Code Monkey home page Code Monkey logo

casestudies's People

Contributors

akm11 avatar b-rando1 avatar bmaclach avatar danscime avatar deviprasad135 avatar elwazana avatar gothicultra avatar mornix avatar niazim3 avatar oluowoj avatar palmerst avatar samm82 avatar smiths avatar vajihehm avatar

Stargazers

avatar avatar avatar

Watchers

avatar avatar avatar avatar avatar avatar avatar

Forkers

balacij daijingz

casestudies's Issues

Improve your typing skills

To help you in your future efforts, improving your proficiency in typing would be very beneficial. Please select a typing tutor style program and use it to learn about the home keys and how to type properly.

Some seemingly reasonable candidate tutorial programs are available at:

http://www.typingmaster.com/typing-tutor/free-download.html

You can close this issue when you are up around 40 words per minute typing. A good word per minute calculator is available at:

https://www.keyhero.com/free-typing-test/

Glass-BR: Unclear Assumption

In section 6.2.1 assumption 1, I think it would be clear if the points 1,2 and 3 are mentioned separately rather than mentioning them as a single paragraph.
assumption 1

Insufficient General System Description in SRS

Section 4 of glassbr_srs.tex states on lines 322-324: "This section provides general information about the system, identifies the interfaces between the system and its environment, and describes the user characteristics and the system constraints," but only user characteristics and system constraints are provided in Sections 4.1 and 4.2, respectively. General information and system/environment interfaces are missing.

Broken Link in SRS

In glassbr_srs.bib, line 95: " Howpublished = {\href{"www.cs.uic.edu/~i442/VolereMaterials/templateArchive16/c Volere template16.pdf"}{"www.cs.uic.edu/~i442/VolereMaterials/templateArchive16/c Volere template16.pdf"}}," needs a backslash before the tildes, as they aren't being transferred over to the PDF.

Grammatical Errors in MG

The following errors should be fixed here.

  • Unclear wording (line 80: "After completing the first stage of the design, the Software Requirements..." could be rephrased: "...design, which is the Software Requirements..."
  • Extra word (line 95: "Designers: Once the module guide has been written, it is can be used to"
  • Unnecessarily short sentence (line 150: "...more complex. Sometimes this complexity is not necessary. Fixing some design..." could be rewritten as "...not necessary, and fixing some...")
  • Missing comma for clarity (line 296: "...properties, processing conditions, and numerical parameters. The values can be..." should have a comma after 'conditions.')

Remove Rigid Finite Element Theory from the SSP Example

We should remove the rigid finite element related (RFEM) material from the ssp example. It would be a considerable amount of effort to correct how the theory is documented. There would be nothing to be gained from fixing it now. The Morgenstern Price portion of the program fulfills our needs, and it is much closer to being correctly presented theory.

To remove the RFEM material, remove the material in the SRS where the headings are blue. This will break some of the cross-references. If the material being referenced is gone, then the reference should be removed. The table of symbols will also get shorter.

Once manual is updated, we will next need to think about simplifying the stable version. It will be an interesting experiment to see how easy this is. Hopefully the Haskell compiler will be helpful because once a part is removed, it will complain to help track down the other parts that need to be removed.

In the future it would be a great experiment to add the RFEM back in. There is an overlap in the theory between Morgenstern Price and the RFEM, so this would be a great exercise in reuse. Really the RFEM should be a separate SRS, but with material borrowed from the slope stability SRS.

We do not want to loose the RFEM information. We should tag the current version of the repo to make it clear that RFEM is available in this version. It wouldn't hurt to copy the current files and give them a name that highlights that they include the RFEM information. Technically this isn't necessary, since all of the information will be available under version control, but in the future it will be easier to see the RFEM ideas if there is a file with this name.

@szymczdm and @JacquesCarette, you should be aware that we are removing a portion of the SSP example. Please let us know if you see any potential problems.

SSP : Data constraints section does not contain any uncertainty values

(Issue #27 )

In section 4.2.6 (i.e. Data Constraints), the use of values in the uncertainty column of the table is described, however, there are no values in the table itself.

Perhaps it can be removed completely?

Or is information missing from the SRS?

image

(

caseStudies/CaseStudies/ssp/Documentation Files/SRS_SSP.tex

Line 2961 in 220c839

Table~\ref{TblInputVar} and \ref{TblOutputVar} shows the data constraints on the input and output variables, respectively. The column for physical constraints gives the physical limitations on the range of values that can be taken by the variable. The uncertainty column provides an estimate of the confidence with which the physical quantities can be measured. This information would be part of the input if one were performing an uncertainty quantification exercise. The constraints are conservative, to give the user of the model the flexibility to experiment with unusual situations. The column of typical values is intended to provide a feel for a common scenario.
)

Minor Grammatical Inconsistencies in SRS

  • On line 427: "...A flat and monolithic, glass lite of..." could be "...A flat, monolithic..." to be consistent.

  • On line 453: "...Any load lasting 3 s or less", 'seconds' could be spelled out instead of the shorthand '3 s' to match 'days' on line 448: "...Any load lasting approximately 30 days."

  • In Table 8 on lines 1395-1399: "\
    ${SD_{min}}$ & minimum stand off distance permissible for input & $6.0$ & m
    \
    ${SD_{max}}$ & maximum stand off distance permissible for input & $130.0$ & m
    \",
    'SDmin' and 'SDmax' should be switched to match the ordering of the rest of the table [see lines 1385-1394]

SSP : SRS Symbol Clarifications required for consistency

(Issue #27)

Under section 1.2 specifically :

Undefined/misdefined instances:

Other:

Game Physics: Awkward Phrasings

(Issue #29)

The following is a list of awkward phrasings within the Game Physics SRS:

  • Section 2.3's first sentence is incomplete and reads awkwardly. "Reviewers of this documentation should have a strong knowledge, which is at the level covered in a second year engineering mechanics course."
  • Section 4.1 has a sentence (3rd sentence) which reads "Developing a physics library from scratch takes a long period of time and is very costly, presenting barriers of entry which make it difficult for game developers to include physics in their products." Games which don't have any form of "physics" seems slim. Maybe a more accurate description would be: "...which make it difficult for game developers to include realistic physics in their products."
  • Section 4.1.1 (Elasticity) has "... after and before the collision." which sounds awkward.
  • Section 4.2.5 (IM3's Description) has the sentence (when describing t and t0) "...denotes the time at collision (s)," which sounds awkward.

Grammatical Errors in SRS

TODO

CaseStudies

  • Commas
  • Spaces
  • Periods
  • Semicolons
  • Singular/Plural
  • Spelling

Drasil

  • Commas
  • Spaces
  • Periods
  • Semicolons
  • Singular/Plural
  • Spelling

The following errors should be fixed here:

Missing spaces

 - line 287: "...civil engineering.In addition, reviewers should be familiar with the applicable..." should have a space between 'engineering.' and 'In'

SSP : .tex file for SRS is broken

(Issue #27)

