Design the strut support for a braced excavation (braced cut) dug deep for an underground structure. Vary the excavation depth, soil weight and strut spacing to see the axial load in a single strut and the number of strut levels update in real time from the Terzaghi-Peck apparent earth pressure, and spot designs where buckling needs attention.
Parameters
Excavation depth H
m
Depth from the ground surface to the dig bottom
Soil unit weight γ
kN/m³
Roughly 17-20 for a sandy soil
Active pressure coefficient Ka
Set by the friction angle; about 0.27-0.40 for sand
Vertical strut spacing sv
m
Spacing between strut levels stacked vertically
Horizontal strut spacing sh
m
Spacing between struts side by side in one level
Results
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Apparent pressure (kPa)
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Total horiz. force (kN/m)
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Tributary area / strut (m²)
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Strut axial load (kN)
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Strut levels needed
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Axial load rating
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Braced excavation section — apparent pressure
Struts prop the two opposing retaining walls apart. The rectangle against the wall is the apparent pressure; the yellow frame is the tributary area of one strut. The pressure envelope gently pulses.
Apparent earth pressure $p_a$ [kPa] ($K_a$: active pressure coefficient, $\gamma$: unit weight kN/m³, $H$: excavation depth m) and the axial load in one strut $P_{strut}$ [kN] ($s_v$: vertical spacing, $s_h$: horizontal spacing).
$$P_{total} = p_a\cdot H, \qquad n = \left\lceil \frac{H}{s_v} \right\rceil$$
Total horizontal force per metre run of wall $P_{total}$ [kN/m] and the number of strut levels $n$. Note that the apparent-pressure diagram is an empirical envelope for estimating strut loads, not the true pressure distribution.
What is a Braced Excavation?
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When they build a subway station or a building basement, they dig a really deep hole. Why don't the walls of that hole just collapse inward?
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Good question. If you dig a deep, narrow excavation, the surrounding ground would slide inward on its own. So you support it. A common solution is the braced cut: vertical walls — sheet piles, soldier piles or diaphragm panels — hold back the soil, and horizontal members called struts span across the excavation, propping the opposing walls apart.
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So the struts are like props between the walls. Then I just compute their load with the textbook triangular earth pressure, right?
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That is exactly the crucial point of this tool — and no, you can't use the triangular active pressure directly. The triangular diagram assumes the wall rotates freely about its base, so the pressure grows linearly with depth. A braced wall simply does not move like that.
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Wait, the wall doesn't rotate freely? How does it move then?
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You install the struts from the top down as you dig deeper. The first row goes in early, so the top of the wall is held almost immobile. The lower part, though, can yield a little before the deeper struts arrive. So the wall deforms in a bulging, restrained pattern — top fixed, bottom bulging — completely unlike free rotation. That means the pressure distribution is not triangular either.
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Then how do engineers actually decide the strut loads?
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Terzaghi and Peck measured strut loads on dozens of real excavation sites. From all that field data they proposed apparent-pressure diagrams that match the real behaviour — for sand, a rectangle that is uniform with depth. It is not the true pressure distribution. It is an empirical envelope deliberately shaped so that, when you use it to compute the load on a strut at any level, you get a safe value. Each strut is taken to carry the pressure over its tributary area. Because struts are long compression members prone to buckling, and one failed strut can trigger progressive collapse, the method is kept deliberately conservative.
Frequently Asked Questions
The textbook triangular diagram (active earth pressure) assumes the wall rotates freely about its base, with pressure growing linearly with depth. A braced wall does not move that way. The top row of struts is installed early in the excavation and holds the upper wall almost immobile, while the lower part can yield a little before the deeper struts go in. So the wall deforms in a bulging, restrained pattern quite unlike free rotation. From decades of field measurements of strut loads, Terzaghi and Peck proposed apparent-pressure diagrams (rectangular for sand) that match this behaviour. They are not the true pressure distribution but empirical envelopes deliberately shaped so the strut loads come out safe.
0.65 is an empirical factor proposed by Terzaghi and Peck for braced cuts in sand. The resultant of the triangular active pressure is (1/2)Ka·γ·H², which corresponds to an average pressure of 0.5·Ka·γ·H. The rectangular apparent-pressure envelope is set slightly higher, at the uniform value 0.65·Ka·γ·H, so that the load computed for a strut at any level — top or bottom — stays on the safe side. Soft clay and stiff clay use different diagrams (trapezoidal, etc.) with their own factors and shapes. This tool covers the rectangular envelope for sand.
In a braced wall, each strut is taken to carry the pressure acting over its tributary area — the rectangle of wall reaching midway to the struts above and below it and midway to the struts on either side. That area equals the vertical spacing sv times the horizontal spacing sh. The axial load is the apparent pressure pa multiplied by this tributary area: P_strut = pa·sv·sh. Widening either spacing increases the load on each strut and makes the buckling check more critical.
