Lifetime-Oriented Structural Design Concepts- P9 pot

198 3 Deterioration of Materials and Structures 0.1M % sodium chloride) increases the scaling by more than a factor of 4 (see Subsection 2.4.2). 3.2.2 High-Cycle Laboratory Tests on Soils Authored by Torsten Wichtmann, Andrzej Niemunis and Theodoros Triantafyllidis The accumulation phenomenon has been studied systematically on quartz sand with sub-angular grain shape. Most of the tests were performed on a grain size distribution curve (No. 3 in Figure 3.85a) with a mean grain size d 50 = 0.55 mm and a uniformity index C u =1.8. Numerous cyclic triaxial tests and cyclic multi-dimensional simple shear tests have been performed. A scheme of the cyclic triaxial device (four similar devices were available in the present study) is given in Figure 3.85b. Details are explained e.g. in [837, 835]. Cylindrical specimens with 10 cm diameter and 20 cm height were used. They were prepared by dry pluviation and afterwards they were water-saturated in order to measure volume changes via the pore water. The tests were performed under drained conditions. In the stress-controlled tests the axial effective stress σ 1 and the lateral effective stress σ 3 could be varied simultaneously using pneumatic loading devices. In Figure 3.85c typical stress paths with in-phase and out-of-phase cycles are presented in the p-q-plane. p = −(σ 1 +2σ 3 )/3andq = −(σ 1 − σ 3 ) denote Roscoe’s invariants. The average stress is described by p av and q av or the ratio η av = q av /p av . Alternatively, the isomorphic variables P = √ 3p and Q =  2/3q are used in the following. In most tests the cycles were applied with a frequency f ≤ 1 Hz, i.e. inertial forces were negligible small. The axial strain ε 1 and the volumetric strain ε v = ε 1 +2ε 3 were calculated from the measured changes of specimen height and volume. The deviatoric strain ε q = 2 3 (ε 1 −ε 3 ), the total strain ε =  (ε 1 ) 2 +2(ε 3 ) 2 and the isomorphic strain variables ε P =  1/3ε v and ε Q =  3/2ε q are derived quantities. In a cyclic test the residual strain in the first cycle may differ significantly from the strain in the subsequent cycles (Figure 3.85e). Thus, it is distin- guished between the first ”irregular” cycle and the subsequent ”regular” ones. The high cycle accumulation model described in Section 3.3.3 describes only the regular cycles (the first cycle is calculated implicitly, see Section 4.2.11). Thus, in the following only test results for the regular cycles are presented. The strain is composed of a residual (or cumulative) portion ε acc and an elastic, resilient portion ε ampl (strain amplitude, Figure 3.85e). In the context of polycyclic loading, ”rate” means a derivative with respect to the number of cycles N c , i.e. ˙  = ∂  /∂N c . The device used for the cyclic multi-dimensional simple shear tests is pre- sented in Figure 3.85d. An arbitrary displacement of the base plate in both horizontal directions is possible while the top cap is guided vertically. The horizontal movement is generated by an electrical motor and an eccentric. 3.2 Experiments 199 p av q av 1 η av = q av / p av σ av CSL max. strength in-phase (IP) cycles q = -(σ 1 -σ 3 ) p = (σ 1 +2σ 3 )/3 out-of-phase (OOP) cycles 2σ 1 ampl 2σ 3 ampl σ 1 av σ 3 av 2ε 1 ampl 2ε 3 ampl ε 1 acc ε 3 acc aluminium rings top cap base plate guidance rods soil specimen drainage ball bearing (hor. guidance) ball bearing (vert. guidance) eccentric rod electric motor F displ. transducer displ. transducer d) c) e) b) a) load cell displacement transducer pressure transducers (u, σ 3 ) diff. pressure transducer cell pressure back pressure u soil specimen (d = 10 cm, h = 20 cm) drainage axial load F av F ampl + - σ av σ ampl + - 33 (pneumatic loading system) 0.1 0.2 0.6 1 2 6 0 20 40 60 80 100 Finer by weight [%] Grain diameter [mm] Sand Gravel coarsefine finemedium 1 2 3 5 6 8 7 4 t,N c average accumulation curve (described by the high-cycle model) ε first "irregular" cycle "regular" cycles 2ε ampl ε acc ε irreg Fig. 