6 errors come up from the line ranges of 1702 to 2564 (

caseStudies/CaseStudies/ssp/Documentation Files/SRS_SSP.tex

Lines 1705 to 2564 in f1a7a49

\cos\left(\beta_{\text{i}}\right) + Q_{\text{i}}
\cos\left(\omega_{\text{i}}\right) \right]
\cos\left(\alpha_{\text{i}}\right) \\
+ \left[ - K_{\text{c}} W_{\text{i}} - \Delta H_{\text{i}} +
U_{\text{t,i}} \sin\left(\beta_{\text{i}}\right) + Q_{\text{i}}
\sin\left(\omega_{\text{i}}\right) \right]
\sin\left(\alpha_{\text{i}}\right) - U_{\text{b,i}} \end{array}
\right) \cdot \tan\left(\varphi'\right) \\
+ c'_{\text{i}} \cdot b_{\text{i}} \cdot
\sec\left(\alpha_{\text{i}}\right) \end{array} \)\\
\hline Description & $R$ is the resistive shear force (N)\newline$W$ is the weight (N)\newline$i$ is the index\newline${U_{t}}$ is the surface hydrostatic force (N)\newline$\beta{}$ is the angle (${}^{\circ}$)\newline$Q$ is the imposed surface load (N)\newline$\omega{}$ is the angle (${}^{\circ}$)\newline$\alpha{}$ is the angle (${}^{\circ}$)\newline${K_{c}}$ is the earthquake load factor\newline$\Delta{}H$ is the difference between interslice forces (N)\newline${U_{b}}$ is the base hydrostatic force (N)\newline$\varphi{}'$ is the effective angle of friction (${}^{\circ}$)\newline$c'$ is the effective cohesion (Pa)\newline$b$ is the base width of a slice (m)
\\
\hline Sources& \cite{ZhuEtAl2005}\\
\hline Ref.\ By & \iref{IM_FS}\\
\hline
\end{tabular}
\end{minipage}\\
% ------------------------------------------ %
% End DD R %
% ------------------------------------------ %
\subsubsection*{Resistive Shear Force, Without the
Influence of Interslice Forces Derivation}
\noindent
The resistive shear force of a slice is defined as $P_\text{i}$ in
\dref{GD_P}. The effective normal in the equation for $P_\text{i}$ of
the soil is defined in the perpendicular force equilibrium of a slice
from \dref{GD_Fy}, Using the effective normal $N'_\text{i}$ of
\tref{TM_EffStress} shown in equation~(\ref{eq:N'}).
\begin{equation} \label{eq:N'}
N'_{\text{i}} \; = \begin{array}{l}
\left[ W_{\text{i}} - X_{\text{i-1}} + X_{\text{i}} +
{U_{\text{t,i}}}\;{\cos\left(\beta_{\text{i}}\right)} +
Q_{\text{i}}\;{\cos\left(\omega_{\text{i}}\right)}
\right]\cos\left(\alpha_{\text{i}}\right) \\ + \left[
{-K_{\text{c}}}\;{W_{\text{i}}} - E_{\text{i}} + E_{\text{i-1}} -
H_{\text{i}} + H_{\text{i-1}} +
{U_{\text{t,i}}}\;{\sin\left(\beta_{\text{i}}\right)} +
Q_{\text{i}}\;{\sin\left(\omega_{\text{i}}\right)}
\right]\sin\left(\alpha_{\text{i}}\right) \\ -
U_{\text{b,i}} \end{array}
\end{equation}
\noindent
The values of the interslice forces $E$ and $X$ in the equation are
unknown, while the other values are found from the physical force
definitions of \ddref{DD_W} to \ddref{DD_EX}. Consider a force
equilibrium without the affect of interslice
forces, to obtain a solvable value as done for $N^*_\text{i}$ in
equation~(\ref{eq:N*}).
\begin{equation} \label{eq:N*}
N^*_{\text{i}} \; = \begin{array}{l}
\left[ W_{\text{i}} +
{U_{\text{t,i}}}\;{\cos\left(\beta_{\text{i}}\right)} +
Q_{\text{i}}\;{\cos\left(\omega_{\text{i}}\right)}
\right]\cos\left(\alpha_{\text{i}}\right) \\ + \left[
{-K_{\text{c}}}\;{W_{\text{i}}}- H_{\text{i}} + H_{\text{i-1}} +
{U_{\text{t,i}}}\;{\sin\left(\beta_{\text{i}}\right)} +
Q_{\text{i}}\;{\sin\left(\omega_{\text{i}}\right)}
\right]\sin\left(\alpha_{\text{i}}\right) -
U_{\text{b,i}} \end{array}
\end{equation}
\noindent
Using $N^*_\text{i}$, a resistive shear force neglecting the influence
of interslice forces can be solved for in terms of all known values as
done in equation~(\ref{eq:R}).
\begin{equation*}
R_\text{i} = N^*_\text{i} \tan\left(\varphi'\right) + c'_\text{i}
\cdot b'_\text{i} \sec\left(\alpha_text{i}'\right)
\end{equation*}
\begin{equation}\label{eq:R} R_{\text{i}} \; =
\left( \begin{array}{l} \left[ W_{\text{i}} + U_{\text{t,i}}
\cos\left(\beta_{\text{i}}\right) + Q_{\text{i}}
\cos\left(\omega_{\text{i}}\right) \right]
\cos\left(\alpha_{\text{i}}\right) \\ + \left[ - K_{\text{c}}
W_{\text{i}} - \Delta H_{\text{i}} + U_{\text{t,i}}
\sin\left(\beta_{\text{i}}\right) + Q_{\text{i}}
\sin\left(\omega_{\text{i}}\right) \right]
\sin\left(\alpha_{\text{i}}\right) - U_{\text{b,i}} \end{array}
\right) \cdot \tan\left(\varphi'\right) + c'_{\text{i}} \cdot
b_{\text{i}} \cdot \sec\left(\alpha_{\text{i}}\right)
\end{equation}
~\newline
% ------------------------------------------ %
% Begin DD T %
% ------------------------------------------ %
\noindent
\begin{minipage}{\textwidth}
\renewcommand*{\arraystretch}{1.6}
\begin{tabular}{| p{1.5cm} | p{14cm} |}
\hline
Number& DD\refstepcounter{datadefnum}\thedatadefnum \label{DD_T}\\
\hline
Label& \bf Mobile Shear, Without Interslice Forces \\
\hline
Equation &
$T$ = $\left(W_{i}+{U_{t,i}}\cos\left(\beta{}_{i}\right)+Q_{i}\cos\left(\omega{}_{i}\right)\right)\sin\left(\alpha{}_{i}\right)-\left(-{K_{c}}W_{i}-{\Delta{}H}_{i}+{U_{t,i}}\sin\left(\beta{}_{i}\right)+Q_{i}\sin\left(\omega{}_{i}\right)\right)\cos\left(\alpha{}_{i}\right)$
\\
\hline Description & $T$ is the mobilized shear force (N)\newline$W$ is the weight (N)\newline$i$ is the index\newline${U_{t}}$ is the surface hydrostatic force (N)\newline$\beta{}$ is the angle (${}^{\circ}$)\newline$Q$ is the imposed surface load (N)\newline$\omega{}$ is the angle (${}^{\circ}$)\newline$\alpha{}$ is the angle (${}^{\circ}$)\newline${K_{c}}$ is the earthquake load factor\newline$\Delta{}H$ is the difference between interslice forces (N)
\\
\hline
Sources& \cite{ZhuEtAl2005}\\
\hline Ref.\ By & \iref{IM_FS}\\
\hline
\end{tabular}
\end{minipage}\\
% ------------------------------------------ %
% End DD T %
% ------------------------------------------ %
\subsubsection*{Mobile Shear Force, Without the
Influence of Interslice Forces Derivation}
\noindent
The mobile shear force acting on a slice is defined as $S_\text{i}$
from the force equilibrium in \dref{GD_Fy},also shown in
equation~(\ref{eq:Si}).
\begin{equation} \label{eq:Si}
S_{\text{i}} = \begin{array}{l} \left[ W_{\text{i}} -X_{\text{i-1}}
+ X_{\text{i}} +
{U_{\text{t,i}}}\;{\cos\left(\beta_{\text{i}}\right)} +
Q_{\text{i}}\;{\cos\left(\omega_{\text{i}}\right)}
\right]\sin\left(\alpha_{\text{i}}\right) \\ - \left[
{-K_{\text{c}}}\;{W_{\text{i}}} - E_{\text{i}} + E_{\text{i-1}}
- H_{\text{i}} + H_{\text{i-1}} +
{U_{\text{t,i}}}\;{\sin\left(\beta_{\text{i}}\right)} +
Q_{\text{i}}\;{\cos\left(\omega_{\text{i}}\right)}
\right]\cos\left(\alpha_{\text{i}}\right) \end{array}
