ANALYSIS OF STATIC AND DYNAMIC HORIZONTAL LOAD
ANALYSIS OF STATIC AND DYNAMIC HORIZONTAL LOAD TESTS ONSTEEL PIPE PILESPastsakorn Kitiyodom, Kanazawa University, Kanazawa, JapanTatsunori Matsumoto, Kanazawa University, Kanazawa, JapanEiji Kojima, Japan Pile Corporation, Tokyo, JapanHiromichi Kumagai, Japan Pile Corporation, Tokyo, JapanKouichi Tomisawa, Civil Engineering Research Institute of Hokkaido, Hokkaido, JapanIn order to estimate the deformation and load distribution of a singlepile subjected to dynamic horizontal load as well as vertical load, asimplified method of three-dimensional numerical analysis,KWaveHybrid program, is developed using a hybrid model. In thehybrid model, the pile is modelled as elastic beams, and the soil ateach pile node is treated as springs and dashpots in both verticaland horizontal directions. KWaveHybrid is also able to analyse thestatic response of the pile. Validity of the newly developed programis examined through comparisons with theoretical values andhorizontal dynamic and static pile load test resultsINTRODUCTIONIn a seismic area such as Japan, application ofthe dynamic or rapid pile load test to horizontalpile load testing would be very useful in theseismic design of the pile foundation. Severalcomputer programs for analysing the onedimensional wave propagation in a pile havebeen developed, such as Smith method (Smith,1960), CAPWAP (Rausche et al., 1972),WEAP (Goble & Raushe, 1976), TNOWAVE(TNO, 1977), KWave (Matsumoto & Takei,1991) and KWaveFD (Wakisaka et al., 2004).However, all of these programs can be appliedto the problem in vertical direction only.It has been believed that the static load test isthe most reliable method to obtain the loaddisplacement relation of a pile. Most static loadtests are conducted using reaction piles as thereaction system. In the work of Kitiyodom et al.(2004), it is suggested that the influence of thereaction piles on the measured loaddisplacement relation may not be neglected,and that an interpretation of the measureddata is required to obtain a true loaddisplacement relation of the pile.In this study, a computer programKWaveHybrid has been developed based on ahybrid model. In KWaveHybrid, the horizontalresistance of the piles is incorporated into thehybrid model so as to be able to analyse thedeformation and load distribution of a singlepile subjected to horizontal load as well asvertical load. The program can be also used tocalculate the static load-displacement relationof the pile in both horizontal and verticaldirections.For axial compressive pile load test, thedynamic load testing or the rapid load testingis widely used because of the fact that thesemethods are unsusceptible to reaction piles,and require less time and cost compared withthe conventional static load test wherereaction piles are employed. The dynamic loadtesting and the rapid load testing, however,require interpretation of the measured signalsto derive a corresponding static loaddisplacement relation. Especially, for dynamicload test in which wave propagationphenomena in the pile cannot be neglected,wave matching analysis is indispensable.In order to examine the validity of the newlydeveloped program, verification analyses arecarried out first. Then the program is applied to690
The slider value is equal to the staticmaximum shaft resistance in the verticaldirection and is equal to the limit horizontalpressure in the horizontal direction.the static and dynamic horizontal load tests ofactual steel pipe piles.METHOD OF ANALYSISThe total dynamic friction in vertical direction,total, is generally taken as a non-linear functionof velocity, according toFig. 1 illustrates the hybrid modelling of thepile and the soil used in this study. The pile ismodelled as beam elements with masses andthe soil is treated as springs and dashpots.totalFig. 2 shows the dynamic shaft soil resistancemodel incorporated into KWaveHybrid. Thevalues of the vertical spring, k, the horizontalxysprings, k and k , the vertical radiationdamping, c, and the horizontal radiationxydamping, c and c , per unit shaft area areapproximated by means of Eqs. 1 and 2,based on the work of Novak et al. (1978).k2.75Gs, kxdkycGs, cxVs4.5GsVscy4Gsdmaxstatic1where v0 is a reference velocity and v is therelative velocity between the pile and theadjacent soil. Non-linear viscous laws similarto Eq. 3 have been proposed by Gibson &Coyle (1968), Heerema (1979), and Litkouhi &Poskitt (1980), all of whom suggest a value ofclose to 0.2, with the parametervaryingfrom about 0.1 for sand, to unity for clay soils(Randolph & Deek, 1992). The relation in Eq.3 was introduced into the viscous damping inFig. 