3.85. a) Tested grain size distribution curves, b) Scheme of the cyclic triaxial device, c) Stress paths of cyclic triaxial tests in the p-q-plane, d) Scheme of the cyclic multi-dimensional simple shear (CMDSS) device, e) Course of strain in a cyclic triaxial test The eccentric runs in a cut-out of the base plate. Different paths of horizontal deformations can be tested by using different eccentrics and cut-outs. Lateral deformations of the specimens (diameter 10 cm, height 20 cm) are prevented by a stack of 200 aluminium rings which are guided by vertical rods in order to guarantee a linear deformation of the specimen boundaries. However, in 200 3 Deterioration of Materials and Structures -0.4 0 0.4 0.8 1.2 -1.5 -1.0 -0.5 0.5 0 1.0 1.5 2.0 2.5 3.0 Accumulated volumetric strain ε acc [%] v Accumulated deviatoric strain ε acc [%] q η av = 0.5 η av = 0.25 η av = 0 η av = -0.25 η av = -0.5 η av = -0.625 η av = -0.75 η av = -0.815 η av = 0.75 η av = 0.875 η av = 1.0 η av = 1.125 η av = 1.25 η av = 1.313 η av = 1.375 0 0 100 100 200 200 300 400 300 Average mean pressure p av [kPa] Average deviatoric stress q av [kPa] η = -0.50 η = -0.375 η = -0.88 = M e (ϕ c ) η = -0.25 η = -0.125 M e (ϕ p ) η = -0.75 η = -0.625 -100 -200 -300 M c (ϕ p ) η = 1.375 η = 1.313 N c = 20 N c = 100 N c = 1,000 N c = 10,000 N c = 100,000 acc. up to cycle: η = 0.75 η = 1.00 η = 0.50 η = 0.25 η = 1.25 = M c (ϕ c ) dilatancy dilatancy contractancy a) b) ε v acc ε q acc all tests: N c,max = 10 4 - 10 5 , p av = 200 kPa, ζ = q ampl /p av = 0.2 - 0.3 I D0 = 0.57 - 0.69, f = 0.1 - 1 Hz η av = -0.88 Fig. 3.86. a) ε acc q -ε acc v strain paths in tests with different average stress ratios η av at p av = constant, b) Direction of strain accumulation presented as a vector in the p-q-plane simple shear tests the distribution of stress and strain within the specimen is not homogeneous [162, 840]. Thus, the CMDSS test results are rather of a qualitative nature. In all CMDSS tests specimens were tested in the air-dry condition. First, the cyclic triaxial test results are discussed concerning the direc- tion of accumulation D acc q /D acc v . Tests were performed with different average stresses, some of them with triaxial compression and others with triaxial ex- tension. Figure 3.86a presents the ε acc q -ε acc v strain paths in tests with an average mean pressure p av = 200 kPa but with different average stress ratios η av .For an isotropic average stress (η av = 0) the accumulation is purely volumetric (D acc q ≈ 0). With increasing stress ratio |η av | the direction of accumulation becomes more deviatoric. If the average stress lies on the critical state line (CSL, known from monotonic tests) a purely deviatoric accumulation takes place. With increasing number of cycles a slight increase of the volumetric portion of the direction of accumulation was observed. For average stresses between the critical state lines a cyclic loading causes a compaction of the sand and a dilative behaviour is observed in the overcritical regime. It could be demonstrated that several other parameters (average mean pres- sure p av , stress amplitude q ampl , void ratio e, polarisation, shape of the cycles, static preloading, grain size distribution curve) do not influence the direction 3.2 Experiments 201 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0 0.5 1.0 1.5 2.0 q ampl [kPa] = 80 70 60 51 42 31 22 12 Acc. volumetric strain ε acc [%] v Acc. volumetric strain ε acc [%] v Acc. deviatoric strain ε acc [%] q Acc. deviatoric strain ε acc [%] q 0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0 1.2 Q [kPa] 82 P [kPa] 100 100 346 80 80 a) b) all tests: N c,max = 10 4 , p av = 200 kPa, η av = 0.5, I D0 = 0.56 - 0.64, f = 0.05 Hz all tests: N c,max = 10 5 , p av = 200 kPa, η av = 0.75, I D0 = 0.58 - 0.61, f = 1 Hz Fig. 3.87. a) ε acc q -ε acc v strain paths in tests with different stress amplitudes q ampl , b) ε acc q -ε acc v strain paths in tests with different polarizations of accumulation [838, 835]. A constant direction of