Concrete Gravity, Arch and Buttress Dams

Introduction

Concrete dams resist reservoir loading through three distinct structural mechanisms. A gravity dam relies primarily on its self-weight and foundation resistance. An arch dam transfers a substantial proportion of loading through arch compression to competent valley abutments. A buttress dam uses an upstream deck or multiple arches supported by buttresses, reducing concrete volume while increasing structural and maintenance complexity.

Safe design requires more than checking nominal dimensions. Engineers must represent material behaviour, foundation interaction, drainage, load combinations, construction joints, temperature history and earthquake actions. The analysis must demonstrate acceptable resistance to sliding, overturning, excessive bearing pressure, cracking, uplift instability and abutment failure under relevant design situations.

Design criteria should be taken from the governing national regulations and owner requirements, supplemented where appropriate by guidance from ICOLD, USACE, USBR, ANCOLD and recognised seismic codes. Allowable stresses and safety factors vary with dam consequence category and load combination; therefore, values from one standard must not be transferred uncritically to another.

Learning Objectives

After studying this chapter, the reader should be able to:

• compare gravity, arch and buttress dam layouts;
• formulate hydrostatic, uplift, sediment, thermal and seismic actions;
• establish normal, unusual and extreme load combinations;
• evaluate sliding, resultant location, bearing pressure and overturning stability;
• perform preliminary analytical assessments of arch and buttress dams;
• assess simplified temperature and earthquake effects;
• interpret analytical results in the context of foundation geology, construction and dam-safety governance.

1. Dam Types and Layout Selection

1.1 Concrete gravity dams

A gravity dam is usually divided by transverse contraction joints into monoliths that act approximately independently under static loading. Its cross-section commonly has a nearly vertical upstream face and an inclined downstream face. Galleries provide drainage, inspection and access for instrumentation.

Gravity dams are suited to relatively broad valleys with strong, low-deformability foundations. Their advantages include structural simplicity, substantial resistance to impact and overtopping, and comparatively transparent load paths. Disadvantages include high concrete volume, significant uplift exposure and mass-concrete temperature control requirements.

1.2 Arch dams

Arch dams are curved in plan and commonly curved vertically. Reservoir pressure is resisted by interacting horizontal arches and vertical cantilevers. Double-curvature dams exploit both mechanisms and can be very slender.

Arch dams require narrow valleys and competent abutments capable of accepting concentrated thrust. Rock discontinuities, weak wedges or asymmetric abutment deformation can govern feasibility even where the concrete stresses are low. Three-dimensional foundation–structure interaction is therefore fundamental.

1.3 Buttress dams

Buttress dams consist of an inclined upstream deck, multiple arches or massive heads supported by buttresses. Principal forms include flat-slab-and-buttress, multiple-arch and massive-head dams.

They use less concrete than gravity dams and may produce lower foundation stresses. However, they contain more exposed surface, reinforcement, joints and thin members. Durability, leakage, freeze–thaw effects and access between buttresses require particular attention.

1.4 Layout decision framework

Selection should consider:

1. Valley geometry: narrow V-shaped valleys favour arch action; broad valleys commonly favour gravity layouts.

2. Geology: arch dams require strong abutments, while gravity dams require adequate base shear and bearing resistance.

3. Hazards: seismicity, floods, landslides, sediment and extreme temperatures may alter the preferred form.

4. Construction resources: aggregate availability, formwork, reinforcement, cooling systems and diversion arrangements are important.

5. Whole-life performance: inspection access, drainage maintenance, repairability and decommissioning must be evaluated.

2. Material and Foundation Behaviour

2.1 Mass concrete

Dam concrete is heterogeneous, time-dependent and susceptible to cracking. Important properties include density, elastic modulus, Poisson's ratio, compressive and tensile strength, fracture energy, thermal expansion coefficient, conductivity, heat capacity, creep and shrinkage.

The modulus used in analysis must correspond to the loading rate. A dynamic modulus may be appropriate for earthquake response, whereas a reduced effective modulus may better represent long-term thermal or sustained loading. Concrete tensile strength should not automatically be credited across lift joints or pre-existing cracks.

2.2 Discontinuities and interfaces

Potential sliding surfaces include the concrete–rock contact, weak seams within the foundation, lift joints and joints within an abutment wedge. Shear resistance may be represented by the Mohr–Coulomb relation

\[

R=cA+(N-U)\tan\phi,

\]

where \(c\) is effective cohesion, \(A\) is the resisting area, \(N\) is total force normal to the plane, \(U\) is uplift force on the plane and \(\phi\) is the effective friction angle. Cohesion should be omitted or reduced where bonding cannot be reliably demonstrated.