2 for vertical shaft resistance model.(1)(2)Fig. 3 shows the dynamic vertical pile baseresistance model. The values of the soil springat the pile base, kb, the damping, cb, and thelumped soil mass, mb, per unit base area canbe estimated as follows (Deek & Randolph,1995):where Gs and Vs are the shear modulus andthe shear wave velocity of the surrounding soilrespectively, and d is the outer diameter of thepile.kh0m0c0ch0k0(Kp)1kb8Gsd (1cb3.4 Gs(1 s ) Vskh1m1c1k1mbch1(Kp)2c2 (Kp)3(Kp) n4s(6)s)The equation of motion of the pile isexpressed asK wchncb0.1(1ch2cnkns(5)in which s and s are the Poisson’s ratio andthe density of the soil respectively.khnmn16ro(4)s)kh2m2k2(v 0 1 m/s) (3)v / v0C wM wF(7)where [K], [C] and [M] are the stiffness matrix,the damping matrix and the mass matrixrespectively. {F} is the external force vector.The stiffness matrix is formed from the pilestiffness matrix and the soil stiffness matrix.The damping matrix is equal to the soildamping matrix. The mass matrix is formedfrom the pile mass matrix and the lumped soilmass at the pile base.cbkbmbFig. 1. Hybrid modelling of the pile and the soil.691
The static horizontal shaft soil spring values ateach pile node are estimated based onMindlin’s solution (Mindlin, 1936) which issimilar to the solution of the integral equationmethod used by Poulos and Davis (1980). Theequations becomePile nodeSlidermaxstaticDashpot cv(viscous)or qhSoil adjacent to pilexkstaticDashpot c(radiation)Spring kEs l(10)pd / uEs(11)where p is the horizontal distributed forceacting uniformly over the pile element and u isthe corresponding horizontal displacement ateach pile node calculated using the integralequation method.Soil far from pile (fixed)Fig. 2. Vertical and horizontal shaft resistancemodel.Note that the shear resistance at the pile basehas not been incorporated in the presentprogram. More details of the static analysismethod can be found in Kitiyodom &Matsumoto (2002, 2003).Pile nodeDashpot cbSlider qbykstaticACCURACY OF THE PROPOSED METHODImpacts on pile without soil resistanceLumpedmass MbSpring kbDashpot cbVertical impacts on a homogeneous pile and anon-homogeneous pile without soil resistanceare calculated by the program KWaveHybrid,and the calculated results are compared withthe theoretical values. Table 1 shows thespecifications of a homogeneous pile to beanalysed here.Fig. 3. Vertical base resistance model.When the stress at a pile-soil interface nodalpoint reaches the soil yield stress, the soilspring stiffness and the dashpot value at thatpoint are set to 0. In order to consider also thenonlinearity of the soil spring stiffness, Eq. 7 isrewritten in incremental form as:FtKtwttCtwttMtwtFtttFig. 4 shows the vertical impact force appliedto the pile head. Fig. 5 shows the calculatedand theoretical distributions of axial forcesalong the pile. Theoretically, the front ofcompression force reaches the pile base at t 2 ms because the bar wave velocity is 5000m/s. The compression force is reflected at thepile base, and the reflected force goes back tothe pile head as the tension force and reachesthe pile head at t 4 ms. The calculatedresults are in good agreements with thesetheoretical solutions. Fig. 6 shows the time vspile displacement at the middle point (z 5 m).A good agreement between the theoreticaland calculated values can be seen again.(8)Eq. 8 can be solved for the pile settlements,deflections and rotations from which the axialforces, the shear forces and the bendingmoments can be obtained. Note thatNewmark’smethod (NewMark, 1959) isused for solving Eq. 8.In the analysis of static pile load test, the staticvertical shaft soil spring, kstatic, is estimated bymeans of Eqs. 9 and 10 following Randolphand Wroth (1978).kstatic(2 / 2.75 ) k ,ln[5.0(1sTable 1. Specifications of a homogeneous pile.Length (m)Diameter (mm)2Cross-sectional area (m )2Young's modulus (kN/m )Bar wave velocity (m/s)3Density (ton/m )Mass (ton))l / d ] (9)where l is the pile embedment length.692104000.12673.0 1050001.21.51