accumulation (= direction of the ε acc q -ε acc v -strain path) is shown for different stress amplitudes q ampl in Figure 3.87a and for different stress polarisation Q ampl /P ampl in Figure 3.87b. The direction of strain accumulation (”cyclic flow rule”) has been found to be almost exclusively influenced by the stress ratio η av . The cyclic flow rule can be clearly illustrated in the p-q-plane (Figure 3.86b). For this purpose an ε acc q -ε acc v -arrow is plotted from the average stress σ av of a test. It could be demonstrated [838, 835] that the ratio D acc q /D acc v can be ap- proximated by the flow rule for the monotonic loading of clay (modified Cam Clay model) or by the hypoplastic flow rule (Section 3.3.3). The intensity of accumulation is a function of several parameters. Figure 3.88a presents typical accumulation curves ε acc (N c ) in tests with IP cycles and different stress amplitudes q ampl . The intensity D acc of accumulation increases with increasing q ampl . If the residual strain ε acc is plotted versus the square of the strain amplitude (¯ε ampl ) 2 linear curves are obtained independently of the number of cycles (Figure 3.88b). Since in the stress-controlled tests the strain amplitude ε ampl varies slightly with N c , a mean value of the strain amplitude was used on the abscissa in Figure 3.88b (here and in the following a bar over a quantity denotes that a mean value over N c is used, i.e. ¯  = 1 N c  N c 0  dN c ). The division of ε acc by a void ratio function ¯ f e (Table 3.23) on the ordinate considers slightly different initial void ratios e 0 and different compaction rates ˙e. The proportionality between D acc and the square of the strain amplitude (ε ampl ) 2 has been described by the function f ampl (Table 3.23) and holds up to ε ampl =10 −3 [835]. Another test series was performed in order to study the influence of the polarization of the cycles in the stress or strain space. One-dimensional stress cycles with six different polarizations (tan α PQ = Q ampl /P ampl )inthe 202 3 Deterioration of Materials and Structures 10 0 10 1 10 2 10 3 10 4 10 5 0 0.4 0.8 1.2 1.6 2.0 ε acc [%] Number of cycles N c [-] all tests: p av = 200 kPa, η av = 0.75, I D0 = 0.58 - 0.61, f = 1 Hz q ampl [kPa] = 80 70 60 51 42 31 22 12 0 0.5 1.0 1.5 2.0 ε acc / f e [%] ( ε ampl ) 2 [10 -7 ] 0 2 4 6 8 10 all tests: p av = 200 kPa, η av = 0.75, I D0 = 0.58 - 0.61, f = 1 Hz N c = 100,000 N c = 50,000 N c = 10,000 N c = 1,000 N c = 100 N c = 20 a) b) e) c) 0 200 400 600 800 1,000 0 1 2 3 4 5 6 7 Residual strain ε acc [%] Number of cycles N c [-] γ 23 γ 13 γ ampl 13 γ ampl = 5.8 10 -3 , I D0 = 0.61 13 γ 23 γ 13 γ ampl 13 γ ampl 13 γ ampl 23 = γ ampl = 6.5 10 -3 , I D0 = 0.56 13 0123456 0 2 4 6 8 ε acc / f e [%] all tests: p av = 200 kPa, η av = 0.5, I D0 = 0.56 - 0.64, f = 0.05 Hz Strain amplitude ε ampl [10 -4 ] Q [kPa] 82 P [kPa] 100 100 346 80 80 0˚ 10˚ 30˚ 54.7˚ 75˚ 90˚ α PQ = d) 0 1,000 2,000 3,000 4,000 5,000 0 2 4 6 8 Number of cycles N c [-] change of the polarization x 1 x 2 x 3 all tests: p av = 16 kPa, γ ampl = 5.8 10 -3 0.53 - 0.54 I D0 = 0.61 - 0.63 0.68 - 0.72 0.81 - 0.81 Residual strain ε acc [%] 13 ε acc / f ampl [%] 0.56 0.60 0.64 0.68 0.72 0.76 0.80 0 0.1 0.2 0.3 0.4 all tests: p av = 200 kPa, η av = 0.75, ζ = 0.3, f = 1 Hz N c = 100,000 N c = 50,000 N c = 10,000 N c = 1,000 N c = 100 N c = 20 f) x 1 x 2 x 3 N c = 10 4 Void ratio e [-] Fig. 3.88. Results of drained cyclic triaxial tests: a) Accumulation curves ε acc (N c ), b) Dependence of D acc on strain amplitude ε ampl andc)onthepolarization tan α PQ = Q ampl /P ampl of the cycles, d) Influence of polarization changes, e) De- pendence of D acc on the shape of the strain loop and f) on void ratio e isomorphic P-Q-plane were tested. For each polarization tests with different amplitudes were performed. In Figure 3.88c the residual strain after 10,000 cycles is plotted versus a mean value of the strain amplitude. For a given ¯ε ampl the residual strain does not significantly depend on the polarization of the cycles (as long as the polarization does not change, see below). The effect of changes of the polarization was studied in the multi-di- mensional simple shear device. 