Rock-mass deformation influences load transfer. For arch dams, unequal abutment stiffness can cause redistribution and local tensile stress. For gravity dams, foundation flexibility modifies base stress from the elementary linear distribution.

2.3 Drainage and deterioration

Drain holes reduce uplift only when they remain effective. Design uplift assumptions must correspond to inspectable and maintainable drainage systems. Calcification, sediment, chemical attack, alkali–aggregate reaction and joint movement can impair performance. Monitoring data should therefore be incorporated into periodic safety reviews.

3. Actions on Concrete Dams

3.1 Self-weight

For a two-dimensional section of area \(A_c\),

\[

W=\gamma_c A_c,

\]

where \(\gamma_c\) is concrete unit weight. The line of action passes through the centroid. Appurtenant structures should be included where significant.

3.2 Hydrostatic pressure

For water depth \(H\) against a vertical face,

\[

p(z)=\gamma_w z,\qquad P_w=\frac{1}{2}\gamma_wH^2,

\]

where \(z\) is depth below the surface. The resultant acts at \(H/3\) above the base. Inclined or curved surfaces also produce vertical components, which must be computed from the pressure integration or the weight of the appropriate imaginary water prism.

3.3 Uplift

For a base of width \(B\) with linearly varying uplift intensities \(u_h\) and \(u_t\) at heel and toe,

\[

U=\frac{u_h+u_t}{2}B.

\]

The line of action is found from the centroid of the trapezoidal pressure diagram. If \(x\) is measured from the heel,

\[

\bar{x}_U=\frac{B(u_h+2u_t)}{3(u_h+u_t)}.

\]

This expression is valid only for a linear distribution. Drain efficiency must be based on project criteria and credible drainage performance.

3.4 Sediment, ice and wave actions

Sediment loading depends on submerged unit weight, lateral pressure coefficient and pore pressure. Ice pressure is climate- and site-dependent and should normally be specified by the governing standard. Wave pressure is often secondary for large dams but can affect crest structures and freeboard.

3.5 Load combinations

Typical design situations include:

• usual: normal reservoir, self-weight, normal tailwater, operational uplift and service temperature;
• unusual: flood reservoir, abnormal tailwater, impaired drainage or unusual temperature;
• extreme: safety-evaluation earthquake, extreme flood or other low-probability hazard.

Actions should not simply be combined at their individually worst values if those values cannot physically occur together. Vertical earthquake inertia and reservoir conditions require explicit sign and concurrence rules.

4. Gravity-Dam Stability and Stress Analysis

4.1 Resultant location

Let \(V\) be the net downward vertical force and \(M_H\) the net moment of all actions about the heel. The base resultant location is

\[

x_R=\frac{M_H}{V}.

\]

For base width \(B\), the eccentricity measured toward the toe is

\[

e=x_R-\frac{B}{2}.

\]

The middle-third condition, \(|e|\le B/6\), prevents tension under a rigid-base, linear-elastic no-tension idealisation. It is a screening criterion, not proof of overall safety.

4.2 Base pressure

If the base remains fully in compression and the stress distribution is linear,

\[

q_{toe}=\frac{V}{B}\left(1+\frac{6e}{B}\right),\qquad

q_{heel}=\frac{V}{B}\left(1-\frac{6e}{B}\right).

\]

These equations apply per metre length to a rectangular base with linear stress distribution. If the resultant lies outside the middle third, a no-tension contact analysis or nonlinear interface model is required; the equations must not be used to imply transferable tensile contact stress.

4.3 Sliding

A simplified sliding safety factor is

\[

FS_s=\frac{cA+(V)\tan\phi+P_p}{H},

\]

where uplift has already been deducted in obtaining net \(V\), \(P_p\) is any reliably mobilised passive resistance and \(H\) is the driving shear force. If gross normal force is used instead, uplift must be deducted explicitly. Shear keys and passive resistance should be credited only when their deformation compatibility and long-term availability are demonstrated.

4.4 Overturning

A traditional factor is

\[

FS_o=\frac{\sum M_{resisting}}{\sum M_{overturning}}.

\]

Although useful for preliminary assessment, it can obscure uplift and contact-stress behaviour. Modern practice also examines resultant location, crack development, foundation stresses and nonlinear response.

