Cross-section distortion and springback characteristics of double-cavity aluminum profile in force controlled stretch-bending

3D elastic-plastic FE model for simulating the force controlled stretch-bending process of double-cavity aluminum profile was established using hybrid explicit−implicit solvent method.Considering the computational accuracy and efficiency,the optimal choices of numerical parameters and algorithms in FE modelling were determined.The formation mechanisms of cross-section distortion and springback were revealed.The effects of pre-stretching,post-stretching,friction,and the addition of internal fillers on forming quality were investigated.The results show that the stress state of profile in stretch-bending is uniaxial with only a circumferential stress.The stress distribution along the length direction of profile is non-uniform and the maximum tensile stress is located at a certain distance away from the center of profile.As aluminum profile is gradually attached to bending die,the distribution characteristic of cross-section distortion along the length direction of profile changes from V-shape to W-shape.After unloading the forming tools,cross-section distortion decreases obviously due to the stress relaxation,with a maximum distortion difference of 13%before and after unloading.As pre-stretching and post-stretching forces increase,cross-section distortion increases gradually,while springback first decreases and then remains unchanged.With increasing friction between bending die and profile,cross-section distortion slightly decreases,while springback increases.Cross-section distortion decreases by 83%with adding PVC fillers into the cavities of profile,while springback increases by 192.2%.

A novel method for simulating nuclear explosion with chemical explosion to form an approximate plane wave: Field test and numerical simulation

A nuclear explosion in the rock mass medium can produce strong shock waves,seismic shocks,and other destructive effects,which can cause extreme damage to the underground protection infrastructures.With the increase in nuclear explosion power,underground protection engineering enabled by explosion-proof impact theory and technology ushered in a new challenge.This paper proposes to simulate nuclear explosion tests with on-site chemical explosion tests in the form of multi-hole explosions.First,the mechanism of using multi-hole simultaneous blasting to simulate a nuclear explosion to generate approximate plane waves was analyzed.The plane pressure curve at the vault of the underground protective tunnel under the action of the multi-hole simultaneous blasting was then obtained using the impact test in the rock mass at the site.According to the peak pressure at the vault plane,it was divided into three regions:the stress superposition region,the superposition region after surface reflection,and the approximate plane stress wave zone.A numerical simulation approach was developed using PFC and FLAC to study the peak particle velocity in the surrounding rock of the underground protective cave under the action of multi-hole blasting.The time-history curves of pressure and peak pressure partition obtained by the on-site multi-hole simultaneous blasting test and numerical simulation were compared and analyzed,to verify the correctness and rationality of the formation of an approximate plane wave in the simulated nuclear explosion.This comparison and analysis also provided a theoretical foundation and some research ideas for the ensuing study on the impact of a nuclear explosion.

Subplanes of PG(2,qr), Ruled Varieties V2r-12 in PG( 2r,q), and Related Codes

In this note we consider ruled varieties V22r−1of PG(2r,q), generalizing some results shown for r=2,3in previous papers. By choosing appropriately two directrix curves, a V22r−1represents a non-affine subplane of order qof the projective plane PG(2,qr)represented in PG(2r,q)by a spread of a hyperplane. That proves the conjecture assumed in [1]. Finally, a large family of linear codes dependent on r≥2is associated with projective systems defined both by V22r−1and by a maximal bundle of such varieties with only an r-directrix in common, then are shown their basic parameters.

Subplanes of PG( 2, q 3 ) and the Ruled Varieties V 2 5 of PG( 6,q )

In this note we study subplanes of order q of the projective plane Π=PG( 2, q 3 ) and the ruled varieties V 2 5 of Σ=PG( 6,q ) using the spatial representation of Π in Σ, by fixing a hyperplane Σ ′ with a regular spread of planes. First are shown some configurations of the affine q-subplanes. Then to prove that a variety V 2 5 of Σ represents a non-affine subplane of order q of Π, after having shown basic incidence properties of it, such a variety V 2 5 is constructed by choosing appropriately the two directrix curves in two complementary subspaces of Σ. The result can be translated into further incidence properties of the affine points of V 2 5 . Then a maximal bundle of varieties V 2 5 having in common one directrix cubic curve is constructed.

