Math & Numbers

Passive Earth Pressure (Rankine)

Calculate the Rankine passive earth pressure on a smooth vertical wall backfilled with cohesionless soil. K_p = tan²(45°+φ/2). Optional uniform surcharge q. Returns the base pressure p₀, the total force P, and the resultant height. Note: theoretical K_p is an upper bound; designers often apply a reduction factor for wall friction.

json· JSON resultOpen tool

Quick start

Call this tool from your code in three languages.

cURL

curl -X POST 'https://api.elysiatools.com/en/api/tools/passive-earth-pressure' \
  -H 'Content-Type: application/json' \
  -d '{"phi":30,"H":2,"gamma":18,"q":0,"decimalPlaces":4}'

API reference

Send a POST request with your inputs as JSON. File parameters require a separate upload first.

Endpoint

HTTP

POST https://api.elysiatools.com/en/api/tools/passive-earth-pressure

Parameters

Name	Type	Required	Description
phi	number	Yes	—
H	number	Yes	—
gamma	number	Yes	—
q	number	No	Optional uniform surcharge on the backfill surface.
decimalPlaces	number	No	—

Response format

MCP integration

Add this tool to your Model Context Protocol server so AI agents can list and call it.

Server configuration

Add this block to your MCP client configuration:

mcp.json

{
  "mcpServers": {
    "elysiatools-passive-earth-pressure": {
      "name": "passive-earth-pressure",
      "description": "Calculate the Rankine passive earth pressure on a smooth vertical wall backfilled with cohesionless soil. K_p = tan²(45°+φ/2). Optional uniform surcharge q. Returns the base pressure p₀, the total force P, and the resultant height. Note: theoretical K_p is an upper bound; designers often apply a reduction factor for wall friction.",
      "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=passive-earth-pressure",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

List available tools

After connecting to the SSE endpoint, list the exposed tools:

tools/list

{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/list"
}

Call this tool

Invoke the tool by its id, passing arguments built from its parameters:

tools/call

{
  "jsonrpc": "2.0",
  "id": 2,
  "method": "tools/call",
  "params": {
    "name": "passive-earth-pressure",
    "arguments": {
  "phi": 30,
  "H": 2,
  "gamma": 18,
  "q": 0,
  "decimalPlaces": 4
}
  }
}

Chain multiple tools in one session with a comma-separated toolId list, e.g. /mcp/sse?toolId=png-to-webp,jpg-to-webp,gif-to-webp (max 20).

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Passive Earth Pressure (Rankine)

json· JSON resultOpen tool

Name

Type

Required

Description

phi

number

Yes

—

number

Yes

—

gamma

number

Yes

—

number

Optional uniform surcharge on the backfill surface.

decimalPlaces

number

—

{ "mcpServers": { "elysiatools-passive-earth-pressure": { "name": "passive-earth-pressure", "description": "Calculate the Rankine passive earth pressure on a smooth vertical wall backfilled with cohesionless soil. K_p = tan²(45°+φ/2). Optional uniform surcharge q. Returns the base pressure p₀, the total force P, and the resultant height. Note: theoretical K_p is an upper bound; designers often apply a reduction factor for wall friction.", "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=passive-earth-pressure", "command": "", "args": [], "env": {}, "isActive": true, "type": "sse" } } }

{ "jsonrpc": "2.0", "id": 2, "method": "tools/call", "params": { "name": "passive-earth-pressure", "arguments": { "phi": 30, "H": 2, "gamma": 18, "q": 0, "decimalPlaces": 4 } } }