30:T500,function pressurePoints(strata, state = "active", water = -10 ^ 9) { const grade = strata[0].top; return Array.from({ length: strata.length }, (d, i) => { const { bot, phi, gam } = strata[i]; let k; if (state === "active") { k = kaCoulomb(phi, 0); } if (state === "passive") { k = kpCoulomb(phi, 0); } if (state === "at-rest") { k = 1 - Math.sin(phi * (Math.PI / 180)); // Jacky's at rest formula } const ztop = i === 0 ? 0 : strata[i - 1].bot; const zbot = bot; const gamma = water < zbot ? gam : gam - 10; const pSoilTop = k * Math.abs(ztop - grade) * gamma; const pSoilBot = k * Math.abs(zbot - grade) * gamma; const pWaterTop = water < ztop ? 0 : Math.abs(ztop - grade) * 10; const pWaterBot = water < zbot ? 0 : Math.abs(zbot - grade) * 10; const pDiag = [ { z: ztop, p: pSoilTop + pWaterTop }, { z: bot, p: pSoilBot + pWaterBot } ]; if (water > zbot && water < ztop) { // need a point in between const pSoilMid = k * Math.abs(water - grade) * gamma; const pWaterMid = Math.abs(water - grade) * 10; pDiag.splice(1, 0, { z: water, p: pSoilMid + pWaterMid }); } return pDiag; }).flat(); }31:[{"id":"be20fd61bf7df71be5dbe5a888d735fc15d68e8b57386d9779f0ebbe0b014a508aaeba85b182da8a5889af2a268837eda733274d6bafd897b5f9bdbfe071e8b1","href":"https://static.observableusercontent.com/files/be20fd61bf7df71be5dbe5a888d735fc15d68e8b57386d9779f0ebbe0b014a508aaeba85b182da8a5889af2a268837eda733274d6bafd897b5f9bdbfe071e8b1","name":"image.png","type":"image/png","lastModified":1611949620631.071,"size":8263},{"id":"f41143d4b24f871e9845e73e27daaa7a2604f9f9b98ba89d1b0ad5d486493290f33497917b4e2f00545a7015bb87284aa6decd5b93f51759cd6ebc2695484a6f","href":"https://static.observableusercontent.com/files/f41143d4b24f871e9845e73e27daaa7a2604f9f9b98ba89d1b0ad5d486493290f33497917b4e2f00545a7015bb87284aa6decd5b93f51759cd6ebc2695484a6f","name":"Screen Shot 2021-03-10 at 6.28.46 PM.png","type":"image/png","lastModified":1615419230751.713,"size":112360},{"id":"b0880575ab7f75e854746d21259a306335b0057a51c7d602ef326ad0c2d8ae55c5b75280990d8b87438bec892ba856ccf9e361e2c679c068cc2d048246e6d783","href":"https://static.observableusercontent.com/files/b0880575ab7f75e854746d21259a306335b0057a51c7d602ef326ad0c2d8ae55c5b75280990d8b87438bec892ba856ccf9e361e2c679c068cc2d048246e6d783","name":"kp_coulomb.png","type":"image/png","lastModified":1615861099042.086,"size":242974},{"id":"8bd9cbf6de4e7d84b3d549f2eb15df672910da1e4af69c2dc517197d211b228f443455e19a2c32b7ec8eed7f200dc76c632e074c35f633dbd0ab9ac6ae626c6a","href":"https://static.observableusercontent.com/files/8bd9cbf6de4e7d84b3d549f2eb15df672910da1e4af69c2dc517197d211b228f443455e19a2c32b7ec8eed7f200dc76c632e074c35f633dbd0ab9ac6ae626c6a","name":"ka_coulomb.png","type":"image/png","lastModified":1615861078537.946,"size":249453}] 2e:{"title":"Soil Equations","cells":[{"id":0,"value":"md`# Soil Equations`","pinned":false,"hidden":false,"mode":"ojs"},{"id":165,"value":"md`## Lateral Earth Pressure`","pinned":false,"hidden":false,"mode":"ojs"},{"id":413,"value":"md`### Rankine's Theory`","pinned":false,"hidden":false,"mode":"ojs"},{"id":428,"value":"tex.block`K_a=\\frac{1-sin({\\phi})}{1+sin({\\phi})}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":432,"value":"tex.block`K_p=\\frac{1+sin({\\phi})}{1-sin({\\phi})}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":416,"value":"function kaRankine(phi_deg, unit = \"deg\") {\n let phi = unit === \"deg\" ? phi_deg * (Math.PI / 180) : phi_deg;\n return (1 - Math.sin(phi)) / (1 + Math.sin(phi));\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":418,"value":"function kpRankine(phi_deg, unit = \"deg\") {\n let phi = unit === \"deg\" ? phi_deg * (Math.PI / 180) : phi_deg;\n return (1 + Math.sin(phi)) / (1 - Math.sin(phi));\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":422,"value":"{\n const svg = d3\n .create(\"svg\")\n .attr(\"width\", width)\n .attr(\"height\", width / 2);\n\n svg\n .append(\"g\")\n .call(chart, {\n height: 0.4 * width,\n width: 0.4 * width,\n xAxis: {\n title: \"Phi\"\n },\n yAxis: {\n title: \"Ka\"\n },\n points: Array.from(Array(50), (d, i) => [i, kaRankine(i)])\n })\n .attr(\"transform\", `translate(${0.05 * width}, ${0.05 * width})`);\n\n svg\n .append(\"g\")\n .call(chart, {\n height: 0.4 * width,\n width: 0.4 * width,\n xAxis: {\n title: \"Phi\"\n },\n yAxis: {\n title: \"Ka\"\n },\n points: Array.from(Array(50), (d, i) => [i, kpRankine(i)])\n })\n .attr(\"transform\", `translate(${width / 2}, ${0.05 * width})`);\n\n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":168,"value":"md`### Coulomb's Theory`","pinned":false,"hidden":false,"mode":"ojs"},{"id":224,"value":"md`\n

Ref: [CALTRANS](https://dot.ca.gov/-/media/dot-media/programs/engineering/documents/structureconstruction/201906-sc-trenchingshoring-a11y.pdf)

\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":173,"value":"tex.block`K_a=\\frac{cos^2(\\phi-\\omega)}{cos^2(\\omega)cos(\\delta+\\omega)[1+\\sqrt{\\frac{sin(\\delta+\\phi)sin(\\phi-\\beta)}{cos(\\delta+\\omega)cos(\\omega-\\beta)}}]^2}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":282,"value":"tex.block`K_p=\\frac{cos^2(\\phi+\\omega)}{cos^2(\\omega)cos(\\delta-\\omega)[1-\\sqrt{\\frac{sin(\\delta+\\phi)sin(\\phi+\\beta)}{cos(\\delta-\\omega)cos(\\beta-\\omega)}}]^2}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":405,"value":"FileAttachment(\"ka_coulomb.png\").image()","pinned":false,"hidden":false,"mode":"ojs"},{"id":408,"value":"FileAttachment(\"kp_coulomb.png\").image()","pinned":false,"hidden":false,"mode":"ojs"},{"id":191,"value":"function kaCoulomb(phi_deg, omega_deg, beta_deg, delta_deg, unit = \"deg\") {\n let rad = deg => deg * (Math.PI / 180),\n phi = rad(phi_deg),\n omega = omega_deg ? rad(omega_deg) : 0,\n beta = beta_deg ? rad(beta_deg) : 0,\n delta = delta_deg ? rad(delta_deg) : (2 * phi) / 3;\n if (unit === \"rad\") {\n phi = phi_deg;\n omega = omega_deg;\n beta = beta_deg;\n delta = delta_deg ? delta_deg : (2 * phi) / 3;\n }\n return (\n Math.cos(phi - omega) ** 2 /\n (Math.cos(omega) ** 2 *\n Math.cos(delta + omega) *\n (1 +\n Math.sqrt(\n (Math.sin(delta + phi) * Math.sin(phi - beta)) /\n (Math.cos(delta + omega) * Math.cos(omega - beta))\n )) **\n 2)\n );\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":289,"value":"function kpCoulomb(phi_deg, omega_deg, beta_deg, delta_deg, unit = \"deg\") {\n let rad = deg => deg * (Math.PI / 180),\n phi = rad(phi_deg),\n omega = omega_deg ? rad(omega_deg) : 0,\n beta = beta_deg ? rad(beta_deg) : 0,\n delta = delta_deg ? rad(delta_deg) : (2 * phi) / 3;\n if (unit === \"rad\") {\n phi = phi_deg;\n omega = omega_deg;\n beta = beta_deg;\n delta = delta_deg ? delta_deg : (2 * phi) / 3;\n }\n return (\n Math.cos(phi + omega) ** 2 /\n (Math.cos(omega) ** 2 *\n Math.cos(delta - omega) *\n (1 -\n Math.sqrt(\n (Math.sin(delta + phi) * Math.sin(phi + beta)) /\n (Math.cos(delta - omega) * Math.cos(beta - omega))\n )) **\n 2)\n );\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":411,"value":"kaCoulomb(30)","pinned":true,"hidden":false,"mode":"ojs"},{"id":396,"value":"kpCoulomb(30)","pinned":true,"hidden":false,"mode":"ojs"},{"id":197,"value":"{\n const svg = d3\n .create(\"svg\")\n .attr(\"width\", width)\n .attr(\"height\", width / 2);\n\n svg\n .append(\"g\")\n .call(chart, {\n height: 0.4 * width,\n width: 0.4 * width,\n xAxis: {\n title: \"Phi\"\n },\n yAxis: {\n title: \"Ka\"\n },\n points: Array.from(Array(50), (d, i) => [i + 10, kaCoulomb(i + 10, 0, 0)])\n })\n .attr(\"transform\", `translate(${0.05 * width}, ${0.05 * width})`);\n\n svg\n .append(\"g\")\n .call(chart, {\n height: 0.4 * width,\n width: 0.4 * width,\n xAxis: {\n title: \"Beta\"\n },\n yAxis: {\n title: \"Ka\"\n },\n points: Array.from(Array(30), (d, i) => [i, kaCoulomb(30, 0, i, 20)])\n })\n .attr(\"transform\", `translate(${width / 2}, ${0.05 * width})`);\n\n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":292,"value":"{\n const svg = d3\n .create(\"svg\")\n .attr(\"width\", width)\n .attr(\"height\", width / 2);\n\n svg\n .append(\"g\")\n .call(chart, {\n height: 0.4 * width,\n width: 0.4 * width,\n xAxis: {\n title: \"Phi\"\n },\n yAxis: {\n title: \"Kp\"\n },\n points: Array.from(Array(30), (d, i) => [i + 10, kpCoulomb(i + 10, 0, 0)])\n })\n .attr(\"transform\", `translate(${0.05 * width}, ${0.05 * width})`);\n\n svg\n .append(\"g\")\n .call(chart, {\n height: 0.4 * width,\n width: 0.4 * width,\n xAxis: {\n title: \"Beta\"\n },\n yAxis: {\n title: \"Kp\"\n },\n points: Array.from(Array(30), (d, i) => [i, kpCoulomb(30, 0, i)])\n })\n .attr(\"transform\", `translate(${width / 2}, ${0.05 * width})`);\n\n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":426,"value":"md`## Mononobe-Okabe's`","pinned":true,"hidden":false,"mode":"ojs"},{"id":435,"value":"tex.block`K_a=\\frac{cos^2(\\phi-\\omega-\\beta)}{cos(\\omega)cos^2(\\beta)cos(\\delta+\\beta+\\omega)[1+\\sqrt{\\frac{sin(\\delta+\\phi)sin(\\phi-\\omega+\\alpha)}{cos(\\delta+\\beta+\\phi)cos(\\alpha-\\beta)}}]^2}`","pinned":true,"hidden":false,"mode":"ojs"},{"id":447,"value":"tex.block`K_p=\\frac{cos^2(\\phi-\\omega+\\beta)}{cos(\\omega)cos^2(\\beta)cos(\\delta-\\beta+\\omega)[1+\\sqrt{\\frac{sin(\\delta+\\phi)sin(\\phi-\\omega+\\alpha)}{cos(\\delta-\\beta+\\phi)cos(\\alpha-\\beta)}}]^2}`","pinned":true,"hidden":false,"mode":"ojs"},{"id":159,"value":"md`## Boussinesq's Equation`","pinned":false,"hidden":false,"mode":"ojs"},{"id":27,"value":"md`### Point Load`","pinned":false,"hidden":false,"mode":"ojs"},{"id":124,"value":"md`${await FileAttachment(\"image.png\").image()}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":4,"value":"tex.block`\\sigma_z = \\frac{3Q}{2\\pi z^2}\\frac{1}{[1+(r/z)^2]^{5/2}}=\\frac{Q}{z^2}I_B`","pinned":false,"hidden":false,"mode":"ojs"},{"id":29,"value":"function boussineqPointLoad(Q, r, z) {\n const depth = Math.abs(z);\n if (depth === 0) return undefined;\n if (r <= 0) return undefined;\n const IB = (1.5 / Math.PI) * (1 + (r / depth) ** 2) ** -2.5;\n return (Q * IB) / depth ** 2;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":46,"value":"md`#### Example`","pinned":false,"hidden":false,"mode":"ojs"},{"id":48,"value":"viewof Q = number({\n title: \"Point Load (kN)\",\n value: 50,\n min: 0,\n step: 5\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":130,"value":"viewof r = slider({\n title: \"Radius (m)\",\n value: 1,\n min: 0.1,\n max: 10,\n step: 0.1\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":81,"value":"{\n const svg = d3\n .create(\"svg\")\n .attr(\"width\", width)\n .attr(\"height\", 300);\n\n svg.append(\"g\").call(chart, {\n width: width / 2,\n height: 300,\n xAxis: {\n title: \"Pressure (kPa)\"\n },\n yAxis: {\n title: \"Depth (m)\"\n },\n // points: x => boussineqPointLoad(Q, 1, x),\n points: Array.from(Array(100), (d, i) => {\n const depth = (i + 0.01) * (0.1 * r);\n return [boussineqPointLoad(Q, r, depth), -1 * depth];\n })\n });\n return svg.node();\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":319,"value":"md`## Helpers`","pinned":true,"hidden":false,"mode":"ojs"},{"id":321,"value":"$30","pinned":true,"hidden":false,"mode":"ojs"},{"id":76,"value":"md`## Imports`","pinned":false,"hidden":false,"mode":"ojs"},{"id":79,"value":"import { chart } from \"@syaleni/line-chart-generator\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":58,"value":"import { dropdown, number, slider, checkbox, select } from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":60,"value":"d3 = require(\"d3@6\")","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W31","stdlib":"1","titling":"auto"}