1,000 cycles with a certain polarization were followed by 4,000 cycles with a perpendicular polarization. Figure 3.88d re- veals that a sudden change of the polarization causes a temporary increase of 3.2 Experiments 203 the accumulation rate. In the high-cycle model (Section 3.3.3) this effect is described by a function f π . The influence of the shape of the strain loop has also been studied in CMDSS tests (Figure 3.88e). A circular cycle compared with a one- dimensional cycle with identical maximum span (i.e. identical shear strain amplitude in the γ 13 -direction) causes an approximately twice larger accu- mulation rate. Thus, the shape of the strain loop significantly influences the accumulation rate. In the accumulation model (Section 3.3.3) the shape of the strain loop has been captured by a tensorial definition of the amplitude (Section 2.5.2). Figure 3.88f presents results of cyclic triaxial tests with identical stresses but different initial void ratios. The residual strain ε acc after different values of N c has been normalized by the amplitude function f ampl (Table 3.23) in order to consider slightly different strain amplitudes and was plotted versus a mean value of the void ratio ¯e. The increase of D acc with increasing void ratio may be described by a hyperbolic function f e as given in Table 3.23. Figure 3.89a presents the dependence of D acc on the average mean pressure p av . Interestingly, the intensity of accumulation increases with decreasing p av . The data of tests with different stress ratios η av are plotted in Figure 3.89b. A normalized stress ratio ¯ Y av ≈ η av /M (ϕ c ) has been used on the x-axis with η = M(ϕ c ) being the inclination of the CSL. The accumulation rate increases with increasing stress ratio. The stress-dependence of D acc may be captured by the functions f p and f Y which are given in Table 3.23. Figure 3.89c contains the accumulation curves from the different test series normalized by the functions ¯ f ampl , ¯ f e , f p , f Y and f π (Table 3.23). The curves for different stress amplitudes, initial densities, average mean pressures and average stress ratios fall together into a band which can be approximated by the historiotropic function f N (Table 3.23). It consists of a logarithmic and a linear portion. The logarithmic portion is pre-dominant up to N c =10 4 while the linear portion is necessary to describe the curves ε acc (N c )forlarger numbers of cycles. The large influence of a cyclic preloading is illustrated in Figure 3.89d. It presents the evolution of void ratio e with the number of cycles N c in three cyclic triaxial tests with identical stresses but slightly different initial values of e. Considering a state with identical void ratio and identical stress (as marked by the horizontal line in Figure 3.89d) the rate of compaction ˙e of a freshly pluviated sample (No. 1) is significantly larger than the rate of a sample (No. 3) which was preloaded by 40,000 load cycles. Thus, the accumulation rate is significantly reduced by a cyclic preloading. For this reason a prediction of accumulation with a high-cycle model the knowledge of void ratio and stress alone is not sufficient. Information about the cyclic preloading of the soil is indispensable. Unfortunately, the cyclic preloading cannot be directly measured in situ. It has to be determined by correlations. Despite considerable efforts a clear correlation of cyclic preloading with dynamic soil properties (e.g. P- and S-wave velocities) could not be established [845, 846]. A correlation 204 3 Deterioration of Materials and Structures 0 0.2 0.4 0.6 0.8 10 0 10 1 10 2 10 3 10 4 10 5 Number of cycles N c [-] ε acc / (f ampl f e f p f Y f e f π ) [%] tests on f ampl tests on f p tests on f Y tests on f e f N c) e) d) 0.61 0.62 0.63 0.64 0.65 0 Number of cycles N c [-] Void ratio e [-] e 1 