單層岩層褶皺力學機制探討

The Mechenical Mechenism of Single Layer Folds

黃國品(Kuo-Pin Huang)

指導教授 ： 鄭富書

國立臺灣大學/工學院/土木工程學研究所/博士(2006年)

https://doi.org/10.6342/NTU.2006.02932

摘要

褶皺之力學成因相當複雜且多種，以致許多褶皺力學問題難以進行理論解推導。挫屈形成褶皺是非常重要且基礎的力學成因之ㄧ，也吸引許多學者嘗試尋求此類問題之理論解，以解釋部份褶皺成因與描述褶皺行為。本研究延續先前許多學者假設褶皺形式為正弦波型，並提出新的岩層褶皺之振幅與側向壓縮應變之間的合理關係，可以應用以推導各種介質與岩層之材料組成之褶皺理論解。本文應用所提出之推導方法，針對依地層深度分佈之六種可能材料組合情形，成功地推導出各種材料組合情形下單層岩層褶皺之理論解。彈性介質中彈性岩層褶皺之理論解與 Currie (1962) 之理論解相同，而黏性介質中黏性岩層褶皺理論解之顯著波長，與 Biot (1961) 之推導相同。本文推導所得之理論解，可定量描述岩層側向壓縮應變與褶皺波長間之關係。
Jeng et al. (2002) 以彈簧模擬彈性介質，成功地推導出可以描述衰減振幅褶皺波形之理論解。本研究藉用相同的方法，修正Jeng et al. (2002) 之彈簧模型，推導出新的彈性衰減振幅褶皺之理論解；再推廣運用此方法，以黏性消能盤桿件、麥斯威爾黏彈性桿件分別模擬黏性介質與黏彈性介質，成功地推導出以上六種可能材料組合情形之衰減振幅褶皺波形理論解。
野外常見之褶皺形式可大致分類成三種－雙頻波、單頻波（顯著波長）以及衰減振幅波形。由連續介質與桿件模擬介質所分別推導之理論解，將之結合適可描述此野外常見之三種波形。經由數值分析之驗證，可以定量或定性地驗證本研究所推導之褶皺波形理論解與行為。
由前人相關研究至本研究為止所獲得之研究成果，可作為描述野外觀察褶皺形式以及後續研究之基礎。

關鍵字

褶皺 ； 挫屈 ； 理論解 ； 雙頻波形 ； 顯著波長 ； 衰減振幅 ； 黏性 ； 黏彈性 ； 彈性

並列摘要

This research proposes a new approach towards obtaining a rational explanation of the relationship between single layer folds and lateral compression. This approach can be used to as a theoretical explanation for the composition of geologic matrix and folds. This research uses the deductive approach on six kinds of composite media by depth to achieve a successful solution of the single layer fold theory. The theoretical solution applied for the elastic layer fold is similar to Currie’s 1962, while the solution used for finding a dominant wavelength in viscous media is analogous to Biot’s theory (1961). The theorem applied in this research can quantitatively describe the relationship between layer’s fold wavelength and lateral shortening strain.
Jeng et al. (2002) discretized the elastic matrix into a spring model, successfully formulating a theory to describe the decay amplitude waveform of folds. This research uses the same technique to adjust the spring model and proposes a new theory for the explanation of the decay amplitude waveform of folds. Thus, the same method is applied for the explanation of decay amplitude waveform fold for six kinds of composite media.
Using a combination of continuous matrix and discretization analysis, we can explain the folding patterns (e.g. double frequency folding, single frequency folding and folding decay) seen on the field. The above theorem has been thoroughly tested through evaluation by mathematical analysis, thus effectively giving a quantitative and qualitative description of frequently seen trends in geologic folding.
We are convinced that the structural geology of most outdoor geologic folding trends can be explained by past studies and this research.

並列關鍵字

buckle ； fold ； theoretical solution ； duel-frequence waveform ； dominante wavelength ； viscous ； elastic ； viscoelastic

參考文獻

胡啟文(2004)，橫移壓縮作用引致黏彈性褶皺生成機制數值模擬初探，國立台灣大學碩士論文，台北。

Abbassi, M. R., Mancktelow, N. S., 1990. The effect of initial perturbation shape and symmetry on fold development. Journal of Structural Geology, 12, 273 - 282.

Biot, M. A., 1937. Bending of an Infinite Beam on an Elastic Foundation. Trans. Am. Soc. Mech. Eng. 55: A1 - A7.

Biot, M. A., 1939. Non-linear theory of elasticity and the linearized case for a body under initial stress. Philos. Mag. 28:468 - 489.

Biot, M. A., 1957. Folding Instability of a Layered Viscoelastic Medium Under Compression. Proc. R. Soc. London. Ser. A 242: 444 - 454.