第五章 結論與建議
第二節 建議
一、本文所用分析方法須配合詳細野外觀察、壓力計選擇與溫度判定。野外觀察重 點於判斷破裂形成力學機制，以增加液壓比值選擇正確性。壓力計選擇會影響 最終應力場評估數值結果。溫度判定則會流變準則的範圍以及地溫梯度的估計。
二、前人文獻所用賓漢空間分布分析為不考慮規模數值之結果，造成集中參數矩 陣由三維矩陣降維至二維矩陣。但在最後計算結果中，應力規模本身也可參 與賓漢空間分布計算應力規模的異向性與誤差計算。若將三軸應力數值改採 賓漢空間分布來計算，則可能獲得更佳的軸差應力與應力比值數值。
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第0 章 參考文獻
第0 章 附錄一：程式碼
附錄一：程式碼 主程式 MC.m
close all clear all
Path='syn.txt';%attitude of pole file=load( Path );
Sm=round(load('sm_syn2.txt')*100);%Stress control T=750;%Temperature
rock=load('experimentS3S1.txt');
set='Vertical'; %Sm is…
filename='syn_170401.mat';
%---HB and
creep---[curve1,curve2,T0,m,UCS]=HB(rock); %HB°Ñ¼Æ Diffmax=max( RheologicStress(T)); %Creeplaw
%---%translate attitude to cart
% % [1 0 0];%N % [0 -1 0];%E % [0 0 1];%U i=1:length(file);
trend=-file(i,1);
plunge=-file(i,2);
[x ,y, z]=sph2cart(trend*pi/180, plunge*pi/180, 1);
PP=[x y z];
BS6=NaN(5000);
%D=[1 2 3 4 5 6 7 8]==[Normal Lognormal Expotential Weibull Gamma Beta GEV Uniform]
%Kstest Ks<alpha<P for q=1:500
Q=randsample(length(PP),length(PP),true);
j=1:length(Q);
K=[PP(Q(j),1) PP(Q(j),2) PP(Q(j),3)];
SM=randsample(length(Sm),length(Sm),true);
k=1:length(SM);
[P,Pstd,KS,a,p,D]=gof(Sm(SM(k)));
if KS~=11 && P~=Inf && P~=11
[FR ,t1, p1, t2, p2, t3, p3, K1,
K2,Sv,PF,s1,s2,s3,Criteriapoint, R, tau]=Stressinversion(K,P,T0,T, curve1,curve2,PP,Q,Diffmax,set);
BS6(q,:)=[Criteriapoint,NaN(1,5000-length(s1))];
BS7(q,:)=[FR ,t1, p1, t2, p2, t3, p3, K1,
第0 章 附錄一：程式碼
g=g+size(AS2(~isnan(AS2)),2);
BS(g,:)=zeros(1,size(BS,2));
g=g+1;
end
clear Diffmax j PF s1 s2 s3 Sv Criteriapoint x y z K K1 K2 g i Number p1 p2 Path Pf plunge trend q Q R raw t1 t2 t3 rock FR a KS SM D P k p3 Sample p Pstd tau AS0 AS1 AS2 AS3 AS4 AS5 AS6 AS7 BS0 BS1 BS2 BS3 BS4 BS5 BS6 BS7
clc
save(filename)
主要分析副程式：Stressinversion.m
function [FR ,t1, p1, t2, p2, t3, p3, K1,
K2,Sv,PF,s1,s2,s3,Criteriapoint, R, tau]=Stressinversion(K,Sm,t0,T, curve1,curve2,PP,N,Diffmax,set)
%---Stress Ratio---B = bingham_fit(K);
K1=max([B.Z]);
K2=min([B.Z]);
FR = max([B.Z])/min([B.Z]);
Sx=B.V(:,1)';
%---add stress ellipsoid
[azimuth,elevation,~]=cart2sph(Sx(1),Sx(2),Sx(3));
sx=[0, -azimuth*180/pi,elevation*180/pi];%S3==Sx [x ,y, z]=sph2cart(azimuth, elevation, sx(1));
SX=[x ,y, z]; %S3
[azimuth,elevation,~]=cart2sph(Sy(1),Sy(2),Sy(3));
sy=[FR, -azimuth*180/pi,elevation*180/pi];%S2==Sy [x, y ,z]=sph2cart(azimuth, elevation, sy(1));
SY=[x, y, z]; %S2
第0 章 附錄一：程式碼
sz=[1, -azimuth*180/pi,elevation*180/pi];%S1==Sz [x,y, z]=sph2cart(azimuth, elevation, sz(1));
SZ=[x, y ,z]; %S1
%---rotated to stress axis r=inv(A);
[R, tau]=Ratiopoint(TTR,SXG(1),SYG(2),SZG(3));
%---orientation
[VR,~] = Ratiopoint(Svg,0,FR,1);
%---fit
magnitude---j=0.1:0.1:round(10*Diffmax)/10;%Creep law Hirth et al.,2009 switch set
Q = repmat((S1+S3)./2,1,901)-(S1-S3)*cosd(m)./2;
M = (S1-S3)*sind(m)./2;
i=1;
while all(M(i,:)<= HB(i,:)) && i<size(M,1) i=i+1;
HB(i,:)=curve1(Q(i,:))';
end
for i=1:size(HB,1)
[X2, Y2]=Ratiopoint(PPR,0,FR*j(i),j(i));
Data=[X2+S3(i),Y2]; %total X3=curve2(Y2);
pf=Data(:,1)-X3;
Pf=max(pf);
criteriapoint=N(find(pf==Pf, 1, 'last' ));
Sv(i)=VR*j(i)+S3(i);
