Results

// 1. Global concrete volume per year

cement_mass = to(3.5e9, 4.7e9)              // tonnes of cement produced globally per year
concrete_to_cement_ratio = to(6, 8)         // mass of concrete per unit mass of cement (dimensionless)
concrete_mass = cement_mass * concrete_to_cement_ratio  // tonnes of concrete produced per year

concrete_density = to(2.3, 2.5)             // density of concrete in tonnes per cubic meter
concrete_volume = concrete_mass / concrete_density      // cubic meters of concrete produced per year


// 2. Grand Canyon volume

canyon_length = to(430e3, 470e3)            // length of main Grand Canyon section, in meters
canyon_width = to(12e3, 20e3)               // average rim-to-rim width, in meters
canyon_depth = to(1.1e3, 1.5e3)             // average depth from rim to river, in meters
cross_section_shape_factor = to(0.3, 0.6)   // fraction of rectangular cross-section that is actual canyon void

canyon_volume = canyon_length * canyon_width * canyon_depth * cross_section_shape_factor  // cubic meters


// 3. Fraction of the Grand Canyon filled by one year's concrete production

fraction_filled = concrete_volume / canyon_volume       // dimensionless fraction (0-1)


{
  p5: quantile(fraction_filled, 0.05),
  p50: quantile(fraction_filled, 0.50),
  p95: quantile(fraction_filled, 0.95)
}

We want:

> fraction filled = (volume of all concrete made in 1 year) / (volume of the Grand Canyon)

I’ll estimate both volumes separately, then take the ratio.

---

## 1. Volume of all concrete produced in one year

### 1.1 Global cement production (mass per year)

Modern global cement production is widely known to be a few billion tonnes per year, not tens of billions, and not less than a billion.

Given historical data up to the 2020s, a 90% confidence interval:

- Lower bound: 3.5 billion tonnes (3.5e9 t)
- Upper bound: 4.7 billion tonnes (4.7e9 t)

This captures “recent typical” years without being too tight.

So:
- `cement_mass ≈ to(3.5e9, 4.7e9)` tonnes/year

### 1.2 Concrete mass per unit cement mass

Concrete is mostly aggregates + sand + water, with cement as the binder.

By mass, a typical structural concrete mix is roughly:
- ~10–20% cement
- the rest aggregates + water + admixtures

So the ratio:

> concrete_mass / cement_mass

is typically in the range:
- If cement is 20% by mass → ratio = 1/0.20 = 5
- If cement is 12.5% → ratio = 1/0.125 = 8
- It’s unlikely to be <5 or >8 on a global average.

So as a 90% interval:
- `concrete_to_cement_ratio ≈ to(6, 8)` (dimensionless)

This also implicitly includes cement used in mortars and similar mixes — they’re concrete-like in density and bulk behavior.

Then:
- `concrete_mass = cement_mass * concrete_to_cement_ratio`

### 1.3 Density of concrete

Normal structural concrete has density around 2.3–2.5 t/m³:
- Lightweight and heavyweight mixes exist, but the global average should be close to “normal” concrete.

So:
- `concrete_density ≈ to(2.3, 2.5)` tonnes per cubic meter

Then annual concrete volume:

> concrete_volume = concrete_mass / concrete_density

Units: m³/year.

---

## 2. Volume of the Grand Canyon

We’ll approximate the Grand Canyon as a long, roughly V-shaped trench.

### 2.1 Length of the main canyon

The commonly referenced length (Colorado River through the main canyon) is around the mid-400s of kilometers.

For a 90% interval:
- Lower: 430 km
- Upper: 470 km

So:
- `canyon_length ≈ to(430e3, 470e3)` meters

### 2.2 Average rim-to-rim width

The canyon is:
- Max width approaching ~30 km in some places
- Much narrower in others

An average “effective” width for the main canyon might be in the low to mid-teens of kilometers.

Reasonable 90% interval:
- Lower: 12 km
- Upper: 20 km

So:
- `canyon_width ≈ to(12e3, 20e3)` meters

### 2.3 Average depth (rim to river)

Maximum depth is around 1.8 km; many sections are shallower.

Average depth of the big canyon sections is plausibly:
- Roughly 1.1–1.5 km

So:
- `canyon_depth ≈ to(1.1e3, 1.5e3)` meters

### 2.4 Cross-section shape factor

If we took a simple rectangular cross-section (width × depth), that would overestimate volume, since the canyon is more like a V/U shape: steep walls, benches, side valleys, etc.

Define:

> shape_factor = (actual cross-sectional area) / (width × depth)

- A perfect triangle would be 0.5
- The Grand Canyon is irregular; some parts are very steep, some stepped, so 0.3–0.6 feels like a reasonable range.

So:
- `cross_section_shape_factor ≈ to(0.3, 0.6)` (dimensionless)

Then:

> cross_section_area = canyon_width * canyon_depth * cross_section_shape_factor  
> canyon_volume = canyon_length * cross_section_area

Units: m³.

This approach should put us in the right ballpark (a few thousand cubic kilometers).

---

## 3. Fraction of the canyon filled

Finally:

> fraction_filled = concrete_volume / canyon_volume

This is dimensionless (a fraction between 0 and 1).

Intuitively, with tens of billions of tonnes of concrete per year and a few thousand cubic kilometers of canyon, we expect the result to be far below “completely full,” but not vanishingly small (i.e., some small fraction of the canyon’s volume).

---

## 4. Squiggle code

```squiggle
// 1. Global concrete volume per year

cement_mass = to(3.5e9, 4.7e9)              // tonnes of cement produced globally per year
concrete_to_cement_ratio = to(6, 8)         // mass of concrete per unit mass of cement (dimensionless)
concrete_mass = cement_mass * concrete_to_cement_ratio  // tonnes of concrete produced per year

concrete_density = to(2.3, 2.5)             // density of concrete in tonnes per cubic meter
concrete_volume = concrete_mass / concrete_density      // cubic meters of concrete produced per year


// 2. Grand Canyon volume

canyon_length = to(430e3, 470e3)            // length of main Grand Canyon section, in meters
canyon_width = to(12e3, 20e3)               // average rim-to-rim width, in meters
canyon_depth = to(1.1e3, 1.5e3)             // average depth from rim to river, in meters
cross_section_shape_factor = to(0.3, 0.6)   // fraction of rectangular cross-section that is actual canyon void

canyon_volume = canyon_length * canyon_width * canyon_depth * cross_section_shape_factor  // cubic meters


// 3. Fraction of the Grand Canyon filled by one year's concrete production

fraction_filled = concrete_volume / canyon_volume       // dimensionless fraction (0-1)


{
  p5: quantile(fraction_filled, 0.05),
  p50: quantile(fraction_filled, 0.50),
  p95: quantile(fraction_filled, 0.95)
}
```