\end{equation}
\noindent
The equation is unsolvable, containing the unknown interslice normal
force $E$ and shear force $X$. Consider a force equilibrium without
the affect of interslice forces, to obtain the mobile shear force
without the influence of interslice forces $T$, as done in
equation~(\ref{eq:T}).n
\begin{equation} \label{eq:T} T_{\text{i}} =
\begin{array}{l}
\left[ W_{\text{i}} + U_{\text{t,i}} \cos\left(\beta_{\text{i}}\right)
+ Q_{\text{i}} \cos\left(\omega_{\text{i}}\right) \right]
\sin\left(\alpha_{\text{i}}\right) \\ - \left[ - K_{\text{c}}
W_{\text{i}} - \Delta H_{\text{i}} + U_{\text{t,i}}
\sin\left(\beta_{\text{i}}\right) + Q_{\text{i}}
\sin\left(\omega_{\text{i}}\right) \right]
\cos\left(\alpha_{\text{i}}\right) \end{array}
\end{equation}
\noindent
The values of $R_\text{i}$ and $T_\text{i}$ are now defined completely
in terms of the known force property values of \ddref{DD_W} to
\ddref{DD_EX}.
~\newline
% ------------------------------------------ %
% Begin DD K Mats %
% ------------------------------------------ %
\noindent
\begin{minipage}{\textwidth}
\renewcommand*{\arraystretch}{1.6}
\begin{tabular}{| p{1.5cm} | p{14cm} |}
\hline Number&
DD\refstepcounter{datadefnum}\thedatadefnum \label{DD_KMats}\\
\hline Label& \bf Force \\
\hline Equation & $p$ = $\begin{bmatrix}
{K_{st,i}} & 0\\
0 & {K_{bn,i}}
\end{bmatrix}\begin{bmatrix}
{\delta{}x}_{i}\\
{\delta{}y}_{i}
\end{bmatrix}$
\\
\hline Description & $p$ is the pressure (Pa)\newline${K_{st}}$ is the shear stiffness ($\frac{\text{Pa}}{\text{m}}$)\newline$i$ is the index\newline${K_{bn}}$ is the normal stiffness ($\frac{\text{Pa}}{\text{m}}$)\newline$\delta{}x$ is the displacement (m)\newline$\delta{}y$ is the displacement (m)
\\
\hline Sources& \cite{StolleGuo}\\
\hline Ref.\ By & \iref{IM_RFEM}\\
\hline
\end{tabular}
\end{minipage}\\
\noindent
\begin{minipage}{\textwidth}
\renewcommand*{\arraystretch}{1.6}
\begin{tabular}{| p{1.5cm} | p{14cm} |}
\hline Number&
DD\refstepcounter{datadefnum}\thedatadefnum \label{DD_KMats}\\
\hline Label& \bf Force \\
\hline Equation & $p$ = $\begin{bmatrix}
{K_{bA,i}} & {K_{bB,i}}\\
{K_{bB,i}} & {K_{bA,i}}
\end{bmatrix}\begin{bmatrix}
{\delta{}x}_{i}\\
{\delta{}y}_{i}
\end{bmatrix}$
\\
\hline Description &$p$ is the pressure (Pa)\newline${K_{bA}}$ is the effective base stiffness A ($\frac{\text{Pa}}{\text{m}}$)\newline$i$ is the index\newline${K_{bB}}$ is the effective base stiffness A ($\frac{\text{Pa}}{\text{m}}$)\newline$\delta{}x$ is the displacement (m)\newline$\delta{}y$ is the displacement (m)
\\
\hline Sources& \cite{StolleGuo}\\
\hline Ref.\ By & \iref{IM_RFEM}\\
\hline
\end{tabular}
\end{minipage}\\
% ------------------------------------------ %
% End DD K Mats %
% ------------------------------------------ %
\subsubsection*{Derivation of Stifness Matrixes}
\noindent
Using the force-displacement relationship of \dref{GD_Hookes} to
define stiffness matrix ${K_\text{st}}$, as seen in
equation~(\ref{eq:Kmat}).
\begin{equation} \label{eq:Kmat}
{K_\text{st,i}} = \left[ \begin{array}{l l}
K_\text{st,i} & 0 \\ 0 & K_\text{bn,i}\end{array} \right]
\end{equation}
\noindent
For interslice surfaces the stiffness constants and displacements
refer to an unrotated coordinate system, ${\delta}$ of
\dref{GD_DispVecs}. The interslice elements are left in their standard
coordinate system, and therefore are described by the same equation
from \dref{GD_Hookes}. Seen as ${K}_\text{st}$ in
\ddref{DD_KMats}. $K_\text{st}$ is the shear element in the matrix,
and $K_\text{sn}$ is the normal element in the matrix, calculated as
in \ddref{DD_Stiff}.
~\newline\noindent For basal surfaces the stiffness constants and
displacements refer to a system rotated for the base angle alpha
(\ddref{DD_Angles}). To analyze the effect of force-displacement
relationships occurring on both basal and interslice surfaces of an
element $i$ they must reference the same coordinate system. The
basal stiffness matrix must be rotated counter clockwise to align with
the angle of the basal surface. The base stiffness counter clockwise
rotation is applied in equation~(\ref{eq:Krot}) to the new matrix
$\bar{K^*_\text{i}}$.
\begin{equation} \label{eq:Krot}
\begin{aligned} \bar{K^*_\text{i}} & =
\left[ \begin{array}{l l} \cos\left(\alpha_\text{i}\right) & -
\sin\left(\alpha_\text{i}\right)\\ \sin\left(\alpha_\text{i}\right)
& \cos\left(\alpha_\text{i}\right)\end{array} \right]
\bar{K_\text{i}}\\ {} & = \left[ \begin{array}{l l} K_\text{bt,i}
\cos\left(\alpha_\text{i}\right) & - K_\text{bn,i}
\sin\left(\alpha_\text{i}\right)\\ K_\text{bt,i}
\sin\left(\alpha_\text{i}\right) & K_\text{bn,i}
\cos\left(\alpha_\text{i}\right)\end{array}\right]
\end{aligned} \end{equation}
\noindent
The Hooke's law force displacement relationship of \dref{GD_Hookes}
applied to the base also references a displacement vector
$\bar{\epsilon}_\text{i}$ of \dref{GD_DispVecs} rotated for the base
angle angle of the slice $\alpha_\text{i}$. The basal displacement
vector $\bar{\epsilon}_\text{i}$ is rotated clockwise to align with
the interslice displacement vector $\bar{\delta}_\text{i}$, applying
the definition of $\bar{\epsilon}_\text{i}$ in terms of
$\bar{\delta}_\text{i}$ as seen in \dref{GD_DispVecs}. Using this with
base stiffness matrix $\bar{K^*}_\text{i}$, a basal force displacement
relationship in the same coordinate system as the interslice
relationship can be derived as done in equation~(\ref{eq:pRot}).
\begin{equation}\label{eq:pRot} \begin{aligned}
\left[ \begin{array}{l} p_\text{bx,i}
\\ p_\text{by,i} \end{array}\right]
& = \bar{K^*_\text{i}} \; \bar{\epsilon} \\
{} & = \left[ \begin{array}{l l} K_\text{bt,i}
\cos\left(\alpha_\text{i}\right) & - K_\text{bn,i}
\sin\left(\alpha_\text{i}\right)\\ K_\text{bt,i}
\sin\left(\alpha_\text{i}\right) & K_\text{bn,i}
\cos\left(\alpha_\text{i}\right)\end{array}\right]
\left[ \begin{array}{l l} \cos\left(\alpha_\text{i}\right)
&\sin\left(\alpha_\text{i}\right)\\
-\sin\left(\alpha_\text{i}\right)
& \cos\left(\alpha_\text{i}\right)\end{array}\right]
\left[ \begin{array}{l} \delta x_\text{i}
\\ \delta y_\text{i} \end{array} \right] \\
{} & = \left[ \begin{array}{l l}
K_\text{bt,i} \cos^2\left(\alpha_\text{i}\right)+
K_\text{bn,i} \sin^2\left(\alpha_\text{i}\right)
& \left(K_\text{bt,i} - K_\text{bn,i}\right)
\sin\left(\alpha_\text{i}\right)
\cos\left(\alpha_\text{i}\right)\\
\left(K_\text{bt,i} - K_\text{bn,i}\right)