Influence of High-Density Bedding Plane Characteristics on Hydraulic Fracture Propagation in Shale Oil Reservoir

The existence of high-density bedding planes is a typical characteristic of shale oil reservoirs.Understanding the behavior of hydraulic fracturing in high-density laminated rocks is significant for promoting shale oil production.In this study,a hydraulic fracturing model considering tensile failure and frictional slip of the bedding planes is established within the framework of the unified pipe-interface element method(UP-IEM).The model developed for simulating the interaction between the hydraulic fracture and the bedding plane is validated by comparison with experimental results.The hydraulic fracturing patterns in sealed and unsealed bedding planes are compared.Additionally,the effects of differential stress,bedding plane permeability,spacing,and the friction coefficient of the bedding plane are investigated.The results showed that a single main fracture crossing the bedding planes is more likely to form in sealed bedding planes under high differential stress.The decrease in bedding plane permeability and the increase in the friction coefficient also promote the fracture propagating perpendicular to the bedding planes.Shale with high-density bedding planes has a poorer fracturing effect than that with low-density bedding planes,as the hydraulic fracture is prone to initiate and propagate along the bedding planes.Moreover,higher injection pressure is needed to maintain fracture propagation along the bedding.An increase in bedding density will lead to a smaller fracturing area.Fracturing fluid seepage into the bedding planes slows shale fracturing.It is recommended that increasing the injection flow rate,selecting alternative fracturing fluids,and employing multi-well/multi-cluster fracturing may be efficient methods to improve energy production in shale oil reservoirs.

THE NONLINEAR STABILITY OF PLANE PARALLEL SHEAR FLOWS WITH RESPECT TO TILTED PERTURBATIONS

The nonlinear stability of plane parallel shear flows with respect to tilted perturbations is studied by energy methods.Tilted perturbation refers to the fact that perturbations form an angleθ∈(0,π/2)with the direction of the basic flows.By defining an energy functional,it is proven that plane parallel shear flows are unconditionally nonlinearly exponentially stable for tilted streamwise perturbation when the Reynolds number is below a certain critical value and the boundary conditions are either rigid or stress-free.In the case of stress-free boundaries,by taking advantage of the poloidal-toroidal decomposition of a solenoidal field to define energy functionals,it can be even shown that plane parallel shear flows are unconditionally nonlinearly exponentially stable for all Reynolds numbers,where the tilted perturbation can be either spanwise or streamwise.

Nonlinear constitutive models of rock structural plane and their applications

Structural planes play an important role in controlling the stability of rock engineering,and the influence of structural planes should be considered in the design and construction process of rock engineering.In this paper,mechanical properties,constitutive theory,and numerical application of structural plane are studied by a combination method of laboratory tests,theoretical derivation,and program development.The test results reveal the change laws of various mechanical parameters under different roughness and normal stress.At the pre-peak stage,a non-stationary model of shear stiffness is established,and threedimensional empirical prediction models for initial shear stiffness and residual stage roughness are proposed.The nonlinear constitutive models are established based on elasto-plastic mechanics,and the algorithms of the models are developed based on the return mapping algorithm.According to a large number of statistical analysis results,empirical prediction models are proposed for model parameters expressed by structural plane characteristic parameters.Finally,the discrete element method(DEM)is chosen to embed the constitutive models for practical application.The running programs of the constitutive models have been compiled into the discrete element model library.The comparison results between the proposed model and the Mohr-Coulomb slip model show that the proposed model can better describe nonlinear changes at different stages,and the predicted shear strength,peak strain and shear stiffness are closer to the test results.The research results of the paper are conducive to the accurate evaluation of structural plane in rock engineering.

A monolithic integrated medium wave Mercury Cadmium Telluride polarimetric focal plane array

A medium wave(MW)640×512(25μm)Mercury Cadmium Telluride(HgCdTe)polarimetric focal plane array(FPA)was demonstrated.The micro-polarizer array(MPA)has been carefully designed in terms of line grating structure optimization and crosstalk suppression.A monolithic fabrication process with low damage was explored,which was verified to be compatible well with HgCdTe devices.After monolithic integration of MPA,NETD<9.5 mK was still maintained.Furthermore,to figure out the underlying mechanism that dominat⁃ed the extinction ratio(ER),specialized MPA layouts were designed,and the crosstalk was experimentally vali⁃dated as the major source that impacted ER.By expanding opaque regions at pixel edges to 4μm,crosstalk rates from adjacent pixels could be effectively reduced to approximately 2%,and promising ERs ranging from 17.32 to 27.41 were implemented.

