摘 要
Terzaghi於1925年所提出的單向度壓密理論其優點是解析解易求得；缺點則是低估了超額孔隙水壓，Gibson等人便根據Terzaghi理論的缺失來進行修正，於1967年提出飽和黏土的壓密方程式，為一非線性的偏微分方程式。其優點為假設條件較符合土壤壓密的實際情況；缺點則是解析解不容易求得。不過由最近發表的文獻中，可知已能將Gibson理論的薄黏土層的單向度壓密方程式予以線性化，進而求出其近似解。
本研究主要是利用差分法來求出Gibson薄、厚土層壓密方程式的近似解，並且跟Terzaghi壓密理論與速算公式的結果作一比較，以提供作為工程設計時的一個參考。

Abstract
Gibson and his co-workers proposed a nonlinear theory of consolidation in 1967, which was derived by conditions more realistic than those applied in the Terzaghi’s theory. Even if the analytic solutions to the nonlinear theory are difficult to obtained, some progress has been made recently using a special type of linearization. A handy formula has thus derived which can calculate the settlement quickly.
This research try to compare this handy formula with the Gibson’s theory as well as the Terzaghi’s theory. And some positive results has been obtained.

參考文獻
[1] Lee,K.,“Discussion on Terzaghi’s Concept of Consoli-
dation,” Geotechnique, Vol.34,No.1,pp. 131-132(1984).
[2] Richart, F.E.,“A Review of the Theories for Sand Dr-
ains,” Proc.Am.Soc.civ.Engrs,SM3,No.1301,(1957).
[3] Lo,K.Y.,“Discussion on Rowe, Measurement of the Coe-
fficient of Consolidation of Lacustrine Clay,” Geote-
chnique, Vol 10,No 1,pp. 36-39(1960).
[4] Janbu, N.,“Consolidation of Clay Layers Basedon Non-
Linear Stress-Strain,”Proc.6th Int. Conf.Soil Mech.Vol.
2,pp. 83-87(1965).
[5] Barden,L. and Berry,P.L.,“Consolidation of Normally
Consolidated Clay,” Pro.Am.Soc.Civ Engrs, SM5 ,No.4481,
pp.15-35(1965)
[6] Davis,E.H.and Raymond,G.P.,“A Non-Linear Theory of
Consolidation,” Geotechnique,Vol 15,No.2,pp.161-173
(1965).
[7] Gibson,R.E.,England,G.L.and Hussey,M.J.L.,“The Theory
of One Dimensional Consolidation of Saturated Clay: I.
Finite Non-Linear Consolidation of Thin Homogeneous Layers,” Geotechnique,Vol 17,pp.261-273(1967).
[8] Gibson, R.E., Schiffman,R.L.and Cargill,K.W.,“The The
-ory of One Dimensional Consolidation of Saturated Clay:
Finite Non Linear Consolidation of Thick Homogeneous
Layers,” Can.Geotech.J﹒,Vol 18,pp.280-293(1981).
[9] Lei,H.C. and Chang,H.W.,“A List of Hodograph Trans
-formations and Exactly Linearizable Systems,”The Ch
-inese Journal of Mechanics，Vol 12，No.3，September
1996.
[10] Poskitt, T.J.,“The Consolidation of Saturated Clay
with Variable Permeability and Compressibility,” Geo
-technique,Vol 19,No 2, pp. 234-252 (1969).
[11] Feldkamp,J.R.,“Permeability Measurement of Clay Pas
-tes by a Non-Linear Analysis of Transient Seepage Co
-nsolidation Tests,” Geotechnique,Vol. 39,No.1,pp.141
-145(1989).
[12] Znidarcic,D.,Schiffman,R.L.,Pane,V.,Croce,P.,Ko,H.Y.
and Olsen,H.W.,“ The Theory of One Dimensional Con
-solidation of Saturated Clays: Constant Rate of
Deformation Testing and Analysis,” Geotechnique,Vol
36,No 2,pp.227-237(1986).
[13] Feldkamp,J.R.,Swartzendruber,D.and Shainberg,I.,“U
-se of an Automated Tension Cell to Measure Physical
Properties of Consolidation System,” Colloid Polymer
Sci., Vol 261,pp. 277-285(1983).
[14] Croce,P.,Pane,V.,Znidarcic, D.,Ko, H.Y.,Olsen,H.W. and
Schiffman,R.L.,“Evaluation of Consolidation Theories
by Centrifugal Modelling,” Proc. Conf.Applications of
Centrifugal Modelling to Geotechnical Design, Manchest
-er University, pp. 380-401(1984).
[15] Mikasa,M.and Takada, N.,“Selfweight Consolidation of
Very Soft Clay by Centrifuge,” In Sedimentation /Conso
-lidation Models ,pp.121-140(eds R.N.Yong and F.C. Tow
-nsend).New York :American Society of Civil Engineers
(1984).
[16] Schiffman,R.L.,Pane,V. and Gibson ,R.E.,“The Theory
of One-Dimensional Consolidation of Saturated Clays:
an Overview of Nonlinear Finite Strain Sedimentation and
Consolidation,”In Sedimentation / Consolidation Mode-
ls,pp 1-29(eds R.N.Yong and F.C. Townsend).New York: Am
-erican Society of Civil Engineers(1984).
[17] Chakarbarty, J.,“Theory of Plasticity,”McGraw-Hill,
New York(1987).
[18] Hill,R.,“The Mathematical Theory of Plasticity,”Oxfo
-rd University Press,London(1950).
[19] Whiteam,G.B.,“Linear and Nonlinear Waves,” Wiley,New
York(1974).
[20] Courant,R. and Friedrich,K.O.,“Supersonic Flow and
Shock Waves,” Springer-Verlag, New York(1948).
[21] Courant,R.and Hibbert,D.,“Methods of Mathemmatical
Physics(Vol. 2),” Inter-science Publishers, New York
(1962).
[22] Garabedian,P.R.,“Partial Differential Equation,”Che
-lsea Publishing Company,New York(1986).
[23] M.R.Spiegel,p252,formula 128