\sin\left(\alpha_\text{i}\right)
\cos\left(\alpha_\text{i}\right)
& K_\text{bt,i} \cos^2\left(\alpha_\text{i}\right)+
K_\text{bn,i} \sin^2\left(\alpha_\text{i}\right)
\end{array} \right]
\left[ \begin{array}{l} \delta x_\text{i}
\\ \delta y_\text{i}
\end{array} \right]\end{aligned}
\end{equation}
\noindent
The new effective base stiffness matrix $K'_\text{i}$,as derived in
equation~(\ref{eq:Krot}) is defined in equation~(\ref{eq:K'}). This is
seen as matrix $\bar{K}_\text{b,i}$ in
\dref{DD_KMats}. $K_\text{bt,i}$ is the shear element in the matrix,
and $K_\text{bn,i}$ is the normal element in the matrix, calculated as
in \ddref{DD_Stiff}. The notation is simplified by the introduction of
the constants $K_\text{bA,i}$ and $K_\text{bB,i}$, defined in
equations~(\ref{eq:KbA}) and (\ref{eq:KbB}) respectively.
\begin{equation} \label{eq:K'}
\begin{aligned} & \bar{ K'_\text{i}}
= \left[ \begin{array}{l l}
K_\text{bt,i} \cos^2\left(\alpha_\text{i}\right)+
K_\text{bn,i} \sin^2\left(\alpha_\text{i}\right)
& \left(K_\text{bt,i} - K_\text{bn,i}\right)
\sin\left(\alpha_\text{i}\right)
\cos\left(\alpha_\text{i}\right)\\
\left(K_\text{bt,i} - K_\text{bn,i}\right)
\sin\left(\alpha_\text{i}\right)
\cos\left(\alpha_\text{i}\right)
& K_\text{bt,i} \cos^2\left(\alpha_\text{i}\right)+
K_\text{bn,i} \sin^2\left(\alpha_\text{i}\right)
\end{array} \right] \\
& \bar{ K'_\text{i}} = \left[ \begin{array}{l l}
K_\text{bA,i} & K_\text{bB,i} \\
K_\text{bB,i} & K_\text{bA,i}
\end{array} \right] \end{aligned} \end{equation}
\begin{equation} \label{eq:KbA}
K_\text{bA,i} = K_\text{bt,i} \cos^2\left(\alpha_\text{i}\right)+
K_\text{bn,i} \sin^2\left(\alpha_\text{i}\right)
\end{equation}
\begin{equation} \label{eq:KbB}
K_\text{bB,i} = \left(K_\text{bt,i} - K_\text{bn,i}\right)
\sin\left(\alpha_\text{i}\right)
\cos\left(\alpha_\text{i}\right)
\end{equation}
\noindent
A force-displacement relationship for an element $\text{i}$ can be
written in terms of displacements occurring in the unrotated
coordinate system $\bar{\delta}_\text{i}$ of \dref{GD_DispVecs} using
the matrix $K_\text{s,i}$, and $K_\text{b,i}$ as seen in
\ddref{DD_KMats}.
~\newline
% ------------------------------------------ %
% Begin DD Eqm %
% ------------------------------------------ %
\noindent
\begin{minipage}{\textwidth}
\renewcommand*{\arraystretch}{1.6}
\begin{tabular}{| p{1.5cm} | p{14.25cm} |}
\hline Number&
DD\refstepcounter{datadefnum}\thedatadefnum \label{DD_Eqm}\\
\hline Label& \bf Force \\
\hline Equation &
$F$ = $\left(-{\ell{}_{s,i-1}}\right){K_{sn,i-1}}\delta{}_{i-1}+\left({\ell{}_{s,i-1}}{K_{sn,i-1}}+{\ell{}_{b,i}}{K_{bn,i}}+{\ell{}_{s,i}}{K_{sn,i}}\right)\delta{}_{i}-{\ell{}_{s,i}}{K_{sn,i}}\delta{}_{i+1}$
\\
\hline Description & $F$ is the force (N)\newline${\ell{}_{s}}$ is the length of an interslice surface (m)\newline$i$ is the index\newline${K_{sn}}$ is the normal stiffness ($\frac{\text{Pa}}{\text{m}}$)\newline$\delta{}$ is the displacement (m)\newline${\ell{}_{b}}$ is the total base length of a slice (m)\newline${K_{bn}}$ is the normal stiffness ($\frac{\text{Pa}}{\text{m}}$)
\\
\hline Sources& \cite{StolleGuo}\\
\hline Ref.\ By & \iref{IM_RFEM}\\
\hline
\end{tabular}
\end{minipage}\\
% ------------------------------------------ %
% End DD Eqm %
% ------------------------------------------ %
~\newline
% ------------------------------------------ %
% Begin DD Soil Stiffness %
% ------------------------------------------ %
\noindent
\begin{minipage}{\textwidth}
\renewcommand*{\arraystretch}{1.6}
\begin{tabular}{| p{1.5cm} | p{14cm} |}
\hline Number&
DD\refstepcounter{datadefnum}\thedatadefnum \label{DD_Stiff}\\
\hline Label& \bf Shear Stiffness \\
\hline Input & $E$ , $\nu$ , $b$ , $c$ , $\sigma$ , $\phi$ , $\kappa$
$a$ , $A$ , $u$ , $v$\\
\hline
Output &
${K_{bt}}$ = $\frac{E}{2\left(1+\nu{}\right)}\frac{0.1}{b}+\frac{{c'}_{i}-\sigma{}\tan\left({\varphi{}'}_{i}\right)}{|\delta{}u|+a}$
\\
\hline Description & ${K_{bt}}$ is the shear stiffness ($\frac{\text{Pa}}{\text{m}}$)\newline$E$ is the interslice normal force (N)\newline$\nu{}$ is the Poisson's ratio\newline$b$ is the base width of a slice (m)\newline$c'$ is the effective cohesion (Pa)\newline$i$ is the index\newline$\sigma{}$ is the normal stress (Pa)\newline$\varphi{}'$ is the effective angle of friction (${}^{\circ}$)\newline$\delta{}u$ is the displacement (m)\newline$a$ is the constant (m)
\\
\hline Sources& \cite{StolleGuo}\\
\hline Ref.\ By & \iref{IM_RFEM}, \iref{IM_RFEMFS}\\
\hline
\end{tabular}
\end{minipage}\\
\noindent
\begin{minipage}{\textwidth}
\renewcommand*{\arraystretch}{1.6}
\begin{tabular}{| p{1.5cm} | p{14cm} |}
\hline Number&
DD\refstepcounter{datadefnum}\thedatadefnum \label{DD_Stiff}\\
\hline Label& \bf Normal Stiffness \\
\hline Input & $E$ , $\nu$ , $b$ , $c$ , $\sigma$ , $\phi$ , $\kappa$
$a$ , $A$ , $u$ , $v$\\
\hline
Output &
${K_{bn}}$ = $\begin{cases}
\frac{E\left(1-\nu{}\right)}{\left(1+\nu{}\right)\left(1-2\nu{}+b\right)}, & \nu{}<0\\
0.01\frac{E\left(1-\nu{}\right)}{\left(1+\nu{}\right)\left(1-2\nu{}+b\right)}+\frac{\kappa{}}{\delta{}v+A}, & \nu{}\geq{}0
\end{cases}$
\\
\hline Description & ${K_{bn}}$ is the normal stiffness ($\frac{\text{Pa}}{\text{m}}$)\newline$E$ is the interslice normal force (N)\newline$\nu{}$ is the Poisson's ratio\newline$b$ is the base width of a slice (m)\newline$\kappa{}$ is the constant (Pa)\newline$\delta{}v$ is the displacement (m)\newline$A$ is the constant (m)
\\
\hline Sources& \cite{StolleGuo}\\
\hline Ref.\ By & \iref{IM_RFEM}, \iref{IM_RFEMFS}\\
\hline
\end{tabular}
\end{minipage}\\
% ------------------------------------------ %
% End DD Soil Stiffness %
% ------------------------------------------ %
\subsubsection{Instance Models} \label{sec_instance}
This section transforms the problem defined in the
Section~\ref{Sec_pd} into one which is expressed in mathematical
terms. It uses concrete symbols defined in Section~\ref{sec_datadef}
to replace the abstract symbols in the models identified in the
Sections~\ref{sec_theoretical} and ~\ref{sec_gendef}.
~\newline\noindent The Morgenstern Price Method is a vertical slice,
limit equilibrium slope stability analysis method. Analysis is
performed by breaking the assumed failure surface into a series of
vertical slices of mass. Static equilibrium analysis using two force
equilibrium, and one moment equation as in \tref{TM_Eqm}. The problem
is statically indeterminate with only these 3 equations and one