4.5 Bearing and foundation capacity

Maximum compressive stress must remain compatible with concrete and rock-mass capacity. Foundation assessment should include weak layers, stress concentrations, settlement, toe crushing and three-dimensional effects. Conventional shallow-foundation bearing formulas are not automatically applicable to jointed rock beneath a large dam.

5. Worked Gravity-Dam Assessment

Consider one metre length of a gravity-dam monolith with base width \(B=20\,\text{m}\). A verified section take-off gives the following vertical actions and moments about the heel:

| Action | Vertical force (kN/m) | Lever arm (m) | Moment (kN·m/m) |

|---|---:|---:|---:|

| Concrete weight | +5,000 | 13.000 | +65,000 |

| Downward water component | +600 | 8.000 | +4,800 |

| Uplift | −2,000 | 8.901 | −17,802 |

Thus,

\[

V=5000+600-2000=3600\ \text{kN/m},

\]

and the signed moment of vertical actions is

\[

M_V=65000+4800-17802=51,998\ \text{kN·m/m}.

\]

Horizontal water and ancillary actions produce an overturning moment of \(13,082\,\text{kN·m/m}\) about the heel. The net base moment is therefore

\[

M_H=51,998-13,082=38,916\ \text{kN·m/m}.

\]

Hence,

\[

x_R=\frac{38,916}{3600}=10.81\ \text{m from the heel},

\]

\[

e=10.81-10.00=0.81\ \text{m toward the toe}.

\]

Because \(B/6=3.33\,\text{m}\), the resultant is inside the middle third. The average pressure is

\[

\frac{V}{B}=\frac{3600}{20}=180\ \text{kPa}.

\]

Therefore,

\[

q_{toe}=180\left(1+\frac{6(0.81)}{20}\right)=223.74\ \text{kPa},

\]

\[

q_{heel}=180\left(1-\frac{6(0.81)}{20}\right)=136.26\ \text{kPa}.

\]

If the net horizontal shear is \(H=1500\,\text{kN/m}\), cohesion and passive resistance are ignored, and \(\tan\phi=0.70\), then

\[

FS_s=\frac{3600(0.70)}{1500}=1.68.

\]

Whether this is acceptable depends on the governing load combination and project criteria. Sensitivity checks should include blocked drains, reduced interface friction and foundation discontinuities.

6. Arch-Dam Analysis

6.1 Arch membrane model

A horizontal circular arch strip of radius \(R\), thickness \(t\), and unit vertical height subjected to uniform radial pressure \(p\) has membrane compression

\[

N=pR

\]

and average compressive stress

\[

\sigma_c=\frac{N}{t}=\frac{pR}{t}.

\]

This thin-arch relationship assumes membrane action, uniform pressure over the strip, negligible bending and adequate abutment restraint. Real arch dams have changing radius and thickness, and vertical cantilever action causes load redistribution.

Example. At a depth of \(20\,\text{m}\), \(p=9.81(20)=196.2\,\text{kPa}\). For \(R=80\,\text{m}\) and \(t=12\,\text{m}\),

\[

N=196.2(80)=15,696\ \text{kN/m},

\qquad

\sigma_c=\frac{15,696}{12}=1,308\ \text{kPa}=1.31\ \text{MPa}.

\]

The result is a preliminary membrane estimate, not a substitute for shell analysis.

6.2 Arch–cantilever interaction

Trial-load methods divide water pressure between horizontal arches and vertical cantilevers. Compatibility requires equal radial deflection at their intersections. The distribution is iteratively adjusted until equilibrium and compatibility are satisfied. Contemporary practice uses three-dimensional finite-element models incorporating contraction joints, foundation flexibility, reservoir interaction and staged construction.

6.3 Abutment-wedge stability

A kinematically admissible rock wedge bounded by discontinuities must be checked against sliding. For a candidate sliding direction,

\[

FS_w=\frac{cA+(N-U)\tan\phi}{T},

\]

where \(T\) is the destabilising shear component. Three-dimensional wedge geometry, joint persistence, water pressure, seismic inertia and arch thrust must be included. A strong concrete arch cannot compensate for an unstable abutment.

7. Buttress-Dam Analysis

The upstream deck transfers pressure to the buttresses through plate or beam action. Buttresses then carry axial force, bending and shear to the foundation.