1200theoretical values can be seen in both thevelocity and displacement.Force (kN)1000800Friction pile with elastic soil response600400A perfect friction pile with elastic frictionresponse is analysed, and the calculatedresults are compared with the theoreticalsolutions of the single mass system shown inFig. 9.20000123Time (ms)45Fig. 4. Pile head force.1200Calculated (t 2 ms)Calculated (t 4 ms)Theoretical (t 2 ms)Theoretical (t 4 ms)Force (kN)800400Specifications of the pile to be analysed hereare the same as those shown in Table 1. Thevalues of the vertical shaft spring stiffness, k,and the vertical radiation damping, c, were set333as k 2.0 10 kN/m and c 5.0 kNs/malong the pile shaft uniformly for convenience.The corresponding values of the total verticalspring stiffness, K, and the total verticaldamping, C, in the single mass system areshown in Fig. 9.t 2 ms0-400t 4 ms-800-12000246Pile distance (m)810Pile displacement (mm)Fig. 5. Distribution of axial force along the pile.Figs. 10 and 11 show time vs displacement ofthe middle point of the pile without damping (c 0) and with damping, respectively. Overall,the calculated results are in good agreementwith the theoretical solutions in both cases.Periodical oscillations can be seen in thecalculated results. These oscillations in thecalculationresultsreflectthewavepropagation phenomena in the pile, whichcannot be simulated using the single masssystem.4CalculatedTheoretical321z 5m00246Time (ms)810Fig. 6. Time vs pile displacement.60Lower5141.4-315.7 1073.0 1050001.2CalculatedTheoretical40200-200246Time (ms)810Fig. 7. Time vs pile head velocity.Pile head disp. (mm)Length (m)Diameter (mm)2Cross section area (m )2Young's modulus (kN/m )Bar wave velocity (m/s)3Density (ton/m )Upper5100-37.85 1073.0 1050001.2Velocity (m/s)Table 2. Specifications of a non-homogeneouspile.A non-homogeneous pile with no soilresistance shown in Table 2 was alsoanalysed using the proposed method. The pileconsists of two sections having the samematerial but different cross-sectional areas.The cross-sectional area of the lower sectionis twice that of the upper section. The impactforce shown in Fig. 4 was applied to the e (ms)810Fig. 8. Time vs pile head displacement.Figs. 7 and 8 show time vs velocity and timevs pile head displacement, respectively. Goodagreements between the calculated and693
measured at the same level of the hit pointwith a sampling rate of 15 ms.M 1.51 tonK 2.51 104 kN/mC 62.8 kNs/mAfter the dynamic pile load test, two statichorizontal pile load tests with different loadingmethods were conducted on each pile. Statichorizontal pile load test with step loadingmethod (JSSMFE, 1983) was conducted first.Load step sequence for the step loading isshown in Fig. 13, following JSF T32-8320). Invertical pile load test standard JGS 1811200221),twoloadingmethodsarerecommended which are the step loadingmethod and the continuous loading methods.However, in JSF T32-83, only the step loadingmethod is prescribed. In this study, the statichorizontal pile load test with the continuousloading method was also conducted. The loadstep sequence of continuous loading is alsoshown in Fig. 13. The static horizontal loadwas applied at the same loading point as thedynamic horizontal pile load test. Thehorizontal displacement of the pile and theapplied force were monitored throughout thestatic pile load tests.Pile displacement (mm)Fig. 9. Single mass system.12z 5m840-4-8-12CalculatedTheoritical50100150Time (ms)0Pile displacement (mm)Fig. 10. Time vs pile displacement (withoutdamping).Table 3. Specifications of test steel piles12Peaks from solutionwith damping84Length (m)Embedment length (m)Outer diameter (mm)Inner diameter (mm)2Cross-sectional area (cm )2Young's modulus (kN/m )Shear wave velocity (m/s)3Density (ton/m )Pile mass (ton)0-4-8-12CalculatedTheoriticalz 5m050100150Time (ms)Fig. 11 Time vs pile displacement (withdamping).CASE STUDYTest descriptionDepth from G.L. (m)2Both static and dynamic horizontal load testswere carried out on each pile. The dynamicpile load test was carried out prior to the staticpile load tests. In the dynamic pile load test,the pile was hit horizontally by a hammer massof 0.96 ton at the point z 0.25 m below daccelerationswere4P210.08.9500482138.882.06 1031877.81.1SPT N-value0 5 10 15 200The test piling on two steel pipe piles wasperformed. Fig. 12 shows the profiles of soillayer and the SPT N-values at the test site.Two test piles, designated as P1 and P2, wereinstalled by preboring. So there is no soil pluginside the piles. The test pile specifications aresummarised in Table 3. The distance betweenthe centres of the two piles is 3.5 m.P16.55.4600582167.182.06 1P210Clay1214Fig. 12. Profiles of soil layers and SPT Nvalues.694