Remazolam combined with transversus abdominis plane block in gastrointestinal tumor surgery:Have we achieved better anesthetic effects?

Laparoscopic surgery is the main treatment method for patients with gastrointestinal malignant tumors.Although laparoscopic surgery is minimally invasive,its tool stimulation and pneumoperitoneum pressure often cause strong stress reactions in patients.On the other hand,gastrointestinal surgery can cause stronger pain in patients,compared to other surgeries.Transversus abdominis plane block(TAPB)can effectively inhibit the transmission of nerve impulses caused by surgical stimulation,alleviate patient pain,and thus alleviate stress reactions.Remazolam is an acting,safe,and effective sedative,which has little effect on hemodynamics and is suitable for most patients.TAPB combined with remazolam can reduce the dosage of total anesthetic drugs,reduce adverse reactions,reduce stress reactions,and facilitate the rapid postoperative recovery of patients.

Testing method of rock structural plane using digital drilling

The rock mass consists of rock blocks and structural planes,which can reduce its integrity and strength.Therefore,accurately obtaining the characteristics of the rock mass structural plane is a prerequisite for evaluating stability and designing supports in underground engineering.Currently,there are no effective testing methods for the characteristic parameters of the rock mass structural plane in underground engineering.The paper presents the digital drilling technology as a new testing method of rock mass structural planes.Flawed rock specimens with cracks of varying widths and angles were used to simulate the rock mass structural planes,and the multifunctional rock mass digital drilling test system was employed to carry out the digital drilling tests.The analysis focuses on the variation laws of drilling parameters,such as drilling pressure and drilling torque,affected by the characteristics of prefabricated cracks,and clarifies the degradation mechanism of rock equivalent compressive strength.Additionally,an identification model for the characteristic parameters of rock mass structural planes during drilling is established.The test results indicate that the average difference of the characteristics of prefabricated cracks identified by the equivalent compressive strength is 2.45°and 0.82 mm,respectively.The identification model while drilling is verified to be correct due to the high identification accuracy.Based on this,a method for testing the characteristic parameters of the surrounding rock structural plane while drilling is proposed.The research offers a theoretical and methodological foundation for precise in situ identification of structural planes of the surrounding rock in underground engineering.

Ultrasound-guided serratus anterior plane block enhances postoperative analgesia and recovery in thoracoscopic surgery

BACKGROUND The serratus anterior muscle,located in the lateral aspect of the thorax,plays a crucial role in shoulder movement and stability.Thoracoscopic surgery,while minimally invasive,often results in significant postoperative pain,complicating patient recovery and potentially extending hospital stays.Traditional anesthesia methods may not adequately address this pain,leading to increased complications such as agitation due to inadequate pain management.AIM To evaluate the application value of ultrasound-guided serratus anterior plane block(SAPB)in patients undergoing thoracoscopic surgery,focusing on its effects on postoperative analgesia and rehabilitation.METHODS Eighty patients undergoing thoracoscopic surgery between August 2021 and December 2022 were randomly divided into two groups:An observation group receiving ultrasound-guided SAPB and a control group receiving standard care without SAPB.Both groups underwent general anesthesia and were monitored for blood pressure,heart rate(HR),oxygen saturation,and pulse.The primary outcomes measured included mean arterial pressure(MAP),HR,postoperative visual analogue scale(VAS)scores for pain,supplemental analgesic use,and incidence of agitation.RESULTS The observation group showed significantly lower cortisol and glucose concentrations at various time points post-operation compared to the control group,indicating reduced stress responses.Moreover,MAP and HR levels were lower in the observation group during and after surgery.VAS scores were significantly lower in the observation group at 1 h,4 h,6 h,and 12 h post-surgery,and the rates of analgesic supplementation and agitation were significantly reduced compared to the control group.CONCLUSION Ultrasound-guided SAPB significantly improves postoperative analgesia and reduces agitation in patients undergoing thoracoscopic surgery.This technique stabilizes perioperative vital signs,decreases the need for supplemental analgesics,and minimizes postoperative pain and stress responses,underscoring its high application value in enhancing patient recovery and rehabilitation post-thoracoscopy.