s1(i)=round(100*S1(i))/100;
s2(i)=round(100*S2(i))/100;
s3(i)=round(100*S3(i))/100;
PF(i)=round(100*Pf)/100;
Criteriapoint(i)=criteriapoint;
end
第0 章 附錄一：程式碼
副程式 Ratiopoint.m
function [R, tau]=Ratiopoint(PPR,SXG,SYG,SZG)
sigma = [sqrt(SXG^2),sqrt(SYG^2),sqrt(SZG^2)]';
R=PPR.^2*sigma;
tau=sqrt(abs((PPR.^2)*(sigma.^2)-R.^2));
副程式 RheologicStress.m
%%
%Hirth et al., 2001
%%
function Dev = RheologicStress(T) e=[10^-12 10^-13 10^-14 ]; %Flow rate R=(8.3145/1000); %Ideal gas constant m=1;
n=4;
f=37;%water fugacity
A=10^-11.2; %material constant Q=135; %activiation energy
Dev = (e'/(A*(f^m)*exp(-Q/(R*T)))).^(1/n);
第0 章 附錄一：程式碼
副程式 HB.m
function [curve2,curve3]=HB(UCS,t0)
% t0=8.854115273;
% UCS=116;
M=UCS/t0;
e=0;
% P=fopen('id.txt', 'w');
i=(-t0+0.0001):0.0001:500;
KS 檢定用副程式：gof.m
function [M,Mstd,Ks,alpha,P, D]=gof(U) R=sort(U);
[A,x]=ecdf(R);
n=length(x);
Da=1.51*sqrt((n+n)/(n*n));%1.51 is two-tail 95% confidence-coefficients for ks G.Borradaile(
[mu,sigma]=normfit(R);
Ncdf=cdf('Norm',x,mu,sigma);
N=max(sqrt((A-[Ncdf]).^2));
NP=double(Qks(sqrt((n*n)/(n+n)),N));
if Da>=N && NP>0.05
Npd=makedist('Norm','mu',mu,'sigma',sigma);
Nm=mean(Npd);
if Da>=B && BP>0.05
Bpd=makedist('Beta','a',b(1),'b',b(1));
Bm=mean(Bpd)*max(R);
Bstd=std(Bpd)*max(R);
第0 章 附錄一：程式碼
LNcdf=cdf('logn',x,lmu(1),lmu(2));
LN=max(sqrt((A-[LNcdf]).^2));
LNP=double(Qks(sqrt((n*n)/(n+n)),LN));
if Da>=LN && LNP>0.05
LNpd=makedist('logn','mu',lmu(1),'sigma',lmu(2));
LNm=mean(LNpd);
EP=double(Qks(sqrt((n*n)/(n+n)),E));
if Da>=E && EP>0.05
Epd=makedist('exp','mu',emu);
Em=mean(Epd);
Wcdf=cdf('wbl',x,w(1),w(2));
WBL=max(sqrt((A-[Wcdf]).^2));
WP=double(Qks(sqrt((n*n)/(n+n)),WBL));
if Da>WBL && WP>0.05
Wpd=makedist('wbl','a',w(1),'b',w(2));
Wm=mean(Wpd);
第0 章 附錄一：程式碼
Gstd=11;
GP=11;
else
g=gamfit(R);
Gcdf=cdf('gam',x,g(1),g(2));
G=max(sqrt((A-[Gcdf]).^2));
GP=double(Qks(sqrt((n*n)/(n+n)),G));
if Da>=G && GP>0.05
Gpd=makedist('gam','a',g(1),'b',g(2));
Gm=mean(Gpd);
if Da>=DGEV && GEVP>0.05 GEVm=mean(GEV); Wstd WP i(4);G Gm Gstd GP i(5);B Bm Bstd BP i(6);DGEV GEVm GEVstd GEVP 7];
O=sortrows(K,1);
Mstd=O(1,3);
Ks=O(1,1);
alpha=Da;
P=O(1,4);
D=O(1,5);
第0 章 附錄一：程式碼
KS 檢定用副程式：QKs.m
function P=Qks(N,D) syms x;
P =round((2000000*
symsum(((-1)^(x-1))*(exp(-2*(x^2)*(((N+0.12+(0.11/N))*D)^2))),x,1,Inf)))/1000000;
附件二：應力分析參數代號
𝐒𝐒 Strike-Slip Faulting Stress Regime 走向滑移斷層應力場 𝐑𝐅 Reverse Faulting Stress Regime 逆斷層應力場
𝑼𝑪𝑺 Uniaxial Compressive Strength 單軸抗壓強度 𝜽 Frictional Angle 摩擦角
𝝁 Frictional Coefficent 摩擦係數 𝑻𝟎 Tensile Strength 抗張強度
𝑷𝒇 Pressure 液壓
𝝈𝟏 Maximum Principle Stress 最大主應力 𝝈𝟐 Intermediate Principle Stress 次大主應力 𝝈𝟑 Minimum Principle Stress 最小主應力 𝑬與𝑬𝑻 Normalized stress eigenvector 單位應力特徵向量
𝝈 單位應力特徵值
第0 章 附件二：應力分析參數代號
v
Pole of dike attitude 岩脈法線向量t
Traction 岩脈面所受的三軸應力場 𝑷(𝑨) Probability of minimum normal stress
orientation
最小正應力方向出現機 率
𝑷𝑩(𝒗) Bingham distribution 賓漢分布
K
Matrix characterizing the distribution 空間分布係數特徵值矩 陣𝜺̇ Strain rate 流變速率
A
Material parameter 物質參數 𝒇𝑯𝒎𝟐𝑶 Water fugacity 水的逸度Q
Activation energy 反應能R
Ideal gas constant 理想氣體係數T
Temperature 溫度𝑷(𝝈𝒎𝟏−𝝈𝟑)→𝟎 Probability of zero differential stress 零軸差機率