For preliminary analysis, a one-metre-high horizontal strip of deck spanning simply between buttresses at spacing \(s\) may be idealised as a beam under uniform line load \(w=p\), giving

\[

M_{max}=\frac{ps^2}{8},\qquad V_{max}=\frac{ps}{2}.

\]

This is valid only for a simply supported strip under locally uniform pressure. Continuity, inclination and two-way plate action require more refined analysis.

Example. At \(15\,\text{m}\) depth, \(p=147.15\,\text{kPa}\). For \(s=6\,\text{m}\),

\[

M_{max}=\frac{147.15(6^2)}{8}=662.18\ \text{kN·m per metre-high strip}.

\]

For an uncracked rectangular strip of unit height and structural depth \(0.60\,\text{m}\), its section modulus is

\[

Z=\frac{1(0.60)^2}{6}=0.060\ \text{m}^3,

\]

so the elastic extreme-fibre stress is

\[

\sigma=\frac{662.18}{0.060}=11.04\ \text{MPa}.

\]

Because one face is in tension, reinforced-concrete or prestressed design and crack control are required. The global stability of each buttress bay must also be checked using its tributary water load, self-weight, uplift and foundation resistance.

Buckling of slender buttresses should be assessed using second-order or finite-element analysis rather than relying solely on Euler buckling, since restraint, cracking and load eccentricity are significant.

8. Temperature Analysis

8.1 Heat transfer

Transient concrete temperature is governed by

\[

\rho c_p\frac{\partial T}{\partial t}=k\nabla^2T+\dot q,

\]

where \(\rho\) is density, \(c_p\) is specific heat, \(k\) is thermal conductivity and \(\dot q\) is internal heat generation per unit volume. Boundary conditions may include reservoir temperature, air temperature, solar radiation and convection.

Hydration heat can raise lift temperatures during construction. Subsequent cooling causes contraction restrained by the foundation or adjacent concrete. Seasonal gradients produce curvature and cyclic joint movement.

8.2 Thermal stress

Free thermal strain is

\[

\varepsilon_T=\alpha\Delta T.

\]

For complete uniaxial restraint in a linear-elastic material,

\[

\sigma_T=E\alpha\Delta T.

\]

This formula does not apply unchanged to biaxial restraint, temperature gradients, creep or cracking.

For \(E=30\,\text{GPa}\), \(\alpha=10\times10^{-6}/^\circ\text{C}\) and a restrained temperature fall of \(15^\circ\text{C}\),

\[

|\sigma_T|=30,000(10\times10^{-6})(15)=4.50\ \text{MPa tension}.

\]

If time-dependent relaxation reduces the effective restraint to 55%, the estimated stress becomes \(2.48\,\text{MPa}\). Such reduction must come from a validated creep model, not an arbitrary factor.

Temperature-control measures include low-heat cementitious systems, aggregate cooling, embedded cooling pipes, lift scheduling, surface insulation, contraction joints and joint grouting at specified temperatures.

9. Seismic Assessment

9.1 Pseudo-static forces

A preliminary earthquake analysis may represent dam inertia as

\[

F_h=k_hW,

\qquad F_v=\pm k_vW,

\]

where \(k_h\) and \(k_v\) are seismic coefficients. Horizontal inertia acts through the mass centroid. Both signs of vertical inertia should be examined where required because upward acceleration reduces effective weight and sliding resistance.

9.2 Hydrodynamic pressure

For a rigid dam with a vertical upstream face and reservoir depth \(H\), the simplified Westergaard distribution is

\[

p_e(y)=\frac{7}{8}k_h\gamma_w\sqrt{Hy},

\]

where \(y\) is depth below the water surface. Integration gives

\[

P_e=\frac{7}{12}k_h\gamma_wH^2,

\]

acting at \(2H/5\) above the base. The approximation has restrictive geometric and dynamic assumptions; modern analyses may model compressible reservoir interaction and radiation boundaries directly.

For \(H=30\,\text{m}\) and \(k_h=0.15\),

\[

P_e=\frac{7}{12}(0.15)(9.81)(30^2)=772.54\ \text{kN/m},

\]

acting \(12\,\text{m}\) above the base.

If a monolith weighs \(7200\,\text{kN/m}\), its horizontal inertia is

\[

F_h=0.15(7200)=1080\ \text{kN/m}.

\]

These forces are added consistently to the extreme load combination, together with static water pressure and the appropriate uplift assumption.