A strut is a long compression member spanning the excavation to prop the opposing walls apart, and its buckling capacity drops sharply as the unsupported length grows. For the same axial load, a longer strut has a higher slenderness ratio and its allowable load is governed by buckling rather than yielding. A braced excavation is also a system of many interacting struts: if one strut buckles or fails, its load is redistributed to its neighbours and can trigger progressive collapse. That is why apparent-pressure methods are kept deliberately conservative, and why this tool flags the axial load with thresholds that prompt a buckling and section check.
Real-World Applications
Subway stations and underground structures: Urban subway stations are often built in narrow, rectangular, deep excavations — a classic use of the braced cut. Sheet piles or diaphragm walls are installed first, then the dig proceeds, with a strut level placed each time the excavation reaches a planned depth. Estimating the load on each strut level from the apparent pressure and carrying out a section check including buckling is the basic design flow.
Building basements and underground car parks: A new building in a built-up area requires a deep excavation right next to neighbouring structures, calling for a stiff support system that limits settlement of the surrounding ground. The number and spacing of strut levels are chosen from the apparent pressure based on the excavation depth and ground conditions, while the effect on adjacent structures is assessed alongside.
Utility shafts, tunnels and lifeline works: Shafts and utility corridors for water, power and telecommunications are also dug as braced cuts supported by struts and walings. A narrow, deep excavation allows short strut spans that keep axial loads low, but the number of levels grows, so managing the construction sequence becomes important.
Preliminary design and sanity checks: Before running a detailed beam-on-spring (elasto-plastic) analysis or a finite element model, an apparent-pressure estimate like this tool gives the order of magnitude of the strut loads, speeding up section sizing and decisions on strut count. Conversely, if a detailed analysis differs from the estimate by an order of magnitude, that is a sanity check pointing to an error in the analysis assumptions.
Common Misconceptions and Pitfalls
The biggest misconception is "the apparent-pressure diagram represents the actual pressure distribution". The Terzaghi-Peck apparent-pressure diagram is not a measurement of the true pressure distribution. It was back-calculated from strut loads measured on many sites and deliberately shaped so that, when used to compute each strut's load, the result stays on the safe side at every level. The apparent pressure is therefore valid for finding strut and waling loads — not for accurately obtaining the bending moments in the wall, which require a separate beam-on-spring or finite element analysis.
Next, "using the sand diagram on a clay site". The rectangular apparent pressure in this tool is for sandy soils. Soft clay and stiff clay use diagrams of a different shape (trapezoidal, etc.) with different factors. In soft clay especially, basal heave at the dig bottom and the stability number must be checked separately — apparent pressure alone does not complete the design. The site investigation must confirm the soil type so the right diagram is chosen. Groundwater, surcharge loads and the effect of nearby structures are also outside this estimate.
Finally, "if the axial load is satisfied, the strut is safe". A strut is a long compression member, so its capacity is almost always governed by buckling, not by strength (yielding). For the same axial load, a longer span gives a higher slenderness ratio and a much lower allowable load. Struts also expand and contract with temperature, and preload, joint slack and the interaction with the walings all affect the load. The axial load from this tool is only the starting point of design; always pair it with checks on the buckling length, section properties and the load changes through each construction stage.
How to Use
Set excavation depth (hNum, range 3–15 m) and soil layer thickness distribution (hRange) to define the cut geometry.
Input number of granular layers (gNum) and their thickness variation (gRange), then specify effective angle of friction (kaNum, typically 25–40°) to calculate active earth pressure coefficients.
Enter surcharge vertical stress (svNum, range 0–50 kPa) and its distribution width (svRange), then execute simulation to compute apparent pressure envelope, total horizontal force per meter, tributary area per strut, individual strut axial load in kN, minimum strut levels required, and axial load rating capacity needed.
Worked Example
Excavation depth 8 m, single granular layer with φ = 32°, soil unit weight 18 kN/m³, surcharge 20 kPa. Active pressure coefficient Ka = 0.307. Maximum horizontal stress at base: σh = 0.307 × (18 × 8 + 20) = 48.4 kPa. Total horizontal force = 0.5 × 48.4 × 8 = 193.6 kN/m. For strut spacing 4 m (tributary area 4 × 8 = 32 m²), single strut axial load = 193.6 × 4 = 774.4 kN. Three strut levels (top, middle, base) distribute load; select W310×129 steel section rated 900 kN compression.
Practical Notes
Increase strut levels from 2 to 4 when excavation depth exceeds 10 m or surcharge exceeds 40 kPa to avoid plastic hinge formation in retained wall.
Reduce hRange (layer uniformity) for clay–sand interbedded sequences; use separate gNum entries for cohesive strata to refine Ka calculation and prevent underestimation of pressure bulges at interface transitions.
Account for construction sequence: strut preload typically 10–20% of calculated axial load to minimize wall deflection; verify buckling length (distance between lateral supports) does not exceed 15 times strut diameter for timber or 30 times for steel box sections.