KWaveHybrid during the loading andunloading states are the same. It can be seenfrom the measured results (Figs. 16 and 17)that the values of the soil spring during theloading and unloading states should bedifferent. These extensions are left for futurework.Step loading (JSF T32-83)Cont. loading806040200050100150Time (min)20060Force, Fdyn (kN)Force, Fsta (kN)100Fig. 13. Load step sequence of static pile loadtests.Measured static and dynamic test signals50403020100The dynamic test signals of P1 and P2 areshown in Figs. 14 and 15, respectively. Themeasured forces increase and decreaserapidly with time and have a peak of about 50kN. The loading duration is about 50 ms.0102030 40 50Time (ms)60708090Horizontal Disp., u (mm)(a) Measured forceThe measured static and dynamic horizontalload-horizontal displacement relations of P1and P2 are shown in Figs. 16 and 17,respectively. It can be seen from the figuresthat there are good agreements between themeasured load displacement relations fromthe static load tests with continuous loadingand that from the static load tests with steploading. On the other hand, the measured loaddisplacement relations from the dynamic loadtests are totally different from the measuredstatic load displacement relations. Therefore,in order to obtain the static load displacementrelation of the pile from the measured signalsof the dynamic load test, wave matchinganalysis of the measured dynamic signals wascarried out using KWaveHybrid.20MeasuredCalculated151050-50102030 40 50Time (ms)60708090400Acceleration,2(m/s )(b) Measured and estimated displacementWave matching analysis resultsMatching analysis was repeated with assumedvalues for the maximum shaft limit horizontalpressure, qh, and the soil shear modulus, Gs,using the measured Fdyn as the force boundarycondition at the loading point, until a goodmatching between the calculated and themeasured pile displacement was obtained.Soil parameters used in the final matching ofP1 are listed in Table 4. Fig. 14(b) and Fig. 18show the displacement vs time and loaddisplacement relation of P1 in the finalmatching analysis, compared with themeasured values.3002001000-100-2000102030 40 50Time (ms)60708090(c) Measured accelerationVelocity, v (m/s)1.20.90.60.30.0-0.3-0.60102030 40 50Time (ms)60708090(d) Velocity (integrate of acceleration by time)It can be seen that the calculated dynamic piledisplacement underestimated the measuredvalues after the peak displacement. This isthought to be due to the soil spring model. Atthe present, the value of the soil springs inFig. 14. Dynamic pile load test signals of P1.695
Force, Fdyn (kN)60The same analysis procedures as P1 werecarried out for P2. Soil parameters used in thefinal matching of P2 are listed in Table 5. Fig.15(b) and Fig. 20 show the displacement vstime and load displacement of P2 in the finalmatching analysis, compared with themeasured values.504030201000102030 40 50Time (ms)60708090Fig. 21 shows the comparison of the estimatedstatic load displacement relation of P2 with themeasured value. Again there is a goodagreement between the estimated and themeasured results.20MeasuredCalculated1510010580Force, F (kN)Horizontal Disp., u (mm)(a) Measured force0-50102030 40 50Time (ms)607080902(m/s )(b) Measured and estimated displacement40400030005 10 15 20 25 30Horizontal Displacement, u (mm)100Fig. 16. Measured load-displacement of P10-100-2001000102030 40 50Time (ms)6070809080Force, F (kN)Acceleration,6020200(c) Measured acceleration1.2Velocity, v (m/s)DynamicStatic (Step)Static (Cont.)0.90.6DynamicStatic (Step)Static (Cont.)6040200.30.0005 10 15 20 25 30Horizontal displacement, u (mm)-0.3-0.60102030 40 50Time (ms)60708090Fig. 17. Measured load-displacement of P2Table 4. Parameters for final matching of P1.(d) Velocity (integrate of acceleration by time)Depth (m)0 to 1 1Fig. 15. Dynamic pile load test signals of P2.Using the same soil parameters as shown inTable 4, the static load displacement relationof P1 was estimated using KWaveHybrid. Fig.19 shows the comparison of the estimatedstatic load displacement relation of P1 with themeasured value. It can be seen that theestimated result matches very well with themeasured one.Gs (kPa)10831083s0.30.3qh (kPa)1Elastic rangeTable 5. Parameters for final matching of P2.Depth (m)0 to 1 1696Gs (kPa)15391539s0.30.3qh (kPa)5Elastic range