9.3 Dynamic analysis

Response-spectrum or time-history analysis is generally required for high-consequence dams. The model may include concrete cracking, contraction-joint opening, foundation radiation damping, reservoir compressibility and spatially varying ground motion. Linear analysis is useful for screening, but tensile stress peaks should not automatically be interpreted as physical resistance where joints can open.

Performance objectives may include limited service damage under an operating-basis earthquake and prevention of uncontrolled reservoir release under a safety-evaluation earthquake.

10. Illustrative Integrated Case: Existing Gravity Dam

Background

An illustrative 45-year-old gravity dam is undergoing a periodic safety review. Instrumentation indicates increasing uplift during wet seasons, while regional seismic hazard estimates have also been revised.

Problem

The original analysis assumed fully effective drains and used only static water loading. The owner must determine whether rehabilitation or more advanced investigation is required.

Analysis and approach

1. Survey and material testing establish geometry, concrete density, joint condition and foundation shear parameters.

2. Piezometer records are used to develop operational and blocked-drain uplift envelopes.

3. Static stability is checked using resultant location, contact pressure and sliding resistance.

4. Westergaard hydrodynamic pressure and dam inertia are used for seismic screening.

5. A foundation model examines a mapped downstream-dipping seam.

6. Sensitivity analyses reduce cohesion to zero and vary friction, drain efficiency and vertical earthquake direction.

The normal-drainage case is represented by the worked calculation in Section 5, giving \(x_R=10.81\,\text{m}\), \(e=0.81\,\text{m}\), pressures of approximately 224 and 136 kPa, and a cohesion-free sliding factor of 1.68. The blocked-drain case reduces net vertical force and moves the resultant downstream. Seismic inertia further reduces the available sliding margin.

Solution and outcome

The review team recommends drain cleaning and redrilling, automated piezometer monitoring, foundation coring across the seam and a nonlinear seismic model. Operational trigger levels are linked to uplift and reservoir elevation. The dam is not declared satisfactory solely from the normal static result because the adverse cases govern risk.

Learning points

• Drainage assumptions must be supported by observed performance.
• A satisfactory middle-third result does not prove adequate sliding resistance.
• Foundation discontinuities may govern before concrete compressive capacity.
• Instrumentation, analysis and emergency planning form a single risk-management system.

11. Professional Practice, Governance and Emerging Methods

Dam design and review require independent checking, traceable calculations, controlled models and explicit documentation of uncertainty. Hazard classification should reflect downstream consequences, not merely dam height. Emergency action plans and public warning arrangements are essential residual-risk controls.

Ethical practice requires engineers to report unfavourable monitoring trends and model uncertainty without distortion. Decisions should consider downstream communities, environmental flows, cultural heritage and equitable risk distribution.

Finite-element analysis, digital twins, satellite deformation monitoring, distributed fibre-optic sensing and automated anomaly detection increasingly support dam management. Machine-learning systems can identify unusual behaviour in large datasets, but they cannot establish structural safety without physically informed interpretation. Data quality, model drift, cybersecurity and explainability must be governed.

Chapter Summary

Gravity dams resist loads mainly through mass and foundation shear; arch dams transfer loads to abutments through shell and arch action; buttress dams use structural members to reduce concrete volume. Stability assessment requires consistent treatment of hydrostatic pressure, uplift, self-weight, sediment, temperature and earthquake actions. Gravity-dam checks include resultant location, base pressure, sliding and foundation capacity. Arch analysis must address arch–cantilever interaction and abutment wedges, while buttress analysis must examine deck bending, buttress stability and buckling. Temperature and seismic actions often require transient or dynamic models beyond elementary formulas. Reliable dam safety ultimately depends on sound geology, monitored drainage, validated analysis, independent review and responsible governance.

Key Terms

Abutment thrust: Compressive force transferred from an arch dam into valley rock.

Arch–cantilever interaction: Sharing of dam loading between horizontal arches and vertical cantilevers.

Bearing pressure: Compressive contact stress transmitted to the foundation.

Buttress: Structural support carrying deck or arch loads to the foundation.

Contraction joint: Deliberate joint accommodating thermal and shrinkage movement.

Eccentricity: Offset between the base resultant and the base centreline.

Hydrodynamic pressure: Earthquake-induced water pressure acting on a dam.

Hydrostatic pressure: Fluid pressure arising from water depth under static conditions.

Middle third: Central third of a rectangular base within which a compressive resultant produces no tensile stress under linear assumptions.

Monolith: Individual dam block separated by contraction joints.