constitutive equation (the Mohr Coulomb shear strength of
\tref{TM_Fmc}) so the assumption of \dref{GD_X} is used. Solving for
force equilibrium allows definitions of all forces in terms of the
physical properties of \ddref{DD_W} to \ddref{DD_EX}, as done in
\ddref{DD_R}, \ddref{DD_T}.
~\newline\noindent The values of the interslice normal force $E$ the
interslice normal/shear force magnitude ratio $\lambda$, and the
Factor of Safety $\text{FS}$, are unknown. Equations for the unknowns
are written in terms of only the values in \ddref{DD_W} to
\ddref{DD_EX}, the values of $R$, and $T$ in
\ddref{DD_R} and \ddref{DD_T}, and each other. The relationships
between the unknowns are non linear, and therefore explicit equations
cannot be derived and an iterative solution method is required.
~\newline
% ------------------------------------------ %
% Begin IM Factor of safety %
% ------------------------------------------ %
\noindent
\begin{minipage}{\textwidth}
\renewcommand*{\arraystretch}{1.6}
\begin{tabular}{| p{1.5cm} | p{14cm} |}
\hline Number&
IM\refstepcounter{instnum}\theinstnum \label{IM_FS}\\
\hline Label& \bf Factor of Safety \\
\hline Input & ${\Psi_{\text{v}}}$ , ${\Phi_{\text{v}}}$ ,
${T_{\text{v}}}$ , ${R_{\text{v}}}$ \\
\hline
Output &
\( {FS}= \frac{\displaystyle\sum_{v=1}^{n-1} \left[ {R_{v}}
\;{\displaystyle\prod_{c=i}^{n-1} \frac{\Psi_{u}}{\Phi_{u}}
}\right] + {R_{n}} }{\displaystyle\sum_{v=1}^{n-1} \left[ {T_{v}}
\;{\displaystyle\prod_{c=i}^{n-1} \frac{\Psi_{u}}{\Phi_{u}}
}\right] + {T_{n}} } \)\\
\hline Description & Equation for the Factor of Safety, the ratio
between resistive and mobile shear the slip surface. The sum of values
from each slice is taken to find the total resistive and mobile shear
for the slip surface. The constants $\Phi$ and $\Psi$ convert the
resistive and mobile shear without the influence of interslice forces,
to a calculation considering the interslice forces. \\
\hline Sources& \cite{ZhuEtAl2005}\\
\hline Ref.\ By & \iref{IM_Lambda}, \iref{IM_E}\\
\hline
\end{tabular}
\end{minipage}\\
% ------------------------------------------ %
% End IM Factor of Safety %
% ------------------------------------------ %
\subsubsection*{Factor of Safety Derivation}
\noindent
Using equation~(\ref{eq:Interslice2}) from
section~\ref{sec:Ederivation}, rearranging, and applying the boundary
condition that $E_{\text{0}}$ and $E_{\text{n}}$ are equal to $0$ an
equation for the factor of safety is found as equation~(\ref{eq:FS}),
also seen in \iref{IM_FS}.
\begin{equation}\label{eq:FS}
\text{FS}= \frac{\displaystyle\sum_{v=1}^{n-1} \left[ {R_{v}}
\;{\displaystyle\prod_{c=v}^{n-1} \frac{\Psi_{u}}{\Phi_{u}}
}\right] + {R_{n}} }{\displaystyle\sum_{v=1}^{n-1} \left[
{T_{v}} \;{\displaystyle\prod_{c=v}^{n-1}
\frac{\Psi_{u}}{\Phi_{u}} }\right] + {T_{n}} }
\end{equation}
\noindent
The constants $\Psi$ and $\Phi$ described in equations \ref{eq:Psi}
and \ref{eq:Phi} are functions of the unknowns: the interslice
normal/shear force ratio $\lambda$ (\iref{IM_Lambda}) and the Factor
of Safety $\text{FS}$ (\iref{IM_FS}).
~\newline
% ------------------------------------------ %
% Begin IM Lambda %
% ------------------------------------------ %
\noindent
\begin{minipage}{\textwidth}
\renewcommand*{\arraystretch}{1.6}
\begin{tabular}{| p{1.5cm} | p{14cm} |}
\hline Number&
IM\refstepcounter{instnum}\theinstnum \label{IM_Lambda}\\
\hline Label& \bf Normal/Shear Force Ratio \\
\hline Input & $b_{\text{v}}$ , $E_{\text{v}}$ , $H_{\text{v}}$ ,
$\alpha_{\text{v}}$ , $h_{\text{v}}$ , $W_{\text{v}}$ ,
$U_{\text{t,v}}$ , $\beta_{\text{v}}$ , $f_{\text{v}}$ ,
${K_{\text{c}}}$ \\
\hline
Output &
\( {C1_{\text{i}}}= \)
\( \left\{
\renewcommand{\arraystretch}{2}
\begin{tabular}{ p{6.5cm} r}
$ {{b}_{\text{1}}}\left[{{E}_{\text{1}} + {H}_{\text{1}}}
\right]{\tan\left(\alpha_{\text{1}}\right) } $ & $
\text{i}={\text{1}} $ \\
\noindent\parbox[c]{\hsize} {$ {{b}_{\text{i}}} \left[
\left({{E}_{\text{i}} + {E}_{\text{i-1}}}\right) +
\left({{H}_{\text{i}} + {H}_{\text{i-1}}}\right)
\right]{\tan\left(\alpha_{\text{i}}\right)} \\ +
{{h}_{\text{i}}}\left( {K_{\text{c}}}\;{W_{\text{i}}} -
{2}\;{U_{\text{t,i}}}\;{\sin\left(\beta_{\text{i}}\right)} -
{2}\;{Q_{\text{i}}}\;{\cos\left(\omega_{\text{i}}\right)} \right) $}
& $ 2\leq\text{i}\leq{\text{n-1}} $ \\ $
{{b}_{\text{n}}}\left[{{E}_{\text{n-1}} +
{H}_{\text{n-1}}}\right]{\tan\left(\alpha_{\text{n-1}}\right)
} $ & $ \text{i}=\text{n} $ \\
\end{tabular}
\renewcommand{\arraystretch}{1}
\right. \)
~\newline~\newline
\( {C2_{\text{i}}}= \)
\( \left\{
\renewcommand{\arraystretch}{2}
\begin{tabular}{ p{7cm} r}
$ {{b}_{\text{1}}}{{E}_{\text{1}}}{f_{\text{1}}} $ & $
\text{i}=\text{1} $ \\ $ {{b}_{\text{i}}}\;{\left({
{f_{\text{i}}}{{E}_{\text{i}}} +
{f_{\text{i-1}}}{{E}_{\text{i-1}}} }\right)} $ & $
2\leq\text{i}\leq{\text{n-1}} $ \\ $
{{b}_{\text{n}}}{{E}_{\text{n-1}}}{f_{\text{n-1}}} $ & $
\text{v}=\text{n} $ \\
\end{tabular}
\renewcommand{\arraystretch}{1}
\right. \)
~\newline
\( \lambda= \frac{ \displaystyle\sum_{i=1}^{n} {C1_{\text{i}}}}
{\displaystyle\sum_{i=1}^{n} {C2_{\text{i}}}} \) \\
\hline Description & $\lambda$ is the magnitude ratio between shear
and normal forces at the interslice interfaces as the assumption of
the Morgenstern Price method in \dref{GD_X}. The inclination function
$f$ determines the relative magnitude ratio between the different
interslices, while $\lambda$ determines the magnitude. $\lambda$ uses
the sum of interslice normal and shear forces taken from each
interslice. \\
\hline Sources& \cite{ZhuEtAl2005}\\
\hline Ref.\ By & \iref{IM_FS}, \iref{IM_E} \\
\hline
\end{tabular}
\end{minipage}\\
% ------------------------------------------ %
% End IM Lambda %
% ------------------------------------------ %
\subsubsection*{Normal/Shear Force Ratio Derivation}
The last static equation of \tref{TM_Eqm} the moment equilibrium of
\dref{GD_M} about the midpoint of the base is taken, with the
assumption of \dref{GD_X}. Results in equation~(\ref{eq:Moment}).
\begin{equation}\label{eq:Moment}
0 = \begin{array}{l} - {E}_{\text{i}} \left[ {z_{\text{i}}} -
\frac{b_{\text{i}}}{2} { \tan\left(\alpha_{\text{i}}\right)}
\right] + {E}_{\text{i-1}} \left[ {z_{\text{i-1}}} +
\frac{b_{\text{i}}}{2} { \tan\left(\alpha_{\text{i}}\right)}
\right] - H_{\text{i}}\left[ z_{\text{w,i}} -
\frac{b_{\text{i}}}{2} { \tan\left(\alpha_{\text{i}}\right)}