60Fig. 22 shows the predicted displacement vstime and the predicted dynamic loaddisplacement relation of P1, compared withthe measured values.Force, Fdyn (kN)5040Fig. 23 shows the predicted static loaddisplacement relation of P1, compared withthe measurement. It can be seen from thefiguresthatalthoughthepredicteddisplacements overestimate the measuredvalues, there are reasonable agreementsbetween the predicted and the measuredvalues.3020100CalculatedMeasured036912 15Horizontal displacement, u (mm)100Fig. 18. Dynamic pile load test results of P1Force, Fsta (kN)Force, Fsta (kN)100806040200400EstimatedMeasured0 5 10 15 20 25 30Horizontal displacement, u (mm)Horizontal Disp., u (mm)Fig. 21. Static pile load test results of P1.Fig. 19. Static pile load test results of P1.60Force, Fdyn (kN)60200 5 10 15 20 25 30Horizontal displacement, u redictedMeasured151050-50102030 40 50Time (ms)6070809020(a) Measured and predicted displacement.10600036912 15Horizontal displacement, u (mm)Force, Fdyn (kN)50Fig. 20. Dynamic pile load test results of P2.Prediction analysisIn actual construction site, it would be veryuseful to estimate the static load displacementrelation of the actual pile from the dynamicload test of another pile having smallerdiameter. In this work, the soil parameters ofP2 (Table 5), which has a smaller diameterthan P1, were employed to predict the loaddisplacement relation of P1.403020100PredictedMeasured036912 15Horizontal displacement, u (mm)(b) Measured and predicted load-displacement.Fig. 22. Predicted dynamic results of P1.697
Force, Fsta (kN)100Heerema, E. P., 1979. Relationships betweenwall friction displacement, velocity andhorizontal stress in clay and in sand for piledriveability analysis. Ground 2002.Standards of Japanese Geotechnical Societyfor vertical load tests of piles. JapaneseGeotechnical Society, Tokyo.40200PredictedMeasuredJapanese Society of Soil Mechanics andFoundation Engineering, 1983. JSSMFEstandard method for lateral loading test for apile. Japanese Society of Soil Mechanics andFoundation Engineering, Tokyo.0 5 10 15 20 25 30Horizontal displacement, u (mm)Fig. 23. Predicted static load-displacement ofP1.Kitiyodom, P. and Matsumoto, T., 2002. Asimplified analysis method for piled raft andpile group foundations with batter piles.International Journal for Numerical andAnalytical Methods in Geomechanics, 26,1349-1369.CONCLUSIONSA new numerical program KWaveHybrid foranalysing pile driving as well as static load testin vertical and horizontal directions has beendeveloped in this study. Performance of theprogram was verified through comparisonswith theoretical solutionsKitiyodom, P. and Matsumoto, T., 2003. Asimplified analysis method for piled raftfoundations in non-homogeneous soils.International Journal for Numerical andAnalytical Methods in Geomechanics, 27, 85109.The developed program was then applied tothe dynamic and static horizontal load tests ontwo steel pipe piles. A good matching betweenthe calculated and measured behaviours ofthe piles during driving and during static loadtest was obtained.Kitiyodom, P., Matsumoto, T. and Kanefusa,N., 2004. Influence of reaction piles on thebehaviour of test pile in static load testing.Canadian Geotechnical Journal, 41(3), 408420.The identified soil resistance parameters of thesmaller diameter pile were used to predict thebehaviours of the bigger pile, and a goodprediction was obtained.Litkouhi, S. and Poskitt, T. J., 1980. Dampingconstant for pile driveability calculations.Géotechnique, 30(1), 77-86.REFERENCESMatsumoto, T. and Takei, M., 1991. Effects ofsoil plug on behaviour of driven pipe piles. Soiland Foundations, 3(2), 14-34.Deek, A. J. and Randolph, M. F., 1995. Asimple model for inelastic footing response totransient loading. International Journal forNumerical and Analytical Methods inGeomechanics, 19, 307-329.Mindlin, R. D., 1936. Force at a point interior ofa semi-infinite solid. Physics, 7, 195-202.Newmark, N. M., 1959. A method ofcomputation for strucural dynamics. Journal ofthe Engineering Mechanics Division ASCE,85(EM3), 67-94.Gibson, G. and Coyle, H. M., 1968. Soildamping constant related to common soilproperties in sands and clays. Report No. 1251, Texas Transport Institute, Texas A&MUniversity.Novak, M., Nogami, T. and Aboul-Ella F., 1978.Dynamic soil reactions for plane strain case.Journal of Mechanical Engineering ASCE,104(EM4), 953-959.Goble, G. G. and Rausche, F., 1976. Waveequation analysis of pile driving-WEAPprogram, prepared for the U.S. department oftransportation, federal highway administration,implementation division, office of research anddevelopment.698