10 5 2 10 4 4 10 4 6 10 4 8 10 4 all tests: p av = 100 kPa, q av = 77 kPa, q ampl = 55 kPa despite identical void ratio and identical stress: e 1 > e 2 > e 3 e 3 e 2 0 25,000 50,000 75,000 100,000 0 0.4 0.8 1.2 1.6 2.0 2.4 Number of cycles N c [-] ε acc [%] q ampl [kPa] = 80 60 40 20 all tests: p av = 200 kPa, η av = 0.75, I D0 = 0.58 - 0.63, f = 0.25 Hz t q 150 20 40 60 80 t q 150 20 40 60 80 t q 150 20 40 60 80 t q 150 20 40 60 80 t q 150 20 40 60 80 1 3 6 4 2 5 t q 150 20 40 60 80 q ampl = 0 100 200 300 0 0.5 1.0 1.5 2.0 Average mean pressure p av [kPa] ε acc / (f ampl f e ) [%] all tests: η av = 0.75, ζ = 0.3, I D0 = 0.61 - 0.69, f = 1 Hz 0 0.2 0.4 0.6 0.8 1.0 1.2 0 0.5 1.0 1.5 2.0 2.5 3.0 all tests: p av = 200 kPa, ζ = 0.3, I D0 = 0.57 - 0.67, f = 1 Hz ε acc / (f ampl f e ) [%] Average stress ratio Y av [-] N c = 100,000 N c = 50,000 N c = 10,000 N c = 1,000 N c = 100 N c = 20 N c = 100,000 N c = 50,000 N c = 10,000 N c = 1,000 N c = 100 N c = 20 a) b) Fig. 3. 89. Results of drained cyclic triaxial tests: a) Dependence of D acc on average mean pressure p av , b) on average stress ratio ¯ Y av ≈ η av /M c (ϕ c ), c) on the number of cycles N c and d) on cyclic preloading. e) Tests with packages of cycles with different amplitudes with the liquefaction resistance, however, could be formulated [844] but its practical application has still to be proven. A correlation of cyclic preloading with acoustic emissions seems to be rather insufficient [581]. As an alternative, the cyclic preloading could be determined by cyclic test loadings in situ (some ideas are explained in [835]). In many practical problems the amplitude of the cycles is not constant but varies with the cycles. Such random cyclic loadings could be replaced by 3.2 Experiments 205 0.1 0.2 0.5 1 2 5 10 0 0.1 0.2 0.3 Mean grain diameter d 50 [mm] Uniformity coefficient C u = d 60 /d 10 [-] 0.06 0.2 0.6 2 6 0 20 40 60 80 100 Finer by weight [%] Grain diameter [mm] Sand Gravel coarsefine finemed. 1 2 3 5 64 1 2 3 5 6 4 12345 0 0.2 0.4 0.6 0.8 1.0 1.2 ε acc / f ampl [%] ε acc / f ampl [%] 0.06 0.2 0.6 2 6 0 20 40 60 80 100 Finer by weight [%] Grain diameter [mm] Sand Gravel coarsefine finemed. 8 7 3 8 7 3 after N c = 10 5 after N c = 10 5 Fig. 3.90. Influence of the grain size distribution curve on D acc packages of cycles each with a constant amplitude if the sequence of applica- tion would not affect the residual strain that means if Miner’s rule [543] were applicable to soil. In order to examine the influence of the order of packages cyclic triaxial tests were performed [839, 835]. In each test four packages each with 25,000 cycles were applied. The amplitudes q ampl = 20, 40, 60 and 80 kPa were applied in different sequences. Figure 3.89e presents the accumulation curves. Irrespectively of the sequence the residual strains at the end of the tests are quite similar. Thus, for a constant polarization of the cycles and as a first approximation Miner’s rule can be assumed to be valid for sand. In cyclic triaxial tests with different frequencies 0.05 ≤ f ≤ 2 Hz no influ- ence of the loading frequency could be detected [835]. Thus, in this range the loading frequency does not need to be considered in a high-cycle model. In [835] also the influence of a static preloading was studied and found small. The grain size distribution curve has also a significant influence on the accumulation rate. In order to develop a simplified procedure for the determi- nation of the material constants of the high-cycle model presented in Section 3.3.3, approx. 