An 8-Node Plane Hybrid Element for StructuralMechanics Problems Based on the Hellinger-Reissner Variational Principle

The finite element method (FEM) plays a valuable role in computer modeling and is beneficial to the mechanicaldesign of various structural parts. However, the elements produced by conventional FEM are easily inaccurate andunstable when applied. Therefore, developing new elements within the framework of the generalized variationalprinciple is of great significance. In this paper, an 8-node plane hybrid finite element with 15 parameters (PHQ8-15β) is developed for structural mechanics problems based on the Hellinger-Reissner variational principle.According to the design principle of Pian, 15 unknown parameters are adopted in the selection of stress modes toavoid the zero energy modes.Meanwhile, the stress functions within each element satisfy both the equilibrium andthe compatibility relations of plane stress problems. Subsequently, numerical examples are presented to illustrate theeffectiveness and robustness of the proposed finite element. Numerical results show that various common lockingbehaviors of plane elements can be overcome. The PH-Q8-15β element has excellent performance in all benchmarkproblems, especially for structures with varying cross sections. Furthermore, in bending problems, the reasonablemesh shape of the new element for curved edge structures is analyzed in detail, which can be a useful means toimprove numerical accuracy.

Semi-analytical solution for mechanical analysis of tunnels crossing strike-slip fault zone considering nonuniform fault displacement and uncertain fault plane position

The tunnel subjected to strike-slip fault dislocation exhibits severe and catastrophic damage.The existing analysis models frequently assume uniform fault displacement and fixed fault plane position.In contrast,post-earthquake observations indicate that the displacement near the fault zone is typically nonuniform,and the fault plane position is uncertain.In this study,we first established a series of improved governing equations to analyze the mechanical response of tunnels under strike-slip fault dislocation.The proposed methodology incorporated key factors such as nonuniform fault displacement and uncertain fault plane position into the governing equations,thereby significantly enhancing the applicability range and accuracy of the model.In contrast to previous analytical models,the maximum computational error has decreased from 57.1%to 1.1%.Subsequently,we conducted a rigorous validation of the proposed methodology by undertaking a comparative analysis with a 3D finite element numerical model,and the results from both approaches exhibited a high degree of qualitative and quantitative agreement with a maximum error of 9.9%.Finally,the proposed methodology was utilized to perform a parametric analysis to explore the effects of various parameters,such as fault displacement,fault zone width,fault zone strength,the ratio of maximum fault displacement of the hanging wall to the footwall,and fault plane position,on the response of tunnels subjected to strike-slip fault dislocation.The findings indicate a progressive increase in the peak internal forces of the tunnel with the rise in fault displacement and fault zone strength.Conversely,an augmentation in fault zone width is found to contribute to a decrease in the peak internal forces.For example,for a fault zone width of 10 m,the peak values of bending moment,shear force,and axial force are approximately 46.9%,102.4%,and 28.7% higher,respectively,compared to those observed for a fault zone width of 50 m.Furthermore,the position of the peak internal forces is influenced by variations in the ratio of maximum fault displacement of the hanging wall to footwall and the fault plane location,while the peak values of shear force and axial force always align with the fault plane.The maximum peak internal forces are observed when the footwall exclusively bears the entirety of the fault displacement,corresponding to a ratio of 0:1.The peak values of bending moment,shear force,and axial force for the ratio of 0:1 amount to approximately 123.8%,148.6%,and 111.1% of those for the ratio of 0.5:0.5,respectively.

Regulating the inner Helmholtz plane structure at the electrolyte-electrode interface for highly reversible aqueous Zn batteries

The development of aqueous Zn batteries is limited by parasitic water reactions,corrosion,and dendrite growth.To address these challenges,an inner Helmholtz plane(IHP)regulation method is proposed by employing low-cost,non-toxic maltitol as the electrolyte additive.The preferential adsorption behavior of maltitol can expel the water from the inner Helmholtz plane,and thus hinder the immediate contact between Zn metal and H_(2)O.Meanwhile,strong interaction between maltitol and H_(2)O molecules can restrain the activity of H_(2)O.Besides,the"IHP adsorption effect"along with the low LUMO energy level of maltitol-CF_(3)SO_(3)^(-)can promote the in-situ formation of an organic-inorganic complex solid electrolyte interface(SEI)layer.As a result,the hydrogen/oxygen evolution side reaction,corrosion,and dendrites issues are effectively suppressed,thereby leading to highly reversible and dendrite-free Zn plating/stripping.The Zn‖I_(2)battery with hybrid electrolytes also demonstrates high electrochemical performance and ultralong cycling stability,showing a capacity retention of 75%over 20000 charge-discharge cycles at a large current density of 5 A g^(-1).In addition,the capacity of the device has almost no obvious decay over20000 cycles even at-30℃.This work offers a successful electrolyte regulation strategy via the IHP adsorption effect to design electrolytes for high-performance rechargeable Zn-ion batteries.

