=10%1.0   ,   w=10%2.0   ,   w=10%0.5   ,   w=20%1.0   ,   w=20%2.0   ,   w=20%      0 0.4 0.8 1.2 1.6 2Normal stress (kg/cm2)00.20.40.60.81Shear strength(kg/cm2 )mudstone (z=-15m)W=20% ResidualW=10% ResidualW=10% Peakcr=0r=7.2ocp=0.07 (kg/cm2)p=17.2ocr=0 (kg/cm2)r=16.5o  (a)shear stress-strain curve                       (b)strength envelope Figure 7. The shear behavior and strengths of faulted mudstone at  =10% and 20%.  3. Vertical cut without lateral support A vertical open-cut to 2.5m depth (with 10m in length and 4m in width) is performed in the field. This test aims to measure the lateral movement of ground by open cut. In order to measure the lateral displacement close to the cut wall of excavation, the inclinometer is setup near to the cut wall in 50cm before excavating (see Fig. 8). No lateral support is applied to this test excavation that we can measure the free displacement of the field ground. Four automatic measurement sensors are setup at the depth of 1.5, 2.5, 5 and 10m to record the lateral displacement. The interval of taking lateral displacement data is 5 minutes. Figure 8(a) shows a tension crack appears at the ground surface in 2 hours after excavating. The maximum opening of the tension crack reaches 5cm. Due to the confinement of corner effect in a three-dimensional excavation, the tension crack is in a circular shape at the ground surface. However, the tension crack is vertically extended. A mudstone block in 0.8m thick was cut apart and pushed over. That is similar to the toppling failure. The base of the block observed is failure by  shear. This ensures the Terzaghi’s theory is applicable for this case. The surface characteristic of tensile fracture shown as Fig.8(b) is very rough. The tension crack depth is 2.4m in the 3m vertical open-cut. The lateral displacement measured by inclinometer as shown in Fig.9 for determining the slide plane is good agreed to the crack depth. At depth of 1.5m, the ground movement rate is 0.3 mm/min and total lateral displacement is up to 45mm in three hours.          (a)tension crack at ground surface                   (b) crack surface characteristic Figure 8. A tension crack accompanied with the vertical open cut and the tension crack surface. 6th Int. Symp. on In-Situ Rock Stress  RS2013   20-22 August 2013, Sendai, Japan  02468100 10 20 30 40 50depth (m)lateral displacement (mm)2min20min30min40min50min60min70min80min90min100min110min120min130min140min150min160min170min180min190min         (a)lateral displacement of cut wall                   (b)movement rate at different depth Figure 9. The lateral displacement and movement velocity measured by inclinometer.  4. Estimate the horizontal in-situ pressure The critical height of vertical excavations in c  soil theorectically is to be twice as deep as the tesnsion crack depth according to Terzaghi’s observation. That is, Hc=2zc. At this vertical open- cut in the thrust fault zone, the tension crack depth (zc) at failure observed is 2.4m. The critical height of open cut without supporting theoretically is estimated as Hc=2zc =4.8 (m). However, in this site the critical self-stand height only comes to Hc=2.5m. This means, see Fig.2, that excavations into this fault ground results in a large horizontal pressure released to soil mass. This large released horizontal pressure enhances the tension crack quick developing. The allowable critical height of excavations to keep self-standing is much less than that for the normally-consolidated deposition soils.                                (a)normally-consolidated ground                (b)fault zone Figure 10. The difference in tension crack depth due to two in-situ earth pressure condtion.  