Poulos, H. G. and Davis E. H., 1980. PileFoundation Analysis and Design, Wiley, NewYork.Randolph, M. F. and Deeks A. J., 1992.Dynamic and static soil models for axial pileresponse. Proceedings of the 4th InternationalConference on the Application of StresswaveTheory to Piles, The Hague, 3-14.Randolph, M. F. and Wroth, C. P., 1978.Analysis of deformation of vertically loadedpiles. Journal of Geotechnical EngineeringASCE, 104(12), 1468-1488.Rausche, F., Moses, F. and Goble, G. G.,1972. Soil resistance predictions from piledynamics Journal of the Soil Mechanics andFoundation Division ASCE, 98(SM9), 917-937.Smith, E. A. L., 1960. Pile driving analysis bythe wave equation. Journal of the SoilMechanics and Foundation Division ASCE,86(SM4), 35-61.TNO, 1977. Dynamic pile testing. Report No.BI-77-13.Wakisaka, T., Matsumoto, T., Kojima, E. andKuwayama S., 2004. Development of a newcomputer program for dynamic and static pilethload tests. Proceedings of the 7 InternationalConference on the Application of StresswaveTheory to Piles, Kuala Lumpur, 341-350.699
Newmark’s method (NewMark, 1959) is used for solving Eq. 8. In the analysis of static pile load test, the static vertical shaft soil spring, k static, is estimated by means of Eqs. 9 and 10 following Randolph and Wroth (1978). kk static (2 /2.75 ) , ln[
simulation method. A dynamic fault tree usually consists of static gates and dynamic gates. The unique function of dynamic gates is depicting interactions in a complex system, which cannot be realized by static gates. In order to understand fault tree better, we apply static fault tree and dynamic fault tree in risk analysis of di erent areas .
variation of the load is small, hence static analysis is sufficient. However, in case of off-shore structures (oil rigs), high rise buildings subjected to lateral loads (wind, earth quake) dynamic effects of the load must be explored for knowing the exact safety and reliability of the structure. Comparison between static and dynamic analysis:
Abstract: Static analysis relies on features extracted without executing code, while dynamic analysis extracts features based on execution (or emulation). In general, static analysis is more efficient, while dynamic analysis can be more informative, particularly in cases where the code is obfuscated. Static analysis of an Android application
l Combines static and dynamic analysis l Static analysis phase Extract program communication structure tree - Loops, branches etc. l Dynamic analysis phase Use this tree as a template "Fill in" runtime information - Loop count MUG'18-Combining Static and 26 Analysis for Top -down Communication Trace Compression 11
Static analysis checks 20 Stages of static analysis Control flow analysis. Checks for loops with multiple exit or entry points, finds unreachable code, etc. Data use analysis. Detects uninitialized variables, variables written twice without an intervening assignment, variables which are declared but never used, etc. Interface analysis.
Dec 06, 2018 · Dynamic Strategy, Dynamic Structure A Systematic Approach to Business Architecture “Dynamic Strategy, . Michael Porter dynamic capabilities vs. static capabilities David Teece “Dynamic Strategy, Dynamic Structure .
5 Vulnerability Analysis Techniques Static analysis Analysis performed before a program starts execution Works mainly on source code Binary static analysis techniques are rather limited Not very effective in practice, so we won't discuss in depth Dynamic analysis Analysis performed by executing the program Key challenge: How to generate input for execution?
Nonlinear Iwan Joints Using Quasi-Static Modal Analysis," Mechanical Systems and Signal Processing, vol 118, pp. 133-157, 2019. Dynamic analysis of a structure is computationally expensive so we use a static analysis 10x increase in speed for a quasi-static case (seconds) vs. static response