Prognostic Role of Preoperative Tricuspid Annular Plane Systolic Excursion (TAPSE) in Mitral Valve Replacement (MVR) for Rheumatic Mitral Stenosis Patients

Tricuspid annular plane systolic excursion has been proposed as a simple and reproducible parameter for quantitative assessment of the right ventricular ejection fraction. The prognostic importance of preoperative TAPSE in patients with mitral valve replacement for rheumatic mitral stenosis patients is still under focused. Therefore, the objective of the study was to predict the outcome after MVR in rheumatic mitral stenosis patients in relation to preoperative TAPSE. This comparative cross-sectional study was conducted at the Department of Cardiac Surgery, National Heart Foundation Hospital and Research Institute. A total of 72 patients of rheumatic mitral stenosis patients who underwent mitral valve replacement were included in the study. They were divided into two groups: Group A and B. Group A included 36 patients with TAPSE 0.05) except for the preoperative TAPSE. Mean TAPSE of Group A was 13.17 (±1.40) and Group B was 18.61 (±1.57), the difference was statistically significant (p 0.05). Among the postoperative complications, including postoperative atrial fibrillation was higher in Group A (30.56%) than Group B (11.11%), mean ventilation time was higher in Group A (27.78%) than Group B (5.56%), length of intensive care was higher in Group A (33.33%) than Group B (11.12%), and hospital stay was higher in Group A (25.0%) than Group B (5.56%), (p < 0.05). Higher preoperative TASPE could be used as a prognostic tool for MVR in rheumatic mitral stenosis patients in our settings.

Review on dynamic analysis of road pavements under moving vehicles and plane strain conditions

This paper reviews works on the dynamic analysis of flexible and rigid pavements under moving vehicles on the basis of continuum-based plane strain models and linear theories.The purpose of this review is to provide in-formation about the existing works on the subject,critically discuss them and make suggestions for further research.The reviewed papers are presented on the basis of the various models for pavement-vehicle systems and the various methods for dynamically analyzing these systems.Flexible pavements are modeled by a homogeneous or layered half-plane with isotropic or anisotropic and linear elastic,viscoelastic or poroelastic material behavior.Rigid pavements are modeled by a beam or plate on a homogeneous or layered half-plane with material properties like the ones for flexible pavements.The vehicles are modeled as concentrated or distributed over a finite area loads moving with constant or time dependent speed.The above pavement-vehicle models are dynamically analyzed by analytical,analytical/numerical or purely numerical methods working in the time or frequency domain.Representative examples are presented to illustrate the models and methods of analysis,demonstrate their merits and assess the effects of the various parameters on pavement response.The paper closes with con-clusions and suggestions for further research in the area.The significance of this research effort has to do with the presentation of the existing literature on the subject in a critical and easy to understand way with the aid of representative examples and the identification of new research areas.

Study on the Evolution of Plane Shape of Guangfu Ancestral Hall Buildings and the Construction of Type Genealogy in the Ming and Qing Dynasties

This paper studies the clan temples in four periods,namely,the development period(early Ming Dynasty and before),the shaping period(mid-Ming Dynasty to early Qing Dynasty),the maturity period(mid-Qing Dynasty),and the programmed period(late Qing Dynasty),analyzes and summarizes their prototypical planform features and attempts to summarize and construct a genealogy of the architectural characteristics of the plane shape of clan temples.During the Ming and Qing dynasties,Guangfu ancestral halls in general showed a journey of development from a centripetal-single-linear-multi-linear-grid pattern,forming the unique Guangsanlu classic pattern in the Guangfu area.

