From 48cb88b871ef5a533ec1ee495d7e16653fce5855 Mon Sep 17 00:00:00 2001 From: Pedro Arduino Date: Mon, 10 Jun 2024 16:57:32 -0700 Subject: [PATCH] small changes to all --- source/.case_1.rst.swp | Bin 40960 -> 0 bytes source/.case_1.rst.un~ | Bin 235866 -> 236329 bytes source/.case_3.rst.un~ | Bin 0 -> 591 bytes source/.case_4.rst.un~ | Bin 0 -> 591 bytes source/case_1.rst | 2 +- source/case_1.rst~ | 2 + source/case_3.rst | 2 +- source/case_3.rst~ | 435 +++++++++++++++++++++++++++++++++++++++++ source/case_4.rst | 2 +- source/case_4.rst~ | 324 ++++++++++++++++++++++++++++++ 10 files changed, 764 insertions(+), 3 deletions(-) delete mode 100644 source/.case_1.rst.swp create mode 100644 source/.case_3.rst.un~ create mode 100644 source/.case_4.rst.un~ create mode 100644 source/case_3.rst~ create mode 100644 source/case_4.rst~ diff --git a/source/.case_1.rst.swp b/source/.case_1.rst.swp deleted file mode 100644 index 640fd82bb637feba22034fc471879f848228e815..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 40960 zcmeI53y@^jS>GGWF@9qkY+{pygIz|my)(TtyV{4wmXqDtUF{<6YP_>rkr;b)r~A(I z)pqwC_wAn9ks=$As|*e)FcO3+z}QalD%k=j@dMd_fm8)k29+Na<*Gmci-Oomg-TK+ zen`&m|DAj8z1`D0BO8*!q`UOj%=EqY+;hJ3o$qzN@9f(AmGc+eiN<`5&kJg`|Mm8b zb^SW?_%mypQNJ}zda3^2>$7}v?!v;6!{_JjT9}`^>H2prEgrfvi~HH3(D0$tX>-_( zdxPxIr8tYDezSe()?{#QxOQmi%*w4tZ@zi;;<+=I&No{5ebFFEdxx@g*l)&%no$<7 zE;Rbt;QFteUYSy0N`Zm`&#N6dyfFWYmw$)*<`>;rd^`PRN`WZ_rWBY`U`l~01*R03 zQeaAfDFy!jpuk}BnYFJl)Te=O2j7t6nfyFn`R?!W`wPJe&^=EF{|LN3|N9&H`E2lD z{`a%^c?|r^{O@P*Q};fW|9t~LPk`^FF|{}SOerv>z?1@03QQ?5rNEQ|QwmHeFr~nh z0#gc1DKMqL|2+ysty=AEIP)))gU|lIVgUd1n`*WH0saX5D)<3;y@>YPH9~XTj%i{{OQA00a@fLSUc;n&3|G9!7?}nZU9dbxcCBi1iTmg47eMtf;RwtT>d$? zdf%`!xZmC4zGuB3HSb$m?caaj!oheoy}y%g%=j-Kdti0_#{2K%M|$J^2hOdg_IRV= zy3wG$xJb_$?)G>BWX?y(0pZ*;HWM|z`+dM*FULHBzP zJ@&wj?$s{s(*fPHXf2ojQ!jUSvH92TVlVA?qfTdMQa9C;l%CWsw_`@Q(MtxyR_sy+ z7!L-WScxI78TH&+>^A#xD`_%BH_VdWhML>rGT9(er_wfmyFoin`#ZBPfI$!M~ZZZFp6#y_={v@=w*Ze`Giq#HZ=6dI}AoI4zTIqKF2`n}GV?Ks(J z57hJZq|*s^91p)N9GQ2U&Gm5ikb%1GiH{tfpD!MoKQnjC%{04*vbcF5JbN`&U4uy z+VkSTxU*qzbBj?Y+2}30CVi#{dT=poMxA)k-E`Ewvc>{lPd0}AcyZA+4kfU9oLTnL z!fMIs`I{S?y^UI}e$r*hAa+sfo=B~_LF!f*^VxpXYbIGUb*G{oiGX2`adskRdu?aJ z9T$czM$7WD*0`T`SWSJ%ldvq-kq51Ki?y(6i;XrmJG{{TfcQt(3#OI`ikXTI3k$iz zB6G+y#?qymFB=`E^XL%ElNb;WhAZqN%PXe6?-_PjUrk9IG zK{wM)Tgkf3Z9nb0m4>@b3#0FpPd9h;*kQ*IGb2iz9YFTp)sB0Rq`S$hk*noQG8qGr zFX?Wk{Xyh;P{T~%IQXs^^DT3`WBec@N6luu$q$&Vw_!sKGJ8u)RRUQr>aa{v2!lRf zF&*$?CmDEoo%H5l)S(-|F0?W0I?-DBhxl$wL>*?1Va6TUKZ6Tsq@|_bMbziCD#(NG z(S)m~)jl`e$(H9pDW{ymUFII*tuwr>C>yAc?S4AkXro3LRhTF(C73`gm-e_Ra_jN7 z%WQgCV9`|wYUA?!%i3ig z$(WVtspvB6N_9fea;Qdxs422RnsyNWXg0X0oL|i?x&m87>-t{k$m(aA73xEsLKMTB z$(FjnYDA-Y>tmK*28^@S=bFi$7^Ak(%j;Q?)st+S&dMuOr{Mm}d7spvXs zgb^dDlw?`5=>u=E2!W{8KmOUb&nDslW0lNm(TillNMF3ED5u1jRJbcaO28;8i#auHa&TWQkDSUedW=4mtl zqaNv*2&)B`^!)Pnb6}b#VtQ$pVJ2zI6a`e`N(a%e7pmhU>Ib5fMhe^7pej;|U*Y6juIyCE%W4jmm#GS* ziTYJ`$m^?gjl6Fyv~;^FhQ*di57o1~70<`s#MotFAZ4mdXSy45V{$cN5i=}Y1bv|t zbnZ$=cu6jW5oT;9=`OKI;g&+=rk#d6i}dMga#+Suf{uas<#0ycF>5nVlYI$OOceyr zhF3_kuw4CI+8Nwy3;worD{5xg&I=25WO3E)sGaW(`e}=0Z*x$+RQz5$IUKap{-V1L zF6l?^!f?=R*J`)y^QpbjE0a05Qm|)MlRdiXljj#}^8Y`GpZc);Rs4VL$-nHmwc1O; z=bnQv4n7Dz0NP*!TmrX%SA$>0&;JPcFnARFQ+)pK24}!&@DM)#gWx`p0L22H4W0!q zk`!q{P-_`kAhzZiUDMxcSEh#1t)-f^=E-+f)C-Be-L~C zJOX|W%z}fU4m8eBgHLI^Utb^j6|aM(#6+)mmm2PL!<8I%m;LSetl{b>d#=h?TE4f& z=^$>ldx*-8JJZ`hG$D$68})`;ruHIBd$Y!%#28jiU351eKQTAIaO5~|J979iOj|pJ z@@k67ZH>!$s9GJY<#L^%7BD1G+FEUGykjJ+`6}pbIr0(`Jg*2w<(u+(TfW>nY{qyn zVZGEY#oefX6&9|E82;m3w|NGEUcmxEyKknMj2iyJjzGn&nM(esb@qXP&FIup3vD+~qBf=Lu8N$OyH8%Gh zK_71orvt$gdBbwgp-M4L8m`P9GpM`{ml!sY$LtQx;1m%%vbc%~uFS2Ib&fj--ArN0 z+mmlb?NVk>K=DZVsb0f&}i6i$TmOWg3a%{@?aM(kmm(2Rf4*Pk1>JKdV2SkFrD`p#o zX5CWBls5h%gq26E6arjorzvD*N%x0&U@P}7b1NJo?ocCz729mf>SKOI$7Uy0JU|+b z2hD(}Ucn8Dz3YkpS}4cMxDW15{H%JN>!zf&)q8+54#f7TR|^ zHP21mgS?6okGLu=Td-cW(2+j7t_ zt2Uzz@3-VGzmK~ayVYIYxHoHT?$pCKD}`!ag`4=kLdAL=Uodo~7i}dpZ4<8!byA`r zEW%*W)a&QXmRd1`j;FMW>-FVept*3t?4?pLR9S9$2Rj2nZcX53W6cvUY7wH5Yldx; ziya?rAh>!pBZ#1-#Mp>IM~q=`ZQuuS$0oj^H?9i4sMqg&Z5UAQYica|8pE2Gi_hTf zdfk=;cCMC0A*l0FjX&wNS$Oi!rIpijdX49GwQunPF?dI@mU{hS+M8=9abG2e(ucbD zj2VMsniX^AX|6Zyu3_E5ZAXc+dU~$Jwie1uCytiysn@I2JPkpRN}X7YTAe=lvZNKS zwvfOezBW+cOu_Jd$qv;eNLefVhdr#QPSRxJeB6nE11@Sg$DXu!Am}|GPRE5szakn? zmDs8bF$7UinY0w1nA_cmgm$5Ucndv{FMW>%=nyw+D2P%_vse`UK?g&A^gYIheM7f- zHtLvkS7ctU>_(be#L~u<@z{EwODsaJv4Z6cF|r=vbG#uOif+^+W*In~wP^88Ce$=L z<1^8r-kGx|s^h+f2-U=n^6Fvcd-EWndSZWyrAT%>Bte?V>67)074n7&pV}l*KB{fZ zVmZ;M80AcR++lHPDno2QQ!-gG?ybDE7{e!6EGPE1SV|FeR{iiQ$|8e#B+k@_q_~fd zL6R|U2^5z&iaHxH#-Z%+@QEoTwWa=C(#Mj)+QuBZwAzV?2`+U-6N25=6WD@5K zqn!Ec_78z-;n`SpQ*bsIguB|e)!EZN7{Qa4kIH!UvB8RBnpo@*Oa>h9)fLF$_rSt_ z*?73rmY~#|k3wvw=yMjPLZTv-MT;x_n28%3jafI}IB`No|3c%)!Z9YINkr>_r<5qG z9zwoy2LM%b-D&-rrgX;^nT=4oywXGKx-P7-{c#n2$8h?wctNY5i4pGyvS7iiDF8#C zz1gk@ZE@sLXfHskOTvU{O4tbj5)`6a>M$dUK8pj4cY^eu-D7pZk`iaRTvEt354Y!