氏名　ピントール　トゥア　シマトパン
学位の種類　博士（工学）
学位記番号　博甲第215号
学位授与の日付　平成12年12月31日
学位論文題目　Study on the Stability of Earth Structures Based on Shakedown Theorem　（シェイクダウン定理に基づく土構造物の静的・動的安定性評価に関する研究）
論文審査委員
　主査　助教授　大塚　悟
　副査　教授　海野　隆哉
　副査　教授　丸山　輝彦
　副査　教授　丸山　久一
　副査　助教授　杉本　光隆
　副査　新潟大学教授　大川　秀雄

• 論文目次
• 論文要旨

［平成12（2000）年度博士論文題名一覧］ ［博士論文題名一覧］に戻る．

Acknowledgments　p.i

Abstracts　p.iii

Contents　p.v

List of Figures　p.ix

List of Tables　p.xiii

1 INTRODUCTION　p.1
1.1 General　p.2
1.2 Objective of study　p.5
1.3 Organization of thesis　p.6

2 LIMIT ANALYSIS AND SHAKEDOWN THEORY　p.7
2.1 General　p.8
2.2 Theoretical Background in Soil Plasticity　p.9
2.2.1 The criteria of yielding　p.9
2.2.2 Stress-strain relations　p.15
2.3 Limit Analysis　p.19
2.3.1 Lower bound theorem　p.21
2.3.2 Upper bound theorem　p.23
2.4 Shakedown Theory　p.24
2.4.1 Lower bound of shakedown　p.27
2.4.2 Dynamic shakedown　p.29

3 STABILITY OF EMBANKMENT　p.33
3.1 General　p.34
3.2 Formulation of Safety Factor　p.35
3.2.1 Stability Analysis with Linear Programming　p.36
3.2.2 Static and Pseudo-static Analyses　p.37
3.2.3 Dynamic Analysis　p.38
3.3 Stability Analysis by means of Pseudo-static Concept　p.39
3.3.1 Effect of Alternating Load　p.39
3.4 Effect of Horizontal and Vertical in the Alternating Load　p.43
3.5 Dynamic Stability Analysis　p.45
3.5.1 Harmonic Wave Loading　p.45
3.5.2 Effect of Damping Properties　p.48
3.5.3 Effect of Damping Models　p.49
3.5.4 Effect of Embankment Rigidity　p.52
3.5.5 Past Earthquake Acceleration　p.53
3.6 Concluding Remarks　p.59

4 SLOPE STABILITY ANALYSES　p.61
4.1 General　p.62
4.2 Static Slope Stability　p.64
4.2.1 Definition of safety factor　p.64
4.2.2 Lower bound of shakedown　p.65
4.2.3 Comparison with conventional methods　p.67
4.3 Seismic Stability of Slope Based on Pseudo-static Concept　p.69
4.3.1 Conventional pseudo-static analysis　p.69
4.3.2 Shakedown pseudo-static analysis　p.74
4.4 Seismic Stability of Slope for Dynamic Consideration　p.81
4.4.1 Formulation of dynamic shakedown　p.81
4.4.2 Frequency dependent factor of safety　p.82
4.4.3 Case study on earthquake records　p.84
4.5 Time Dependent Factor of Safety for Slope　p.87
4.5.1 Comparative discussion with shakedown analysis　p.89
4.6 Concluding Remarks　p.92

5 STATIC AND DYNAMIC EARTH PRESSURES　p.95
5.1 General　p.96
5.2 Earth Pressure on Retaining Wall　p.98
5.2.1 Definition of limit earth pressure　p.98
5.2.2 Safety factor assessment　p.99
5.3 Static Earth Pressure on Retaining Wall　p.100
5.3.1 Coulomb earth pressure　p.100
5.3.2 Proposed Model　p.103
5.4 Active Earth Pressure Based on Pseudo-static Analyses　p.104
5.4.1 Comparison with Mononobe-Okabe method　p.104
5.4.2 Effect of inertia force change　p.105
5.5 Dynamic active earth pressure for harmonic wave　p.106
5.5.1 Effects of damping ratio　p.109
5.5.2 Effects of structural rigidity　p.109
5.6 Dynamic active earth pressure for irregular wave　p.110
5.6.1 Effects of damping　p.112
5.6.2 Effect of structural rigidity　p.113
5.7 Adjustment of Dynamic Earth Pressure　p.113
5.7.1 Normalized dynamic displacement Dp　p.114
5.7.2 Normalized dynamic displacement Ds　p.116
5.8 Concluding remarks　p.116