Erector Spinae Plane Block Combined with Serratus Anterior Plane Block Versus Thoracic Paravertebral Block for Postoperative Analgesia and Recovery After Thoracoscopic Surgery:A Randomized Controlled Non-inferiority Clinical Trial

Objective This study aimed to compare the postoperative analgesia and recovery of ultrasound-guided erector spinae plane block combined with serratus anterior plane block(ESPB combined with SAPB)versus thoracic paravertebral block(PVB)after thoracoscopic surgery.Methods Ninety-two patients who underwent video-assisted thoracoscopic surgery(VATS)were randomly divided into group S(n=46)and group P(n=46).After anesthesia induction,the same anesthesiologist performed ultrasound-guided ESPB at T5 and T7 levels combined with SAPB at the level of the fifth rib in the midaxillary line in group S and ultrasound-guided PVB at T5 and T7 levels in group P.Patients in both groups were given 40 mL of 0.4%ropivacaine.Eighty-six patients completed the study(group S,n=44;group P,n=42).The morphine consumption,visual analogue scale(VAS)scores at rest and coughing,and frequency of remedial analgesia were recorded at 1,2,4,8,and 24 h postoperatively.Pulmonary function parameters were recorded at 1,4,and 24 h postoperatively,and the quality of recovery(QoR)-15 score at 24 h postoperatively.The adverse effects,duration of chest tube drainage and length of stay were also recorded.Results The morphine consumption at postoperative 4 and 8 h and the incidence of ipsilateral shoulder pain(ISP)were significantly lower in group S than in group P.The QoR-15 questionnaire score at postoperative 24 h was significantly lower in group P than in group S(P<0.05).The morphine consumption was lower at 24 h postoperatively in group S than in group P,with no significant difference found yet.The morphine consumption at other observed times,VAS scores,pulmonary function parameters,frequency of remedial analgesia,duration of chest tube drainage,length of stay,and incidence of other adverse events were comparable between group S and group P.Conclusion Ultrasound-guided ESPB combined with SAPB is non-inferior to PVB in terms of morphine consumption at postoperative 24 h and postoperative recovery.But,this approach can significantly reduce morphine consumption in the early postoperative period(0–8 h)after thoracoscopy with lower incidence of ISP.It is a simpler and safer operation.

Crystal plane induced in-situ electrochemical activation of manganese-based cathode enable long-term aqueous zinc-ion batteries

Rapid capacity decay and sluggish reaction kinetics are major barriers hindering the applications of manganese-based cathode materials for aqueous zinc-ion batteries.Herein,the effects of crystal plane on the in-situ transformation behavior and electrochemical performance of manganese-based cathode is discussed.A comprehensive discussion manifests that the exposed(100)crystal plane is beneficial to the phase transformation from tunnel-structured MnO_(2) to layer-structured ZnMn_(3)O_(7)·3H_(2)O,which plays a critical role for the high reactivity,high capacity,fast diffusion kinetics and long cycling stability.Additionally,a two-stage zinc storage mechanism can be demonstrated,involving continuous activation reaction and phase transition reaction.As expected,it exhibits a high capacity of 275 mAh g^(-1)at 100 mA g^(-1),a superior durability over 1000 cycles and good rate capability.This study may open new windows toward developing advanced cathodes for ZIBs,and facilitate the applications of ZIBs in large-scale energy storage system.

Dynamic damage evolution of bank slopes with serrated structural planes considering the deteriorated rock mass and frequent reservoirinduced earthquakes

To investigate the dynamic damage evolution characteristics of bank slopes with serrated structural planes,the shaking table model test and the numerical simulation were utilized.The main findings indicate that under continuous seismic loads,the deformation of the bank slope increased,particularly around the hydro-fluctuation belt,accompanying by the pore water pressure rising.The soil pressure increased and then decreased showed dynamic variation characteristics.As the undulation angle of the serrated structural planes increased(30°, 45°, and 60°),the failure modes were climbing,climbinggnawing,and gnawing respectively.The first-order natural frequency was used to calculate the damage degree(Dd)of the bank slope.During microseisms and small earthquakes,it was discovered that the evolution of Dd followed the“S”shape,which was fitted by a logic function.Additionally,the quadratic function was used to fit the Dd during moderately strong earthquakes.Through the numerical simulation,the variation characteristics of safety factors(Sf)for slopes with serrated structural planes and slopes with straight structural planes were compared.Under continuous seismic loads,the Sf of slopes with straight structural planes reduce stalely,whereas the Sf for slopes with serrated structural planes was greater than the former and the reduction rate was increasing.