> z>3N7KRdiJyFQiemJH1%eKRnkk|Nn>ZoBuvOwfukO^#A+k*J{57eu2IGp9h~L7Vru1 z8WQ|(0e^{K|KGrGfL{hb4Sou|8Qc&4IcS5+;5qpB&jt_S%RdNa!K1wEUErNy4!jiT z{a>OVp9B99d7?)?LhnVZvrv61AG@a0KN^p z1WZ3qi2_m}HLpc57i2b#{-w<{+%MgM;U_EA|1tTl$=~vCtD$F4_jwI0?)$lR9>rRVP9{vKX&-)v#|+8aOeqlx;J6JJZdW zU4;Q8r-7qDvIAxX*YbX#nTj1Yb9?h_h7spr7K;i+&3=`3RZixym01@LnvDbFIxNLd zm3p^rly#G%1Iz~5zWMf|83>Z?xv6hm5x3*26!XSq|0iY-dk+d1n}e2n8hX44@`RyI za297vL2dC7(Gjd`$EP%gcxy$4yh>&ip=WdY?2;T5y+1@2_|p4&yKa=S56LkhvS6M& zvxPC{ccj_kSD1kzl;HsFCKf8}wdqi-kdIt9%CXm;WyLL>Jm2c7-~@^lF^KziFU0!CbJ zhJ)F|3|JHad#KVP;jd1}Ukdvf*$|6mM~MJjJ3yXzL7p`KyXk=jE;EDxGf;K|5w%EPkms-g|ML>zQZA;4Bp~JGMeO68@ ziD02_?&XYy<{Y2k)f}DQJGmxr@O0juW!9Ya>@n-gu*gywazjRqtm2ZQ@W-%swWnMa zpN=7)lOWct+psP0$lG0R24;iMGNrvSe?Y&Mb5U6Tj2D|Sj}ci=tZ-xDM*P>PZ>vaR zfB-5Rfy#AYHnhy@^)q?I?_^2%43(5e=o;=0#6aG7VCbxrF(X4JQ$`!;Se4$H@rf$= zD#+aF5v#WHBoj1A-Ubqqr7^;jc|y+Q?LHfo7h7Vg3G}ikuzcp-5*I<5tRjK3|Gm|VHOG}Ap|ZJ$BP`UtPKY@r_dQA z4p{I_NE|RO4;&?ehJ-MaR%}TpF``smne3a*vVKPL9(Aj-Kitel)a^#A`d!4K>FavE zrWEzyb+-iAJ)97V%~$m}OHSC1E*H1h9u_9zn|1tVMp|x%pqH4R32d5k$GFZXDrd28 z-viqTv!os)n9s7&w25>Ijo2C}r;wF)xzKjZRq)GAS1SOZ2_8sbz!K(-o6>`fVXv)Z z9-AW)ozmWoQhS@`_*e8T1At%rHlMXpxu)C)g=iJnAqoa>PayX7tT0XNM4<~McO^QN zBizRx&>j$-fNj)izk5|G%InD9klUu;2suaCSi1(MWYtl-%d1>X zwN_5qS7JOv!g$yawj6z{F`F=I+BXr>mkGXRn@WRZ#wz=1>agr%r51@`*e(1vo`%IL z!P<^lJN%ru4$&nTvdWi1mtS`|K|JmMzYrfk0rLM<HpSMcBRatoiSq%a_aghdmqg(b$x8#`0LR1 zkxC4ovR3s@t3qQ#VWkMI)xur+x&NJwaQhy&hFeB{`uoFIdpzCK3FYCwIk$+*)?U1u z`rf-K$0do!*R9F-TMDTPayoBUWOw&-R?Mp>mx@}QD~i7mHFRf+f}IsB*xCIw#l@R9 z>gnb2)Caz>lA4Lnr1s4D+%^5`-nVYgTIAJz6;Dzkt$tpTla34P^Eb{be`9wKsiW4t zSEx^Mm!t}I-?FsYG@{}0@7G#BmAZWrd#PxSV$O0(%c@Fo2GKLNi9-Vc5b90$k1yYTtn3EE%-G{8557lA(^ z4)Dj|KY@pc1w05Y0Ocmkf`i~`;2VGrB>Y3-1Rnw)1pkJ7g!h3zBWCb8_&E3_@CdjJ zR>0H24Pb+ug>`TTv4e}?<=}d%)e`0{FZB(Z)yES-DQG3?W8se6au6T6D>Qi?<(Mx#M<=h$YE^ zJC-jWJa}uwj>yG$dyw|n+ntuz8`XLV(4-zDF@^eOBcM73SCMIn$S4-@nC z`v}&%JnzeTIJQkGB@F?gFW|dlp<&_HBIXq8haK9V_0KRrZbi zK2xXx*yGK|p8AXPLI5Jd#ZJn)rFF?LnXqLw%1NVp@eOxp8T;2h1N!PZS&HJVs(SS4 zjm4&gm`2f%4eHU9$~h8RqG4U5aqSYoP$fHH5-}2D+r*z0qV}uN(jeIbCf%?|n9FII zm+|LKj_rdn#jp7Ks9IoO_4G2^c7%7?uVVZn5Q!&BY@kdLGAQ^&`p|?urhISA5B7Z6 zr~R9)B&dnANkJ+0QL;R#zgkdGtpX?t3RcR9Y^A7x#C6sDYDnSR7P$wO@L$Q6_uHt- zk-uFv2c9gJsZNP@+jfb36V+EkMscUVU>&v%wXz7|RAq-Y6dXwAmEsmzrpGJA1|!t< zi8qygPFiW|hMzP`+_{j~7>taZhKdS;N#ie)7kp7cKDoXr3Z{1x>;e_gF}X?oPFk%( zpzfe3D9F>9R2g6)KUEm8ucJMmTy9W@K&gTAkCgW<%pZda`%C9Hy{VMXXgSq@?v_Jd zIGe1biXqo+A^k*2Jft)a>|g@k3GeL|mLVDAroB_lD{Zb`v_pY(=D?~sZL8%=EJx!q za~|Z%*mktvh89z(3cFO@tV}3ZoRdKEk3TgAicZvZ%0XsLD+O75H^tciUQbSFNX}VB zL6Sk9Uco(>ZyY;@`Jo;+)9RjHF{D|y7AbQBTHcOh(sSo_2-Y=+>@8WDi8cUdZa=r8 zt#7N3FGMR99Vr$5lFa@XrIA89$7bgiiRScPspZOSx5Yw0xv0fckqDDkd~BX?vT7Bp zR;o-&Ah@6A;)${O-lNVf7m3Sd0n{a5A~(6>8Vw@v21c0{J$)8 z8&Me{nNSQ`q*}l^X6;D-B8s%E!|_(Rj8yH;1~aIfj0r_B}o@!(Hv0T2fg~s8L#`sJA|2ICL{dXY$UvBeT z@aJCzwBP?xzW*?IE9e0E@@IhVKLw8BhtGpg^5E}+e+G2^pZxAW03GnH;Dz9w_}+)X zOTdf3yYREWAABG9UT_s$0Xiq}0KWGOcm{YJzx)08(*F+p`3=M-z{kO(;8(z_@tI!* zl;8hF_U}In{uF!+ybt^&xF4io87zS#;FaJRpduvqo$B@&A1{m$^hnLm3;*B0r4c4s z2}k^#4yvo#)aZd{{vC7IUFTOqt?NZB*J5yEhoXh%7q^qvpv^I99M{Hwk9c^ zukT*f1+WKBM^}lFsFUYqSecP%nXy*D=ud0&4kG{0-_CIe zD>{|Q$_YXlabdvAgw$b;;z8;85$j$TZ@!7c3(oX(tX1hYk>wQ=*S{7wttM}z(<>^0 zy({forB{n8dakae*A%j%35?t3RWg_M_Z139L0Q9dle}9?%Ypa9SxtGKF{QHA6YC1Q zrmRCI0MUxODhebT=7*&fp)=e_K8)5l?@pPc8h-A5AQ&*r(>{fxvX@B)t^`BI(qSwi zPZJojjBJrHAtPc*=v7~x6Vr%euLOO!#R5E;=dp(`jX;;|eAdy|s!)aoG_>$`9`{4{|F51~ zGS+i@%mPDADnq)Q!Jxs|Au8hdB;z16ogYY*j1}guD6v;A+%yM2U-`p7)h3{bQLxhpiHG(Sznd$SEC-21Os)SHiZI$&L z#WtLJJ4#jSr2=Lm;pogQl|4P{tNQ6_)mNEBg|l`x$aT0Tr@gpW@3mRm{oXN-i7H`g zF^s&+5MyC2O?Z{g7^qUQmOH5>`*6U4KizG}g7J#JUbjVhMTZ|qE>qB>7=ax{sU>c_ z;zPGA41ctruNw)W4+$Xe&C|=v+Hy3pt|^rGTqmT9reOI|cb!{P6JMG$Ij5RyoCSV&TcAH*u7OPL@POWQmHq zlU~u#VvVtcaD(-vpo(pTm}=zI7Rr+Y*@DL0P0>K>mC*-^79+RTPvUjQLE*NX%p6qb zi%lOZsMAoq!3Aa5E|F}olMKD249D!CJghR#3$3I)V27hKt(pryk!aHkAosAx0K}W+ zK|P^`e7-DDp@TOwliRAr>qx`^RNBX(AYs&1IO5=60YPh+@r zMa!WWg8ws&K(adT{+KV|W1p%xkQwaPTg9&N(;aGCM|wo9u>Ak?`0qEfw=VzxI6uCE z-~S|d0{lMsD0nY;5BN#&gCGX419yP4Ks5q~z;}Xw0A2u|0lrL(;4i_SgFghH0RI8} zEckKoL*N0>1#93|pge&?K)C|?_XVB~o+K~e3GjLF8L$f808}q<5d1^%M~vY!;M3p- z!4H6Y!K=U`urV^e>1RrTDFvn!m{MR$fhh&16qr(AN`WZ_zG@1{|I+8FWm}A>Tniko_`l=!>9kWmGPDB>rek_t0LF0R)Z`Pc5!#@;OcYfV6sUu50e{6f{sJh!UgrY72fPE=_%z_@=Wi1QY@zFa`=?7x z6EFM;=F`NBu-!LJyx9BfcfUbX=#OdQ#We9^nt0(e9%TEN?$H`y(?tj1O%pHLWk!Ig zGrE00wv9ebyeQKdrimAD%f1{lO}v;UUQ81&LWu|&K!44|3v||YMD`@fCVBP;|5A$n n?FpYu;`k>zRXC%6WRt)Xi5&cU1Ehp3%=6DM4*S0Rwf27iPpI54 diff --git a/source/.case_1.rst.un~ b/source/.case_1.rst.un~ index 07a81153a820379db7fe19629b284d51b43a1adf..bbd0fd891f3712588de901ab03372bbb40d63f12 100644 GIT binary patch delta 247 zcmcb$iErgLzWT7t-1(t-F8NOxn2g-TCh6&3$b5V@JzU(}JXDySsVIK#nvjLB8>(Yh zNCz@7Fh(&jFo+bE=DWH2D(ET%r8eLVVHp-Eq&51 z7LW=lhWHC$c?O2Y?AC0?)