Therefore, in the fault ground the in-situ horizontal pressure at rest 0H (see Fig. 10) should be different to that at-rest 0h in sedimention ground. That is, this released horizontal pressure ( AH  0 ) in fault zone (see Fig. 2) during the vertical cut to push the ground is more larger than )( 0 Ah   in normally-consolidated deposition. According to the difference in self-stand 6th Int. Symp. on In-Situ Rock Stress  RS2013   20-22 August 2013, Sendai, Japan  excavation height, the ratio of released stress ( AH  0 ) to )( 0 Ah    can estimate as the ratio of critical excavation height ( 92.15.2/8.4  ). That is, )(2)(92.1)( 0000 AhAhAH                           (4) Therefore, the in-situ horizontal at-rest earth pressure in fault zone can express as, AhH   00 2                                               (5) where the 0h is the horizontal at-rest earth pressure and A  is the active earth pressure for normally-consolidahereted deposition soils. This means that the in-situ horizontal stress at rest 0H  in fault zone is directly related to the stresses in normally-consolidated deposite soils. Therefore, Eq.(5) is rearranged into  )2(2 00 AAH KcKzzK                                (6) That is, AAH KcKKz 2]2[ 00                                      (7) The in-situ horizontal earth pressure at rest in fault zone can estimate using the emperical formula those adopted in normally-consolidated depostion. For example, we get 28.0)2/45(tan2  AK  and 57.0sin10  K  using 28 . The vertical earth pressure is zv  0 . This horizontal earth pressure at rest in fault zone is calculated by Eq.(7) as czH 56.086.00      [for this fault zone]                      (8) However, the in-situ horizontal earth pressure at rest in the normally-consolidated deposition soils is zh  57.00           [for NC deposite]                          (9) It is found that the 0H in fault zone is close to the vertical earth pressure 0v . Fig. 11 shows the variation of 0v , 0h and 0H  using c=0.4 kg/cm2 and 28 . This indicates the in-situ horizontal earth pressre in fault zone is greater than that in normally-consolidated deposite soils. However, that AK  and 0K  formula may be different for various ground condition depended upon the soil properties and geological histroy.   5. Conclusions The Rankine’s active earth pressure theory in soil mechanics is derived according to Mohr-Coulomb shear failure criterion. The soil is tensile cracking at where the horizontal earth pressure is negative in excavations. The tension crack depth of c  soils by vertical cut can be approximately estimated. Terzaghi suggested from experimental observations that the critical height of vertical excavations with no lateral supports is twice as deep as the tension crack depth. However, in this paper a vertical cut without lateral supports in fault zone shows that the critical self-stand height of excavations by Terzaghi’s formula is over-estimated. This implies that a large horizontal earth pressure is released from the faulting materials. According to the ratio of critical self-stand height between the fault zone and normally-consolidated deposite soils, we estimate the in-situ horizontal earth pressure in this fault zone is AAH KcKKz 2]2[ 00   . This in-situ horizontal earth pressure in fault zone can be estimated directly by the coefficients of earth pressure at rest and at active state in normally-consolidated deposition. 6th Int. Symp. on In-Situ Rock Stress  RS2013   20-22 August 2013, Sendai, Japan  05101520253035400 2 4 6 8 10depth (m)In‐situ stress (kg/cm2) Figure 11.  The variation of in-situ horizontal stress 0h in normall-consolidated deposite soils and 0H in thrust fault zone.   References Kutschke, W.G. and Vallejo, L.E., 2011, Stability and Impacts of Unsupported Vertical Cuts in Stiff Clay, Geo-Frontiers 2011, 3619-3628. McCarthy, D.F., 1993, Essentials of Soil Mechanics and Foundations: Basic Geotechnics, Regents/ Prentice Hall, New Jersey.  Terzaghi, K., 1943, Theretical Soil Mechanics, John Wiley and Sons, New York. Thorne, C.R. and Abt, S.R., 1993, Analysis of a Riverbank in Stability Due to Toe Scour and Lateral Erosion, Earth Surface Processes and Landforms 18, 835-843. Yang,Z.Y., Hsiao,J.Q. and Chen,H.M., 2006, Stress-released Slope Movement Induced by Excavation in Fault Zone, Eurock2006, ISRM, Liege, Belgium, 671-674. 

Estimate the In-situ Earth Pressure in a Thrust Fault Zone by Vertical Cut

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Estimate the In-situ Earth Pressure in a Thrust Fault Zone by Vertical Cut

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