At higher ductilitiestheir absolute value remains about constant and their percentagecontribution to the measured top displacement reduces.Test Unit W3 was able to complete two full cycles at ductility8 before failing on its way to ductility 10. However, significantdamage already occurred during the second cycle to ductility 8with the fracture of a D12 reinforcing bar on the south side of thewall. The hysteretic behaviour plotted in Fig. 7e is similar to thatof Test Unit W2 and does not require further discussion. On theother hand, the shear deformation of Test Unit W3 is larger thanthe shear deformation of Test Unit W2 (see Fig. 7d and f) and isconsistentwith the crack patterns shown in Fig. 8. At displacementductility 1 the total deformation of Test UnitW3 ismade up by 44%fixed-end deformation, 42% flexural deformation and 14% sheardeformation. The peak base shear measured during the test was262 kNwhich corresponds to a nominal peak shear stress of  max DVmax=.0:8bwlw/ D 7:1 MPa (0:61pf0cMPa) hence showing that HFCis potentially capable of transferring large shear forceswithout theneed for additional bar reinforcement.However, this large nominalpeak shear stress should be interpretedwith caution because of thebarbelled section of Test UnitW3 whose large boundary elementssurely helped resisting shear and because of the relatively lowaspect ratio of the unit which allowed an inclined-strut load-carryingmechanism. In fact, very little information on the ultimateshear strength of HFC is available and additional investigations areneeded.Fig. 8 displays the three test units at failure where the differentcrack patterns and the spalling of the concrete cover in theboundary regions of Test Unit W1 can be observed. Two differentkinds of cracks formed in the HFC walls during testing: a largecrack formed at the construction joint and thinner cracks formedalong almost the entire height of the wall. Test Unit W1 showedno cracking along the first 500 mm of the wall because thesleeves prevented bonding between the flexural reinforcementand the HFC. Owing to the shorter sleeves Test Unit W2 hada more extensive crack pattern. After yielding of the flexuralreinforcement the maximum crack width measured on the wallwas about 0.1 mm. All cracks fully closed upon unloading. Thecrack at the construction joint opened considerably and remainedopen after unloading causing almost the totality of the residualdeformations. During the test two kinds of cracks formed in theplastic hinge zone of Wall W3: bending cracks and shear cracks.Bending cracks appeared in the boundary regions and were almosthorizontal, while shear cracks formed in the web zone of the walland their orientation was diagonal to vertical. The shear cracksopened because of the reduced thickness of the web zone of TestUnit W3, which led to higher shear stresses in this zone than wasthe case for Test Units W1 and W2. The maximum crack widthmeasured during the test was 0.3mm, which is still very small andcan easily be bridged by the fibres of HFC [15,16].4. Numerical simulations4.1. Numerical model and relevant material propertiesThe behaviour of the test units was simulated numerically bymeans of the fully nonlinear 3D finite element models depicted in  Fig. 9. In this paper only the principal characteristics of the modelsbelonging to Test Units W2 and W3 are discussed, for furtherdetails the reader is referred to [4].The models were built using the well-known general purposefinite element program ABAQUS [6]. The HFC was modelled with3D 8-node solid elements (Type C3D8) and every vertical reinforc-ing bar was modelled using beam elements (Type B31) that weredirectly connected to the nodes of the concrete mesh. To allow forstrain penetration the free length of the beam elements crossingthe construction joint was increased from 200 mm, i.e. the lengthof the steel sleeves, to 300 mm based on a conservative applica-tion of the equation for the estimation of the strain penetrationlength proposed by Paulay and Priestley in [1]. The constructionjoint between the wall and the footing was modelled using gap el-ements (Type GAPUNI)which allowed no horizontal slipwhile fea-turing perfect contact in compression and unrestrained opening intension. The mechanical properties of the reinforcing steel weredescribed by means of ABAQUS’s standard elasto-plastic modelusing nonlinear isotropic/kinematic hardening. The input param-eters for this model were calibrated against the stress–strain re-lationships obtained from the monotonic and cyclic coupon testspresented in [4]. The mechanical properties of HFC were modelledusing ABAQUS’s own Concrete Damage Plasticity (CDP) formula-tion. The *CONCRETE COMPRESSION HARDENING curve was fittedto the stress–strain relationship of the cylinder compression testthat was the closest to the average of the three curves plotted inFig. 4.As no direct tension tests on HFC material samples couldbe conducted in the framework of the structural wall tests, the*CONCRETE TENSION HARDENING curve was computed usingback-analysis on the 3-point bending tests presented in Section 2.2.The HFC prisms used for the 3-point bending tests were modelledwith ABAQUS using the CDP material model and making differentassumptions on the tensile behaviour of HFC based on directtensile tests carried out by other researchers on HFC samples witha similar fibre mix [17]. Two of these assumptions are shownin Fig. 10a while the respective force–deflection curves of thenumerically simulated 3-point bending tests are compared toexperimental evidence in Fig. 10b. The simulation of the 3-pointbending test using Assumption 2 as a characterization of thetensile behaviour of HFC yielded a very good agreement betweenthe test results and the numerical simulation up to a verticaldeflection of about 1.8mmwhich corresponds to 1=122 of the spanlength (Fig. 10b). Afterwards a difference between experimentand simulation is noticeable. However, this was not deemed tobe significant because during the test of Walls W2 and W3 muchsmaller strains were reached. Hence, Assumption 2 in Fig. 10a wasFig. 10. Different assumptions regarding the uniaxial tensile behaviour of HFC (a)and results of the relevant numerical simulations of the 3-point bending tests onthe Test UnitW3 material samples (b).retained as the better estimate of the actual tensile behaviour ofHFC. These simulations refer to thematerial that was used to buildTest UnitW3; for Test UnitW2 a similar approach was used.Unfortunately, in the framework of this research project nomaterial tests could be carried out in order to characterize thecyclic behaviour of HFC. In the literature little information wasfound and for this reason it was decided to choose the parametersgoverning the cyclic behaviour of the CDP model based onthe findings presented in [18] even if they actually refer to adifferent fibre-reinforced cementitious material. A key issue wasthe definition of the unloading and reloading branches after atensile excursion. According to [18] the behaviour after a tensileexcursion is characterized by steep initial elastic unloading toalmost zero stress followed by crack closing with low stiffnessand afterwards by reloading with gradually increasing stiffnessin the region of zero absolute strain. It is not possible to exactlyreproduce this kind of behaviourwith ABAQUS’s CDPmodel, hencethe parameter *CONCRETE TENSION DAMAGE (*CTD) governingthe unloading after a tensile excursion was chosen to obtain anunloading stress–strain curve as origin-oriented as possible. It wasnot possible to set the parameter *CTD in such a way as to obtaina perfectly origin-oriented behaviour because in that case thenumerical model did no longer converge.4.2. Comparison of the numerical and the experimental resultsThe numerical and the experimental results are compared inFig. 11 in terms of force–deformation relationships. The qualityof the numerical results is similar for Test Units W2 and W3;hence in the following only the results for 非线性循环行为混杂纤维混凝土结构墙英文文献和中文翻译(5):http://www.751com.cn/fanyi/lunwen_57270.html