200 cyclic triaxial tests have been performed on eight different grain size distribution curves (Figure 3.85a) of a natural quartz sand. The re- sults have been documented in detail in [841]. Figure 3.90 compares the strain remaining in the eight sands for similar test conditions (similar values of ε ampl , I D0 , σ av ). The accumulation rate increases with decreasing mean grain size d 50 and grows significantly with increasing coefficient of uniformity C u .Inthe accumulation model (Section 3.3.3) the influence of the grain size distribution curve has to be considered by different sets of material constants which enter the f-functions. Correlations of these constants with index properties (d 50 , C u , e min ) are discussed in [841]. In contrast to drained cyclic tests the pore water pressure u accumulates in tests without drainage. Results of a typical test with an isotropic initial 206 3 Deterioration of Materials and Structures 0 1,000 2,000 3,000 4,000 5,000 6,000 Time [s] 0 1,000 2,000 3,000 4,000 5,000 6,000 Time [s] 0 100 200 300 400 500 Stresses σ 3 , u [kPa] u σ 3 σ 3 + u = const. Vertical strain ε 1 [%] -10 -5 0 5 10 43 44 45 46 47 N c = 0 -60 -40 -20 20 40 60 -10 -8 -6 -4 -2 0 2 4 6 8 10 Vertical strain ε 1 [%] Deviatoric stress q [kPa] 43 4544 46 47 N c = 1-42 4546N c = 43 4244 1-41 0 20 40 60 80 100 p [kPa] 0 20 40 60 -20 -40 -60 q [kPa] a) b) c) d) I D = 0.66 q preload = 50 kPa N c,preload = 10 ampl q ampl = 45 kPa Fig. 3.91. Results of an undrained cyclic triaxial test (after a drained cyclic preload- ing with N c,preload cycles at amplitude q ampl preload , see [844]): a) excess pore pressure accumulation u(t), b) vertical strain ε 1 (t), c) stress-strain hysteresis, d) effective stress path in the p-q-plane stress are presented in Figure 3.91. The axial cyclic loading was applied stress- controlled. The excess pore water pressure increased with each cycle (Figure 3.91a). When after some cycles the condition u ≈−σ 1 = −σ 3 was approached (i.e. the effective stress was σ ≈ 0, so-called ”initial liquefaction”), the strain amplitude ε ampl 1 started to grow rapidly (Figure 3.91b). During the subse- quent cycles the stress-strain-hystereses (Figure 3.91c) showed no shearing resistance over a wide range of ε 1 and the stress path in the p-q-plane fol- lowed a butterfly-like curve (Figure 3.91d). After several such ”cyclic mobility loops” the specimens failed during triaxial extension. A ”full liquefaction” is often quantified with a double amplitude 2ε ampl 1 above approx. 10 %. The stiffness E E E of a high-cycle model (Section 3.3.3) may be developed by comparing e.g. the accumulation of strain in drained cyclic triaxial tests and the relaxation of stress in undrained cyclic triaxial tests with similar initial conditions. From the rate of pore water pressure ˙u in undrained cyclic triaxial tests and the rate of volumetric strain accumulation D acc v in drained cyclic triaxial tests one can derive the bulk modulus K =˙u/D acc v . A study of the stiffness E E E is documented in [841]. 3.2 Experiments 207 340 380 420 460 u [kPa] 0 500 1000 1500 Time t [s] 3500 4000 4500 23000 23500 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 0.58 0.60 0.62 0.64 Void ratio e [-] Δe 2 = 0.021 Δe 1 = 0.010 Δe 3 = 0.024 undrained cycles package No. 3, N c = 900 at σ av = 0 undrained cycles package No. 2, N c = 100 at σ av = 0 undrained cycles package No. 1, N c = 0 at σ av = 0 Re-cons. 1 Re-cons. 2 Re-cons. 3 0 40 80 120 -80 -60 -40 -20 0 20 40 60 80 q [kPa] p [kPa] Fig. 3.92. Change of void ratio Δe during re-consolidation after different numbers of cycles in the liqefied state (σ = 0) An unsolved problem in connection with the post-cyclic behaviour is de- picted in Figure 3.92 [579]. It presents displacement-controlled tests with three test phases. In the first phase the specimen was re-consolidated directly after a zero effective stress (σ = 0) was reached. In the second and third phase the specimen was monotonically re-consolidated after different numbers of cycles at σ = 0. Evidently the compaction during re-consolidation increases with the number of cycles at σ = 0. Similar observations were made by Shamoto et al. [734]. A latent accumulation in the grain skeleton seem to take place during the undrained cycles and it becomes visible during re-consolidation. Future investigations on this phenomenon are necessary. 