\right] \\[5pt] + H_{\text{i-1}}\left[ z_{\text{w,i-1}} +
\frac{b_{\text{i}}}{2} { \tan\left(\alpha_{\text{i}}\right)}
\right] -\lambda \frac{b_{\text{i}}}{2} \left( E_{\text{i}}
f_{\text{i}} + E_{\text{i-1}} f_{\text{i-1}} \right) +
K_{\text{c}} W_{\text{i}} \frac{h_{\text{i}}}{2} - U_{\text{t,i}}
\sin\left(\beta_{\text{i}}\right) h_{\text{i}} -
Q_{\text{i}}\;{\sin\left(\omega_{\text{i}}\right)}
h_{\text{i}} \end{array}
\end{equation}
\noindent
Rearranging the equation in terms of $\lambda$ leads to equation
~(\ref{eq:lambda1}).
\begin{equation}\label{eq:lambda1}
\lambda = \frac { \begin{array}{l} - {E}_{\text{i}} \left[
{z_{\text{i}}} - \frac{b_{\text{i}}}{2} {
\tan\left(\alpha_{\text{i}}\right)} \right] +
{E}_{\text{i-1}} \left[ {z_{\text{i-1}}} +
\frac{b_{\text{i}}}{2} { \tan\left(\alpha_{\text{i}}\right)}
\right] - H_{\text{i}}\left[ z_{\text{i}} -
\frac{b_{\text{i}}}{2} { \tan\left(\alpha_{\text{i}}\right)}
\right] \\[5pt] + H_{\text{i-1}}\left[ z_{\text{i-1}} +
\frac{b_{\text{i}}}{2} { \tan\left(\alpha_{\text{i}}\right)}
\right] + K_{\text{c}} W_{\text{i}} \frac{h_{\text{i}}}{2} -
U_{\text{t,i}} \sin\left(\beta_{\text{i}}\right) h_{\text{i}} -
Q_{\text{i}}\;{\sin\left(\omega_{\text{i}}\right)}
h_{\text{i}} \end{array} } { \frac{b_{\text{i}}}{2} \left[
E_{\text{i}} f_{\text{i}} + E_{\text{i-1}} f_{\text{i-1}}
\right] }
\end{equation}
\noindent
Taking a summation of each slice, and considering the boundary
conditions that $E_{\text{0}}$ and $E_{\text{n}}$ are equal to zero, a
general equation for the constant $\lambda$ is developed in
equation~(\ref{eq:Lambda}), also found in \iref{IM_Lambda}.
\begin{equation}\label{eq:Lambda}
\lambda= \frac{ \displaystyle\sum_{i=1}^{n} { {b_{\text{i}}} \left[
\left({{E}_{\text{i}} + {E}_{\text{i-1}}}\right) +
\left({{H}_{\text{i}} + {H}_{\text{i-1}}}\right)
\right]{\tan\left(\alpha_{\text{i}}\right)} \\ +
{{h}_{\text{i}}}\;\left[ {K_{\text{c}}}\;{W_{\text{i}}} -
{2}\;{U_{\text{t,i}}}\;{\sin\left(\beta_{\text{i}}\right)} - {2}
\; Q_{\text{i}}\;{\sin\left(\omega_{\text{i}}\right)} \right] }}
{\displaystyle\sum_{i=1}^{n} { {{b}_{\text{i}}}\;{\left[{
{f_{i}}{{E}_{\text{i}}} +
{f_{\text{i-1}}}{{E}_{\text{i-1}}} }\right]} }}
\end{equation}
\noindent
Equation~(\ref{eq:Lambda}) for $\lambda$, is a function of the unknown
interslice normal force $E$ (\iref{IM_E}).
~\newline
% ------------------------------------------ %
% Begin IM E %
% ------------------------------------------ %
\noindent
\begin{minipage}{\textwidth}
\renewcommand*{\arraystretch}{1.6}
\begin{tabular}{| p{1.5cm} | p{14cm} |}
\hline Number&
IM\refstepcounter{instnum}\theinstnum \label{IM_E}\\
\hline Label& \bf Interslice Forces \\
\hline Input & $\text{FS}$, $T_\text{i}$, $R_\text{i}$, $\Psi$,
$\Phi$\\
\hline
Output &
\( E_{\text{i}}= \)
\( \left\{
\renewcommand{\arraystretch}{1.75}
\begin{tabular}{ p{3cm} l}
$ \frac{ \left(\text{FS}\right) T_{\text{1}} - R_{\text{1}} }{
\Phi_{\text{i}} } $ & $\text{i=1}$ \\
\noindent\parbox[c]{\hsize} {$ \frac{ \Psi_{\text{i-1}} \cdot
E_{\text{i-1}} + \left(\text{FS}\right) \cdot T_{\text{i}} -
R_{\text{i}} }{ \Phi_{\text{i}} } $} &
$2\leq\text{i}\leq\text{n-1}$ \\
\noindent\parbox[c]{\hsize} {$0 $} & $\text{i=0}$ $\vee$ $\text{i=n}$
\end{tabular}
\renewcommand{\arraystretch}{1}
\right. \) \\
\hline Description & The value of the interslice normal force
$E_\text{i}$ at interface $\text{i}$. The net force the weight of the
slices adjacent to interface $\text{i}$ exert horizontally on each
other.\\
\hline Sources& \cite{ZhuEtAl2005}\\
\hline Ref.\ By & \iref{IM_FS}, \iref{IM_Lambda}\\
\hline
\end{tabular}
\end{minipage}\\
% ------------------------------------------ %
% End IM E %
% ------------------------------------------ %
\subsubsection*{Interslice Force Derivation} \label{sec:Ederivation}
Taking the perpendicular force equilibrium of \dref{GD_Fx} with the
effective stress definition from \tref{TM_EffStress} that
$N_{\text{i}}=N'_{\text{i}} - U_{\text{b,i}}$, and the assumption of
\dref{GD_X} the equilibrium equation can be rewritten as
equation~(\ref{eq:F_perp}).
\begin{equation}\label{eq:F_perp} N'_{\text{i}} = \begin{array}{l}
\left[ W_{\text{i}} - \lambda \cdot f_{\text{i-1}} \cdot
E_{\text{i-1}} + \lambda \cdot f_{\text{i}} \cdot E_{\text{i}} +
U_{\text{t,i}} {\cos\left(\beta_{\text{i}}\right)} +
Q_{\text{i}} \cos\left(\omega_{\text{i}}\right)
\right]\cos\left(\alpha_{\text{i}}\right) \\ + \left[
-K_{\text{c}} W_{\text{i}} - E_{\text{i}} + E_{\text{i-1}} -
H_{\text{i}} + H_{\text{i-1}} + U_{\text{t,i}}
\sin\left(\beta_{\text{i}}\right) + Q_{\text{i}}
\sin\left(\omega_{\text{i}}\right) \right]
\sin\left(\alpha_{\text{i}}\right) - U_{\text{b,i}} \end{array}
\end{equation}
\noindent
Taking the base shear force equilibrium of \dref{GD_Fy} with the
definition of mobilized shear from \dref{GD_MobShear} and the assumption
of \dref{GD_X}, the equilibrium equation can be rewritten as
equation~(\ref{eq:F_par}).
\begin{equation} \label{eq:F_par}
\frac{ N_{\text{i}} \tan\left(\varphi'\right_{i}) + c'_{\text{i}} \cdot
b'_{\text{i}} \cdot \sec\left(\alpha_{\text{i}}\right) }{
\text{FS} } = \begin{array}{l} \left[ W_{\text{i}} - \lambda \cdot
f_{\text{i-1}} \cdot E_{\text{i-1}} + \lambda \cdot f_{\text{i}}
\cdot E_{\text{i}} + U_{\text{t,i}}
\cos\left(\beta_{\text{i}}\right) + Q_{\text{i}}
\cos\left(\omega_{\text{i}}\right) \right]
\sin\left(\alpha_{\text{i}}\right) \\ - \left[ -K_{\text{c}}
W_{\text{i}} - E_{\text{i}} + E_{\text{i-1}} - H_{\text{i}} +
H_{\text{i-1}} + U_{\text{t,i}} \cdot
\sin\left(\beta_{\text{i}}\right) + Q_{\text{i}}
\sin\left(\omega_{\text{i}}\right) \right]
\cos\left(\alpha_{\text{i}}\right) \end{array}
\end{equation}
\noindent
Substituting the equation for $N'_{\text{i}}$ from
equation~(\ref{eq:F_perp}) into equation~(\ref{eq:F_par}) and
rearranging results in equation~(\ref{eq:Interslice1})
\begin{equation}\label{eq:Interslice1}
E_\text{i} \left[ \begin{array}{l} \left[ \lambda \cdot f_\text{i}
\cos\left(\alpha_\text{i}\right) -
\sin\left(\alpha_\text{i}\right) \right]
\tan\left(\varphi'\right_{i}) \\ - \left[ \lambda \cdot f_\text{i}
\sin\left(\alpha_\text{i}\right) +
\cos\left(\alpha_\text{i}\right) \right]
\left(\text{FS}\right) \end{array} \right] = E_\text{i-1}
\left[ \begin{array}{l} \left[ \lambda \cdot f_\text{i-1}
\cos\left(\alpha_\text{i}\right) -
\sin\left(\alpha_\text{i}\right) \right]
\tan\left(\varphi'\right_{i}) \\ - \left[ \lambda \cdot f_\text{i-1}
).