@-J&+05(fnHcN0%QP@AXB4f2N<%5IdCc1#{h2)(r?cndv$(*LkpV*gdQIxA#P9 z;>9}*42)3>5TFR98G&MT5H^U0VFre@^og%ofU*pdjis%njIE_iTT7XD)-y3MY&U3N NUe36EQZw^(aR7f*Cf)!5 diff --git a/source/.case_3.rst.un~ b/source/.case_3.rst.un~ new file mode 100644 index 0000000000000000000000000000000000000000..8dd473367fecb7dd909e07c2169c096d5d70b2ad GIT binary patch literal 591 zcmWH`%$*;a=aT=Ffk_}CfJZU&*1InTP4j|{^gnHtD%N1^zO7cxnAhJN6Hvgwz_^)# zfk7!aM!~AMw7@FCI6)yJu_#+XS0OmFBvm0OwYVTZuQ*k~5U7e7iWz}42!jBO4d$n% zPdd*65sAM5kw+mxQZPdp{sRHr7!+lr9O{GsFgngbqvNXt&`2gAW`V{yC@P4Eb<@V@ Fs{p5sHW&Z^ literal 0 HcmV?d00001 diff --git a/source/.case_4.rst.un~ b/source/.case_4.rst.un~ new file mode 100644 index 0000000000000000000000000000000000000000..56c3a99ff1463dd37ea20b0e2d89289084474ed4 GIT binary patch literal 591 zcmWH`%$*;a=aT=FfoZ|Cq#I8~JQsed$&cP7{EqdHj^X4~n}nLI#^ivVFPe8TFfh6> zFfb?u$0%48mljwh7$+!XBo<{W=qdzfmZT~Kr4|?D=M|?a7y(r=Lop+e24N6@vBCVb z^htMEAR_S>Ao3_AND5{M!+#)v8-t>3ltY~m07l1cXmos)02;{z#4OMl2So)Dv2NP< Gd=&tSkT_=m literal 0 HcmV?d00001 diff --git a/source/case_1.rst b/source/case_1.rst index dc47874..9594fad 100644 --- a/source/case_1.rst +++ b/source/case_1.rst @@ -1,6 +1,6 @@ .. _case_1: -quoFEM - Settlements +QuoFEM - Settlements ================================ Author: Kendra Mutch diff --git a/source/case_1.rst~ b/source/case_1.rst~ index a300176..dc47874 100644 --- a/source/case_1.rst~ +++ b/source/case_1.rst~ @@ -30,6 +30,8 @@ The example problems in this project will utilize the scenario, soil profile, an Fig. 1. Problem statement. + + .. list-table:: Soil Profile Parameters :widths: 25 25 50 :header-rows: 1 diff --git a/source/case_3.rst b/source/case_3.rst index 8eebe30..382bb99 100644 --- a/source/case_3.rst +++ b/source/case_3.rst @@ -1,6 +1,6 @@ .. _case_3: -S\ :sup:`3` hark - Site Response 1 +S\:sup:`3` hark - Site Response 1 ================================== Author: José Manuel Barreto Espinola diff --git a/source/case_3.rst~ b/source/case_3.rst~ new file mode 100644 index 0000000..8eebe30 --- /dev/null +++ b/source/case_3.rst~ @@ -0,0 +1,435 @@ +.. _case_3: + +S\ :sup:`3` hark - Site Response 1 +================================== + +Author: José Manuel Barreto Espinola +------------------------------------ + +Introduction +------------ + +One-dimensional (1-D) site response analysis is a geotechnical engineering method used to evaluate how seismic waves propagate through soil layers from bedrock to the ground surface. This type of analysis is crucial for understanding the local effects of an earthquake on a particular site, enabling engineers to design structures that can better withstand seismic events. +The primary goal of 1-D site response analysis is to predict how different soil layers will affect the amplitude, frequency content, and duration of seismic ground motions. + +Problem Description +------------------- + +On this problem, we will perform a site response analysis on an specfic location subjected to a seven different earthquakes in order to analyze the propagation of seismic waves through soil and obtain the ground surface response. The ground surface response is typically the major output from these analyses, along with profile plots such as peak horizontal acceleration along the soil profile. + +In cases where liquefiable soils are present, maximum shear strain and excess pore pressure ratio plots are also important. + +In the figure below, we can observe a representation of the one-dimensional response analyses, which assume that all boundaries are horizontal and that the response of a soil deposit is predominately caused by SH-waves propagating vertically from the underlying bedrock. + +.. figure:: ./images/Case3_siteResponse2.png + :scale: 50 % + :align: center + :figclass: align-center + + Figure 1. One-dimensional response analyses + + +Solution Strategy +----------------- + +For this example it will be implement the Site-Specific Seismic Hazard Analysis and Research Kit (S\ :sup:`3` HARK) tool, which focuses on simulating wave propagation along soil depth using finite element (FE) method, to perform site-specific analysis of soil in response to earthquakes. This tool provides multiple nonlinear material models for simulating the soil behavior under earthquake loading, The available constitutive models are listed below:: + + * ElasticIsotropic (Elastic). + * PM4Sand. + * PM4Silt. + * PressureIndependendeMultiYield (PIMY). + * PressureDependMultiYield (PDMY). + * PressureDependMultiYield02 (PDMY02). + * Mazari Dafalias. + * J2CyclicBoundingSurface (J2Bounding). + +For the porpuse of this example we will implement and provide basic definitions for two of these constitutive models: + + * **PM4Sand Model:** this constitutive model is developed to simulate the behavior of sandy soils under various loading conditions, especially during seismic events. It is specifically designed to capture the cyclic and dynamic behavior of sands, including the phenomena of liquefaction and cyclic mobility. + + .. note:: + **What is Liquefaction?