6 CONCLUSIONS　p.119

Bibliography　p.127

　The seismic stability of earth structures are often predicted by pseudo-static method, which assumes the earthquake loading as an inertia force acts horizontally in the body of structures. However, this method contains a crucial drawback since it assumes that the earthquake loading is not a repeated load, which alternates both in magnitude and direction. Such assumption on the pseudo-static method came originally from stability analysis in the static condition. Meanwhile, the stability analyses such as limit equilibrium method or limit analysis are valid for static condition only. Therefore, to cover a repeated load, which alternates in magnitude and direction, a new stability analysis should be developed. The shakedown theory was established to encompass all possibilities of acting load in the certain prescribed load domain included if the acting loads are repeated. Then, a new seismic stability analysis was developed by means of shakedown theory.
　In this study, the numerical studies were done to earth structures such as embankment, slope, and earth pressure on the retaining wall. The shakedown theory was applied to develop a new method, where the important aspects of an earthquake such as: 1） effect of repeated load, which alternates in magnitude and direction, 2） time history acceleration, 3） frequency property of acceleration, 4） vibration property of earth structures, and 5） resonant phenomenon were considered in the determination of stability of earth structures during earthquake. The results exhibited that all aspects gave a significant contribution in the seismic stability analysis, especially on the item 1）. It has justified that the seismic stability analysis of earth structures must consider the item 1, such that a rational design could be proposed.
　In this study, the applicability of proposed method has been examined through the static slope stability analysis. In the static condition, the shakedown analysis coincides with the conventional analysis, which usually based on limit analysis. Therefore, the obtained factors of safety have been compared with those of conventional methods. It was clearly shown that the proposed method gave the almost same results with the conventional methods. It means that the proposed method could evaluate the stability of earth structures properly.
　In the case of embankment problem, the effects of alternating load either in the magnitude or direction were significantly clarified. The comparison between alternating and single loads in the value of their safety factor was clear that the alternating of load reduces the safety factor. Moreover, the reduction for clayey and sandy soils is completely different. In the every case, the reduction of safety factor is more for sandy soils than clayey soils.
　The seismic stability of slope and embankment were investigated against regular and irregular wave accelerations excited at the bedrock of subsoil. The obtained factor of safety for low frequency wave acceleration coincided with that of pseudo-static stability analysis and, on the other hand, the factor of safety coincided with that of static stability analysis for high frequency wave acceleration. The past acceleration records in several earthquake were also employed for case studies. In the case of slope stability, the combined stability method of deformation and stability analyses was conducted. By this method, the total stability of slope could not be evaluated from the obtained time dependent factor of safety. It was found that the least factor of safety obtained during earthquake, however, gave a coincident factor of safety by the proposed method. It was a limited case study, but the possible engineering meaning of time dependent factor of safety obtained by the combined method was clarified.
　In the earth pressure problem, the applicability of proposed method was examined through the Coulomb model. The active and passive earth pressure by the proposed method exhibited the good agreement with the Coulomb method. The dynamic active earth pressures for enforcing both regular and irregular wave accelerations were investigated for case studies. The past earthquake records were directly employed as irregular waves. The dynamic active earth pressures were obtained dependent of both frequency of sine waves and damping coefficient of retaining wall-backfill system. An attempt was also conducted to relate the dynamic earth pressure and the earth pressure obtained from pseudo-static analysis. There exists a good possibility that the dynamic active earth pressure could be adjusted from the pseudo-static analysis resulted. Nevertheless, in the future research, the clear performance of this effort will be developed elaborately.