3.2.3 Structural Testing of Composite Structures of Steel and Concrete Authored by Gerhard Hanswille and Markus Porsch 3.2.3.1 General In recent decades as a result of the benefits of combining the advantages of its components, steel-concrete composite beams have seen widespread use in buildings and bridges. The composite action of the components steel and con- crete is realized by the shear connectors welded on the steel flange. Because of its economic and fast application headed shear studs are the most common used type of shear connectors in steel-concrete composite constructions. Typ- ical examples of applications of headed studs in composite bridges are given in Figure 3.93. [...]... Fig 3.94 Load-deflection behaviour of headed shear studs embedded in solid concrete slabs under static loading design codes for bridges (DIN-Fachbericht 104) [18], which is based on the design rules of the Eurocode 4 [22, 23] the peak load level under service loads is limited to 60 % of the design value of the shear resistance of a stud Due to this limitation mainly the components PW and PB are activated... 2[33]) associated with the test begin for each series according to EN 206-1 [12] In test series S1 - S6 on one side and in series S9, S11 and S13 otherwise structural steel beams, headed shear studs and reinforcing bars were from the same batch Structural steel beams of HEB 260 section with the material quality S235 J2G3 were used in each test Stud shear connectors, which were welded automatically... double logarithmic scale this model represents a linear relationship between the stress range Δτ in the stud shank and the number of cycles to failure N with the slope 1/m It was taken as the basis for the design rules of 210 3 Deterioration of Materials and Structures R (log) 1000 m 1m R Nc N N c c Nc test results: m = 8.658 Eurocode 4: m = 8 R cm 100 = 110 N/mm² 5%-fractile P d P ck = 90 N/mm² 4 P d2 N... points in earlier investigations was that the repeated loading causes a reduction of the static strength of the shear studs not only at the end of their lifetime but within [593] This indicates that the design concepts in the current codes [22, 23] does not describe sufficiently the real behaviour, because the determination of the ultimate load bearing capacity and the fatigue resistance takes place with... (a) Safety concept to determine the lifetime of composite structures subjected to high cycle loading according to present codes, (b) Actual influence of high cycle loading on lifetime In Figure 3.96 the design concept of the present codes is compared with the actual influence of high cycle loading on the lifetime of composite structures So far the deterioration in strength of stud shear connectors and... a certain number of load cycles, before determining the residual static strength In most cases these numbers were only a small fraction of the mean number of cycles to failure according to the current design concept [685], taking into account a slope m = 8 3.2.3.2.2 Test Specimens The specimen used in the push-out tests consists of a 650 mm high HEB260 profile and two 650 mm high, 600 mm wide and 150... additional frictional forces in the interface between concrete and steel flange, resulting in component PR Because of the complex load deflection behaviour of headed studs embedded in solid slabs so far no design formula exists, which describes the ultimate shear resistance and the amount of each component by means of a mechanical model The lifetime of cyclic loaded headed shear studs is effected by the load . loading design codes for bridges (DIN-Fachbericht 104) [18], which is based on the design rules of the Eurocode 4 [22, 23] the peak load level under service loads is limited to 60 % of the design. P R . Because of the complex load deflection behaviour of headed studs embedded in solid slabs so far no design formula exists, which describes the ultimate shear resistance and the amount of each component. visible during re-consolidation. Future investigations on this phenomenon are necessary. 3.2.3 Structural Testing of Composite Structures of Steel and Concrete Authored by Gerhard Hanswille and