** + + Liquefaction occurs when seismic waves induce cyclic loading in saturated, loose, sandy soils, causing the soil grains to rearrange and densify. This rearrangement increases the pore water pressure within the soil, reducing the effective stress and consequently the soil's shear strength. When the pore pressure approaches the overburden pressure, the soil behaves like a liquid, losing its ability to support loads. + + * **ElasticIsotropic Model:** Often referred to simply as the Elastic model, this is one of the simplest constitutive models used in geotechnical and structural engineering. It is based on the assumption that the material behaves elastically and isotropically, meaning that the material's properties are the same in all directions and that it returns to its original shape upon unloading + +SimCenter Tool Used +------------------- + +#. Click on the icon of s\ :sup:`3` hark to open the application. + +.. figure:: ./images/Case3_Step1.png + :scale: 70 % + :align: center + :figclass: align-center + + Figure 3. S\ :sup:`3` hark executable icon. + +#. Operations Area: In the upper toolbar, you can see three options (Figure 4.): + + #. In **Height**, you can choose the depth of your soil column. + #. In **GWT**, you can choose the depth of the groundwater table of your specific site. + #. In **Total layer**, you can modify the number of soil layers on your specific site. Click the "+" button to add a soil layer (a layer will be added below the selected layer) and the "-" button to delete a selected soil layer. Click several times to add more layers. + + .. figure:: ./images/Case3_Step2.png + :scale: 45 % + :align: center + :figclass: align-center + + Figure 4. Main window - Operations area + +#. Soil Layer Table: In this table the user provides the characteristics of each soil layer, such as layer thickness, density, V\ :sub:`s`, material type, and element size in the finite element mesh (Figure 5.). + + .. note:: + Variables are assumed to have m, kPa, and kN units in the Site Response panel. + + +#. Soil Column Graphic: The first graphic on the left of the panel shows a visualization of the soil column (Figure 5.). + +#. Finite Element Mesh Graphic: The second graphic on the left shows the finite element mesh (Figure 5.). + +#. Configure Tab: This section shows the configuration options (Figure 5.). + + * Under the *"OpenSees"* label, type the path of OpenSees executable. You can also select the executable from your local computer by clicking on the "+" button on the right of the input area. + * Under the *"Rock motion"* label, type the path of a ground motion file. You can also select the file from your local computer by clicking on the "+" button on the right of the input area. + * Under the *"Slope parameters"* label, we can modify the degree of inclination of our study terrain if this were the case. + + .. note:: + The rock motion file must follow the SimCenter event format. + + + .. figure:: ./images/Case3_Step3.png + :scale: 45 % + :align: center + :figclass: align-center> + + Figure 5. Main window - Soil layer table, graphics and configure tab. + +#. Layer Properties Tab: This tab allows the user to enter additional material properties for the selected soil layer (Figure 6.). + + .. figure:: ./images/Case3_Step4.png + :scale: 45 % + :align: center + :figclass: align-center> + + Figure 6. Main window - Layer properties tab. + +#. Response Tab: Once the site response analysis has been performed, this tab provides information about element and nodal time varying response quantities (Figure 7.). + + .. figure:: ./images/Case3_Step5.png + :scale: 45 % + :align: center + :figclass: align-center> + + Figure 7. Main window - Response tab. + +#. Click the “Analyze” button on the right side of the upper toolbar to run the finite element analysis. + + * You will see a progress bar displayed at the bottom of the right hand side of the app, which shows the percentage of steps perfomed (Figure 8.). + + * Once the simulation is done, the *"Response"* tab and the *"PGA"* profile plot will be displayed. At the same time, a pop up window showing *"The analysis is done"* will show up. And when you click *"I know"*, the progress bar will disappear (Figure 8.). + + .. figure:: ./images/Case3_Step6.png + :scale: 45 % + :align: center + :figclass: align-center> + + Figure 8. Main window - Analyze Done. + + * You can see the profile plots of the PGA, γ\ :sub:`max` \, maximum displacement and maximum r\ :sub:`u` \ by clicking on the respective tabs on the right side of the Finite Element Mesh Graphic and the surface and ground motion by clicking the Response tab (Figure 8.). + + .. figure:: ./images/Case3_Step7.png + :scale: 45 % + :align: center + :figclass: align-center> + + Figure 9. Main window - Results. + + +Example Application +------------------- + +Soil Condition +~~~~~~~~~~~~~~ + +The soil column being analyzed is a 20.29 meters high sitting on rock. The ground water table is at 4.57 meters below the soil surface. In the column, there are a total of three layers. Each layer is meshed by elements with size of 0.20 meter in height. The soil profile is shown in Figure 10. and basic properties of soil layers are shown in Table 1. The first two layers are modeled by PM4Sand and the third layer is modeled by elastic isotropic material. + +.. figure:: ./images/Case3_soil_profile.png + :scale: 70 % + :align: center + :figclass: align-center + + Figure 10. Soil profile representation + +.. list-table:: *Table 1. Soil Profile Parameters* + :widths: 5 5 5 5 5 5 5 5 5 5 + :header-rows: 1 + + * - Layers + - Thickness \ + (m) + - V\ :sub:`s` \ + (m/s) + - ρ\ :sub:`unsat` \ + (kg/m\ :sup:`3`) + - ρ\ :sub:`sat` \ + (kg/m\ :sup:`3`) + - G\ :sub:`o,ref` \ + (MPa) + - D\ :sub:`R` \ + (%) + - h\ :sub:`po` + - v + - E\ :sub:`50,ref` \ + (kPa) + * - ESU1 + - 0.91 + - 266.09 + - 2.08 + - 2.16 + - 335.16 + - 79.50 + - 0.52 + - 0.3 + - 167580.91 + * - ESU2 + - 17.4 + - 202.39 + - 2.00 + - 2.08 + - 76.61 + - 39.67 + - 0.52 + - 0.32 + - 14364.08 + * - ESU3 + - 1.98 + - 380.39 + - 2.24 + - 2.32 + + - 316.01 + - 85.98 + - + - 0.25 + - 153216.83 + +Earthquake Condition +~~~~~~~~~~~~~~~~~~~~ + +Information on the seven ground motions to be used in this example is shown in Table 2, and in Figure 11, you can see the response spectrum of the 7 earthquakes in a single graph. + +.. list-table:: *Table 2. Ground Motion Parameters* + :widths: 10 10 10 10 10 + :header-rows: 1 + + * - Motion + - PGA (g) + - dT (sec) + - Duration (sec) + - N° of steps + * - Tohoku 41207-EW + - 0.58 + - 0.01 + - 359.98 + - 35999.00 + * - RSN6911_DARFIELD_HORCN18E + - 0.61 + - 0.01 + - 60.17 + - 12036.00 + * - RSN803_LOMAP_WVC270 + - 0.67 + - 0.01 + - 39.98 + - 7998.00 + * - RSN4457_MONTENE + - 0.68 + - 0.01 + - 40.39 + - 4040.00 + * - Tohoku Ishinomaki-NS + - 0.77 + - 0.01 + - 299.98 + - 29999.00 + * - Conception-L + - 0.82 + - 0.01 + - 141.67 + - 28335.00 + * - RSN727_SUPER + - 0.96 + - 0.01 + - 22.20 + - 2221.00 + +.. figure:: ./images/Case3_logSpectraCombined.png + :scale: 60 % + :align: center + :figclass: align-center> + + Figure 11. Response spectrum. + +The rock motions, in SimCenter format, can be downloaded from the `rock motions `_ folder (this can be found in the GitHub Repository). + +Results +~~~~~~~ + +The below images present the PGA, maximum shear strain, maximum displacement, maximum excess pore pressure ratio, ground surface response and rock motions results obtained from S\ :sup:`3` HARK. + +*Peak Ground Acceleration* +^^^^^^^^^^^^^^^^^^^^^^^^^^ + +.. figure:: ./images/Case3_PGA_1.png + :scale: 45 % + :align: center + :figclass: align-center> + +.. figure:: ./images/Case3_PGA_2.png + :scale: 45 % + :align: center + :figclass: align-center> + + Figure 12. Peak Ground Acceleration. + +*Maximum Shear Strain* +^^^^^^^^^^^^^^ + +.. figure:: ./images/Case3_Shear_strain_1.png + :scale: 45 % + :align: center + :figclass: align-center> + +.. figure:: ./images/Case3_Shear_strain_2.png + :scale: 45 % + :align: center + :figclass: align-center> + + Figure 13. Maximum Shear Strain. + +*Maximum Displacement* +^^^^^^^^^^^^^^ + +.. figure:: ./images/Case3_Displacement_1.png + :scale: 45 % + :align: center + :figclass: align-center> + +.. figure:: ./images/Case3_Displacement_2.png + :scale: 45 % + :align: center + :figclass: align-center> + + Figure 14. Maximum Displacement. + +*Maximum Excess Pore Pressure Ratio* +^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +.. figure:: ./images/Case3_Ru_1.png + :scale: 45 % + :align: center + :figclass: align-center> + +.. figure:: ./images/Case3_Ru_2.png + :scale: 45 % + :align: center + :figclass: align-center> + + Figure 15. Maximum Excess Pore Pressure Ratio (r\ :sub:`u` \). + +*Ground Surface Response* +^^^^^^^^^^^^^^^^^^^^^^^^^ + +.. figure:: ./images/Case3_Ground_surface_response_1.png + :scale: 45 % + :align: center + :figclass: align-center> + +.. figure:: ./images/Case3_Ground_surface_response_2.png + :scale: 45 % + :align: center + :figclass: align-center> + + Figure 16.1. Acceleration (m/s\ :sup:`2`). + + +.. figure:: ./images/Case3_Ground_surface_response_3.png + :scale: 45 % + :align: center + :figclass: align-center> + +.. figure:: ./images/Case3_Ground_surface_response_4.png + :scale: 45 % + :align: center + :figclass: align-center> + + Figure 16.2. Velocity (m/s). + +.. figure:: ./images/Case3_Ground_surface_response_5.png + :scale: 45 % + :align: center + :figclass: align-center> + +.. figure:: ./images/Case3_Ground_surface_response_6.png + :scale: 45 % + :align: center + :figclass: align-center> + + Figure 16.3. Displacement (m). + + Figure 16. Ground Surface Response. + +*Rock