Software Carpentry

Please review the basics of the Unix shell by completing the Software Carpentry lesson at:

http://swcarpentry.github.io/shell-novice/

These basic skills will really help you. Much of what is written for the Unix command line also applies at the Windows Command Prompt. Instead of ls (listing) you type dir. If there are any commands that don't work, you could use google to find out the Windows equivalent.

In the longer term, you will want a Unix style shell on your computer. Options include VirtualBox for a virtual Linux installation, or you could ssh into the CAS department's servers. I've also heard that Windows 10 makes it easy to use Unix style commands, but I don't know the details on this. Another option is to install Cygwin.

When you have completed the tutorial exercises, you can close this issue with a comment explaining what you have learned.

SSP : Missing References within SRS

(Issue #27)

  • section 2.1 (Purpose of Document) --> "...as Parnas and Clements point out..." should reference some source as to where the notion is pointed out (

    caseStudies/CaseStudies/ssp/Documentation Files/SRS_SSP.tex

    Line 376 in f1a7a49

    as Parnas and Clements point out, the most logical way to present the documentation
    )
  • section 2.3 (Characteristics of Intended Reader) --> missing reference (noted by "??" in output); as a result of attempting to reference a section of the document that is not labelled

    caseStudies/CaseStudies/ssp/Documentation Files/SRS_SSP.tex

    Line 389 in 220c839

    Reviewers of this documentation should have a strong knowledge in solid mechanics. The reviewers should also have an understanding of undergraduate level 4 physics. The users of SSA can have a lower level of expertise, as explained in Section~\ref{Sec:UserChar}.