Motion* +^^^^^^^^^^^^^ + +.. figure:: ./images/Case3_Input_rock_motion_1.png + :scale: 45 % + :align: center + :figclass: align-center> + +.. figure:: ./images/Case3_Input_rock_motion_2.png + :scale: 45 % + :align: center + :figclass: align-center> + + Figure 17.1. Acceleration (m/s\ :sup:`2`). + +.. figure:: ./images/Case3_Input_rock_motion_3.png + :scale: 45 % + :align: center + :figclass: align-center> + +.. figure:: ./images/Case3_Input_rock_motion_4.png + :scale: 45 % + :align: center + :figclass: align-center> + + Figure 17.2. Velocity (m/s). + +.. figure:: ./images/Case3_Input_rock_motion_5.png + :scale: 45 % + :align: center + :figclass: align-center> + +.. figure:: ./images/Case3_Input_rock_motion_6.png + :scale: 45 % + :align: center + :figclass: align-center> + + Figure 17.3. Displacement (m). + + Figure 17. Input Rock Motion. + + +Remarks +------- + +.. note:: + In the out_tcl folder, located on your computer (SimCenter -> s3hark -> out_tcl), you can find all the results of the analysis performed by Shark and plot them in the tool of your preference. + +.. warning:: + If you perform more than one analysis, make sure to copy the results before running the next analysis, as s\ :sup:`3` hark will overwrite the new results on the old ones. + + diff --git a/source/case_4.rst b/source/case_4.rst index 63c7c2e..d3c07ac 100644 --- a/source/case_4.rst +++ b/source/case_4.rst @@ -1,6 +1,6 @@ .. _case_4: -S\ :sup:`3` hark - Site Response 2 +S\:sup:`3` hark - Site Response 2 =================================== Author: Chungen Tai diff --git a/source/case_4.rst~ b/source/case_4.rst~ new file mode 100644 index 0000000..63c7c2e --- /dev/null +++ b/source/case_4.rst~ @@ -0,0 +1,324 @@ +.. _case_4: + +S\ :sup:`3` hark - Site Response 2 +=================================== + +Author: Chungen Tai + + + +Introduction +------------ + +This page shows basic concepts of one-dimensional nonlinear site response analysis by using various soil material models (ex: Elastic, PM4Sand.) and the lateral spreading. + + +Problem Description +------------------- + +Site response analysis is commonly performed to analyze the propagation of seismic waves through soil. As shown in the below figure, one-dimensional response analyses, as a simplified method, assume that all boundaries are horizontal, and that the response of a soil deposit is predominately caused by SH-waves propagating vertically from the underlying bedrock. Ground surface response is usually the major output from these analyses, together with profile plots such as peak horizontal acceleration along the soil profile. When liquefiable soils are presenting, maximum shear strain and excess pore pressure ratio plots are also important. + +.. figure:: ./images/case4_siteResponse.png + :scale: 60 % + :align: center + :figclass: align-center + + Figure 1. Site Response Analysis + + +Solution Strategy +----------------- + +OpenSees +~~~~~~~~~~~~~~~~~ +OpenSees (Open System for Earthquake Engineering Simulation) is an open-source software framework used for simulating the response of structural and geotechnical systems to earthquakes and other loading conditions. It is widely used in research and practical applications for the analysis and design of structures subjected to dynamic loading. S3hark created a GUI to help user doing nonlinear site response analysis easily. + + +Soil model +~~~~~~~~~~~~~~~~~ +PM4Sand Model +~~~~~~~~~~~~~~~~~ +PM4Sand is a constitutive model used in geotechnical engineering to simulate the behavior of sand under various loading conditions, including seismic events. Developed by Boulanger and Ziotopoulou, this model captures the complex behaviors of sand such as cyclic mobility, dilatancy, and liquefaction. It's particularly useful in finite element analysis for evaluating the performance of soil-structure systems during earthquakes. PM4Sand is known for its ability to represent the stress-strain behavior of sandy soils accurately, aiding in the design and analysis of foundations, slopes, and embankments in seismic regions. The model parameters are grouped into two categories: a primary set of six parameters (three properties, two flags, and atmospheric pressure) that are most important for model calibration, and a secondary set of parameters that may be modified from their default values in special circumstances. The three primary input properties are the sand’s apparent relative density :math:`D_R`, the shear modulus coefficient :math:`G_o`, and the contraction rate parameter :math:`h_po`. +Apparent relative density (:math:`D_R`) can be calculated by correlation to penetration resistance.Commonly estimated based on CPT or SPT penetration resistances, such as the following relationships used by Idriss and Boulanger (2008): + +.. math:: + + D_R = \frac{(N_1)_{60}}{C_d} + +Where + +:math:`D_R` = Apparent Relative density (%) + +:math:`C_d` = 46 (Idriss and Boulanger ,2008) + + +Shear modulus coefficient is the primary variable controlling the small strain shear modulus, G_max. Should be chosen to match estimated or measured shear wave velocities. + +The shear modulus \( G_{max} \) can be described by the following equations: + +.. math:: + + G_{max} = \rho V_s^2 + +Usign following equation to calculate :math:`G_0` + +.. math:: + + G_{max} = G_0 p_a \left(\frac{p}{p_a}\right)^{0.5} + +Contraction rate parameter :math:`h_{po}` is one of primary variable that adjusts contraction rates and hence can be adjusted to obtain a target cyclic resistance ratio, as commonly estimated based on CPT or SPT penetration resistances and liquefaction correlations. + + + + +Elasticisotropic Model +~~~~~~~~~~~~~~~~~~~~~~~ + +In the context of geotechnical engineering and computational modeling, the "elastic model" refers to a mathematical representation of soil or rock behavior under loading conditions, where the material responds to stress with a proportional strain, following Hooke's Law. This model assumes that the material returns to its original shape once the load is removed, provided the stress is within the elastic limit.We can get the shear modulus from shear wave velocity, and then use the following equation convert to elastic modulus, + +.. math:: + + E= (2G)(1+\nu) + + +Where +:math:`\nu` = Poisson’s ration (default is 0.3) + + + + +Lateral Spreading +~~~~~~~~~~~~~~~~~ + +Lateral spreading refers to the horizontal movement of soil, typically caused by liquefaction during an earthquake. When an earthquake occurs, seismic waves can cause loose, water-saturated, granular soils to temporarily lose their strength and behave like a liquid. This process is known as liquefaction. Once liquefaction occurs, the affected soil can flow or spread laterally, especially if there is a slope or free face (like a riverbank or retaining wall) nearby. Lateral spreading can cause significant ground displacement and can lead to damage of structures, utilities, and infrastructure. In this example, we will focus on the lateral movement cause by different slope angles. + +.. figure:: ./images/case4_lateralspreading.png + :scale: 60 % + :align: center + :figclass: align-center + + Figure 2. Lateral spreading + + + + +SimCenter Tool Used +------------------- + +S\ :sup:`3` hark is the acronym of site-specific seismic hazard analysis and research kit. This tool focuses on simulating wave propagation along soil depth using finite element (FE) method. The intended audience for s3hark is researchers and practitioners interested in performing site-specific analysis of soil in response to earthquakes, and educators interested in teaching site response analysis in their classes. The tool provides a friendly interface for users to input and modify soil layers using tables, while the built soil profile and the FE mesh being visualized simultaneously. Results including acceleration, velocity, displacement, pore pressure, spectral acceleration, etc., are visualized for the soil profile and for each node as well, from which the user can comprehend the wave propagation and liquefaction status along the soil depth. + +Features of S\ :sup:`3` hark include: + +#. 2D and 3D elements for dynamic analysis of fluid saturated porous media + +#. Advanced linear / nonlinear soil material models + +#. Total stress / effective stress analysis + +#. Bi-directional motions + +#. Flat / slope free field analysis + +#. Finite rigidity of the bedrock + +Click on the icon of S\ :sup:`3` hark to open the application. Figure 3 illustrates the main window. It is split into the following areas: + +.. figure:: ./images/case4_window.png + :scale: 20 % + :align: center + :figclass: align-center + + Figure 3. S\ :sup:`3` hark HARK Main Window + + + + + +#. Soil Column Graphic: The first graphic on the left of the panel shows a visualization of the soil column. + +#. FE Mesh Graphic: The second graphic on the left shows the finite element mesh and profile plots. Selecting any of the tabs on the right inside this graphic (i.e, PGA, γmax,maxDisp, maxRu, maxRuPWP) will show various results from the simulation at the mesh points. + +.. figure:: ./images/case4_plot.png + :scale: 50 % + :align: center + :figclass: align-center + + Figure 4. S\ :sup:`3` hark HARK FE Mesh Graphic + + +#. Operations Area: The right side of this area shows some information (e.g., total height and number of soil layers), includes the Ground Water Table (GWT) input field, and plus and minus buttons. If the user presses the plus button, a layer is added below the selected layer. If the minus button is pressed the selected layer is removed. The GWT input field allows the user to specify the level of the ground water table. + +#. Soil Layer Table: This table