SSP : Grammatical/Formatting Fixes Needed

(Issue #27)

Grammar, Punctuation, and Spelling :

  1. section 4.1 (Problem Description)--> missing apostrophe from "slopes" (see

    caseStudies/CaseStudies/ssp/Documentation Files/SRS_SSP.tex

    Line 438 in f1a7a49

    of a slopes slip surface and, calculate the displacement the slope
    )
  2. section 4.1.1 (Terminology)--> possible confused word ("dominate" should be "dominant")? (see

    caseStudies/CaseStudies/ssp/Documentation Files/SRS_SSP.tex

    Line 471 in f1a7a49

    the others. Stresses in the dominate dimensions direction are the
    )
  3. section 4.1.3 (Goal Statements) --> unnecessary capitalization of 's' and 'f'? (see

    caseStudies/CaseStudies/ssp/Documentation Files/SRS_SSP.tex

    Line 563 in f1a7a49

    Factor of Safety.}
    )
  4. T2 description --> awkward wording and misuse of commas
    image
    (see

    caseStudies/CaseStudies/ssp/Documentation Files/SRS_SSP.tex

    Lines 690 to 695 in f1a7a49

    \hline Description & For a body in static equilibrium the net
    forces, and net moments acting on the body will cancel out. Assuming
    a 2D problem (\aref{A_2D}) the x-component of the net force ${F_{x}}$
    and y-component of the net force ${F_{y}}$ will be equal to $0$. All forces
    and their distance from the chosen point of rotation will create a net
    moment equal to, $0$ also able to be analyzed as a scalar in a 2D problem. \\
    )
  5. T3 description --> misuse of comma
    image (see

    caseStudies/CaseStudies/ssp/Documentation Files/SRS_SSP.tex

    Line 735 in f1a7a49

    effective normal force is strong enough it can be approximated with
    )
  6. T5 description --> awkward wording
    image (see

    caseStudies/CaseStudies/ssp/Documentation Files/SRS_SSP.tex

    Lines 805 to 808 in f1a7a49

    \hline Description & Description Stiffness $K$ is the resistance a body others to
    deformation by displacement $\delta{}$ when subject to a force $F$, along the
    same direction. A body with high stiffness will experience little deformation when
    subject to a force. \\
    )
  7. section 4.2.6 (Data Constraints) --> instances of "vertices's" and "vertexes" should be changed to "vertices'" and "vertices"
    image
    (

    caseStudies/CaseStudies/ssp/Documentation Files/SRS_SSP.tex

    Lines 2972 to 3005 in f1a7a49

    $(x,y)$ of water table vertices's & Consecutive vertexes have
    increasing x values. All layers start and end vertices's go to the
    same x values. & N/A & / \\
    $(x,y)$ of slip vertices's & Consecutive vertexes have increasing x
    values. All layers start and end vertices's go to the same x
    values. & N/A & / \\
    $(x,y)$ of slope vertices's (*) & Consecutive vertexes have
    increasing x values. All layers start and end vertices's go to the
    same x values. & N/A & / \\
    $E$ (*) & $E > 0$ & 15000 & /\\
    $c$ (*) & $c >0$ & 10 & /\\
    $v$ (*) & $ 0 < v < 1 $ & 0.4 & \\
    $\varphi'$ (*) & $ 0 < \varphi < 90 $ & 25 & / \\
    $\gamma$ (*) & $\gamma > 0$ & 20 & / \\
    $\gamma_{\text{Sat}}$ (*) & $\gamma_{\text{Sat}} > 0 $ & 20 & /
    \\
    $\gamma_{\text{Wat}}$ & $\gamma_{\text{Wat}} > 0 $ & 9.8 & / \\
    \bottomrule
    \end{longtable}
    %\end{table}
    \noindent \begin{description}
    \item[(*)] Input coordinates needed for each layer.
    \end{description}
    %\begin{table}[!h]
    %\caption{Output Variables}
    \renewcommand{\arraystretch}{1.2}
    \noindent \begin{longtable}{l l}
    \toprule \label{TblOutputVar}
    \textbf{Var} & \textbf{Physical Constraints} \\
    \midrule
    $FS$ & $FS>0$ \\
    $(x,y)$ Slip vertices's & Vertices's monotonic \\
    )
  8. IM4 --> missing a comma between input symbols
    (see

    caseStudies/CaseStudies/ssp/Documentation Files/SRS_SSP.tex

    Lines 2627 to 2628 in f1a7a49

    \hline Input & $E$ , $\nu$ , $b$ , $c$ , $\sigma$ , $\phi$ , $\kappa$
    $a$ , $A$ , $u$ , $v$\\
    )
  9. "Stifness Matrixes" --> "Stiffness Matrices" (see

    caseStudies/CaseStudies/ssp/Documentation Files/SRS_SSP.tex

    Line 1954 in f1a7a49

    \subsubsection*{Derivation of Stifness Matrixes}
    )

Formatting:

  • section 4.2.1 (Assumptions) --> "The numbers given in the square brackets..." there are no square brackets with numbers in this section, can probably remove this sentence completely or add the numbers
    image
    (see

    caseStudies/CaseStudies/ssp/Documentation Files/SRS_SSP.tex

    Lines 576 to 582 in f1a7a49

    \subsubsection{Assumptions}
    This section simplifies the original problem and helps in developing
    the theoretical model by filling in the missing information for the
    physical system. The numbers given in the square brackets refer to the
    data definition, or the instance model, in which the respective
    assumption is used.
    )

Game Physics: Spelling, Grammar, and Typos

(Issue #29)

The following is a list of spelling errors, grammatical mistakes, and typos within the Game Physics SRS:

  • Section 4.2.3 (Derivation of GD2, last line of text on Page 10) reads "Generalizing for multiple (k) colliding objects:" when It should read "Generalizing for multiple (n) colliding objects:"
  • Section 4.2.4 (DD8's Description) reads "...two rigid bodies (A1, A2) ." there is a space between ')' and '.'.
  • Section 4.2.5 (IM1's Description) reads "...equation using DD2, DD3 and DD4." There is a missing comma before the and as the sentence is forming a list.
  • Section 4.2.5 (Collision Diagram) reads " the collision normal vector n and the vectors", however there is a comma missing before the and as the sentence is forming a list.

Fix Hardcoded References in SRS

Lines 288-289 of glassbr_srs.tex are missing a reference to another section: "...standards for constructions using glass from {[}4-6{]} in
Section. The users of GlassBR can have a lower level of..."

TODO

  • Fix in caseStudies
  • Fix in Drasil
    • Characteristics of Intended Reader
    • Terminology and Definitions
      • Glass Type
      • Load
    • Calculation of Capacity IM

PCM SRS - Software Diameter constraint makes no sense

Table 2 has D/L_min <= D/L <= D/L_max.

First, this does not constrain D at all (given that it is positive), since it can be eliminated.

Second, since L_min <= L <= L_max, this is 'backwards' !

No idea what the right constraints ought to be. I will, for now, eliminate this constraint from the SWHS example in the Drasil repo, until this can be figured out.

Glass-BR: Missing information in section 4 in SRS

In section 4 it is mentioned that information about the system, identifies the interfaces between the system and its environment will be provided in that section, but no information about that is provided.
section 4

Recommend Projects

  • React photo React

    A declarative, efficient, and flexible JavaScript library for building user interfaces.

  • Vue.js photo Vue.js

    🖖 Vue.js is a progressive, incrementally-adoptable JavaScript framework for building UI on the web.

  • Typescript photo Typescript

    TypeScript is a superset of JavaScript that compiles to clean JavaScript output.

  • TensorFlow photo TensorFlow

    An Open Source Machine Learning Framework for Everyone

  • Django photo Django

    The Web framework for perfectionists with deadlines.

  • D3 photo D3

    Bring data to life with SVG, Canvas and HTML. 📊📈🎉

Recommend Topics

  • javascript

    JavaScript (JS) is a lightweight interpreted programming language with first-class functions.

  • web

    Some thing interesting about web. New door for the world.

  • server

    A server is a program made to process requests and deliver data to clients.

  • Machine learning

    Machine learning is a way of modeling and interpreting data that allows a piece of software to respond intelligently.

  • Game

    Some thing interesting about game, make everyone happy.

Recommend Org

  • Facebook photo Facebook

    We are working to build community through open source technology. NB: members must have two-factor auth.

  • Microsoft photo Microsoft

    Open source projects and samples from Microsoft.

  • Google photo Google

    Google ❤️ Open Source for everyone.

  • D3 photo D3

    Data-Driven Documents codes.