is where the user provides the characteristics of the soil layer, such as layer thickness, density, Vs30, material type, and element size in the finite element mesh. + +#. Tabbed Area: This area contains the three tabbed widgets described below. + + #. Configure Tab: This tab allows the user to specify the path to the OpenSees executable and to a ground motion file. + + #. Layer Properties Tab: This tab allows the user to enter additional material properties for the selected soil layer. + + #. Response Tab: Once the site response analysis has been performed, this tab provides information about element and nodal time varying response quantities. + +.. figure:: ./images/case4_response.png + :scale: 50 % + :align: center + :figclass: align-center + + Figure 5. S\ :sup:`3` hark HARK Response Tab + + +#. Analyze Button: This button shall be used to run the simulation locally. A progress bar will show the status of the analysis. This allows the user to review the ground motion predicted at the surface + + + + + +Example Application +------------------- +Treasure Island, situated atop sand fill strata overlaying Bay Mud within the San Francisco Bay, was subjected to seismic activity during the 1989 Loma Prieta Earthquake. Adjacent to Treasure Island lies Yerba Buena Island, characterized by its natural rock outcrop. Utilizing the site's soil profile and seismic data recorded on Yerba Buena Island, we endeavor to analyze the site response of Treasure Island. This entails computing parameters such as peak horizontal acceleration and peak horizontal displacement along the soil profile. Furthermore, we aim to investigate the influence of lateral spread in varying slopes on the site's response characteristics. +For lateral spreading, we change the slope :math:`\alpha` as 0, 2, 5 to see the influence of it. + + +Analysis Processes +~~~~~~~~~~~~~~~~~~~~~~~~ +There is the analysis process of site response analysis: + +#. Input the earthquake motions: Covent the earthquake motion record into '.json' file. Then, input the path into 'Configure Layer'. + +#. Input ths soil parameters: This is the most important step in site response analysis. The soil parameters are obtained from theory or investigation reports. Then, type all of the soil parameters into the 'Soil Layer Table'. + +#. Click "analysis" bottom: Click the button to run the analysis. The program will notify you when it is finished. + +Earthquake motion +~~~~~~~~~~~~~~~~~ +The motion recorded at Yerba Buena Island from the Loma Prieta earthquake is used in this sample. Figure 6 shows the acceleration, velocity, and displacement of this motion. + +.. figure:: ./images/case4_YERBAISL2_Records.png + :scale: 50 % + :align: center + :figclass: align-center + + Figure 6. Input ground motion (acceleration, velocity, and displacement) + +Figure 7 illustrates the spetrum of this motion. + +.. figure:: ./images/case4_YERBAISL2_RSpectra.png + :scale: 50 % + :align: center + :figclass: align-center + + Figure 7. Input ground motion spetrum (acceleration, velocity, and displacement) + + +Soil condition +~~~~~~~~~~~~~~~~~ + +The following table shows the soil parameters in this site. Using PM4Sand to stimulate sand , and using Elasticisotropic to model clay. + + +.. list-table:: Table1. Soil Profile Parameters + :widths: 20 20 20 20 20 20 20 20 + :header-rows: 1 + + * - Layers + - Thickness(m) + - :math:`V_s (m/s)` + - :math:`\rho (kg/m^3)` + - :math:`G_o(kPa)` + - :math:`E (kPa)` + - :math:`D_R` (%) + - Model + * - SAND1 + - 15 + - 175.3 + - 2.01 + - 0.69 + - -- + - 0.33 + - PM4Sand + * - CLAY1 + - 14 + - 198.8 + - 1.68 + - -- + - 172.8 + - -- + - Elasticisotropic + * - SAND2 + - 12 + - 300 + - 2.08 + - 1.33 + - -- + - 0.77 + - PM4Sand + * - CLAY2 + - 32 + - 280 + - 2.08 + - -- + - 423.8 + - -- + - Elasticisotropic + * - SAND3 + - 8 + - 380 + - 2.08 + - 1.46 + - -- + - 0.62 + - PM4Sand + * - CLAY3 + - 8 + - 300 + - 2.08 + - -- + - 486.6 + - -- + - Elasticisotropic + * - WRock + - 5 + - 600 + - 2.16 + - -- + - 2022.8 + - -- + - Elasticisotropic + * - Rockbed + - -- + - 1830 + - 2.24 + - -- + - 19526.7 + - -- + - Elasticisotropic + + +Result +~~~~~~~~~~~~~~~~~~ + +The following plots show maximun displacement in different slope angles. + + +Displacement +~~~~~~~~~~~~~~~~~ + +Figure 8 shows the result of maximun displacement, we can see that the displacement on the surface increases with increasing the slope. + + +.. figure:: ./images/case4_d.png + :scale: 50 % + :align: center + :figclass: align-center + + Figure 8. The maximum displacement in different slope + + +Figure 9 illustrates the relationships between slope and the displacement on the surface. + + +.. figure:: ./images/case4_dd.png + :scale: 60 % + :align: center + :figclass: align-center + + Figure 9. The relationships between slope and the displacement on the surface