Overturning: Rotational tendency caused by moments about a potential pivot region.

Resultant: Single equivalent force representing a system of forces and moments.

Sliding safety factor: Ratio of available shear resistance to driving shear.

Thermal strain: Expansion or contraction caused by temperature change.

Uplift: Water pressure acting within a base, joint or foundation discontinuity.

Westergaard pressure: Simplified earthquake-induced hydrodynamic pressure distribution.

Foundation–structure interaction: Coupled deformation and load transfer between a dam and its foundation.

Trial-load method: Iterative procedure for distributing load between arches and cantilevers.

Review Questions

Short Answer Questions

1. Distinguish the primary load paths of gravity, arch and buttress dams.

2. State the assumptions underlying the linear base-pressure equations.

3. Explain why uplift is deducted from effective normal force in sliding analysis.

4. What geological conditions are especially important for an arch dam?

5. Why must both signs of vertical seismic acceleration sometimes be examined?

Long Answer Questions

1. Explain how concrete time dependence, joints and foundation flexibility influence dam analysis.

2. Develop a systematic procedure for evaluating gravity-dam sliding, overturning and bearing performance.

3. Discuss the analytical progression from thin-arch theory to three-dimensional arch-dam modelling.

4. Explain the structural behaviour and principal failure modes of flat-slab-and-buttress dams.

5. Discuss temperature control from concrete placement through long-term operation.

Analytical / Application Questions

1. A gravity dam has \(B=24\,\text{m}\), net vertical load \(V=4800\,\text{kN/m}\) and resultant location \(x_R=13.2\,\text{m}\) from the heel. Calculate eccentricity and heel and toe pressures, stating whether the middle-third condition is satisfied.

2. For an arch strip with \(R=95\,\text{m}\), \(t=14\,\text{m}\) and water depth \(25\,\text{m}\), estimate membrane force and compressive stress. Explain why the result is only preliminary.

3. Develop normal, blocked-drain and seismic load combinations for an existing gravity dam and identify the measurements needed to reduce uncertainty.

Multiple Choice Questions with Answers

Question 1

A 20 m wide gravity-dam base carries a net vertical load of 3600 kN/m at an eccentricity of 0.81 m toward the toe. What are the approximate toe and heel pressures?

A. 224 kPa and 136 kPa

B. 236 kPa and 124 kPa

C. 260 kPa and 100 kPa

D. 180 kPa and 180 kPa

Correct Answer: A. 224 kPa and 136 kPa

Question 2

For a vertical upstream face retaining 20 m of water, what is the hydrostatic resultant per metre length using γw = 9.81 kN/m³?

A. 981 kN/m

B. 1,962 kN/m

C. 3,924 kN/m

D. 196.2 kN/m

Correct Answer: B. 1,962 kN/m

Question 3

Under the simplified Westergaard formulation, the hydrodynamic resultant acts at what height above the base?

A. H/3

B. H/2

C. 2H/5

D. 3H/5

Correct Answer: C. 2H/5

Question 4

What tensile stress is generated by a 15°C temperature fall under complete uniaxial restraint when E = 30 GPa and α = 10 × 10⁻⁶/°C?

A. 2.00 MPa

B. 3.00 MPa

C. 4.50 MPa

D. 6.75 MPa

Correct Answer: C. 4.50 MPa

Question 5

A thin circular arch strip has p = 200 kPa, radius 75 m and thickness 10 m. What is its average membrane compressive stress?

A. 0.75 MPa

B. 1.50 MPa

C. 15.0 MPa

D. 150 MPa

Correct Answer: B. 1.50 MPa

Question 6

A simply supported one-metre-high deck strip spans 6 m between buttresses under a local pressure of 160 kPa. What is its maximum bending moment?

A. 360 kN·m

B. 480 kN·m

C. 720 kN·m

D. 960 kN·m

Correct Answer: C. 720 kN·m

Question 7

If uplift increases while all other forces remain unchanged, which effect is most likely in a gravity dam?

A. Effective normal force and sliding resistance increase

B. Effective normal force and sliding resistance decrease

C. Hydrostatic force becomes zero

D. Concrete unit weight increases

Correct Answer: B. Effective normal force and sliding resistance decrease

Question 8

For a rectangular base under linear elastic compression, what eccentricity limit corresponds to the middle-third condition?

A. |e| ≤ B/12

B. |e| ≤ B/8

C. |e| ≤ B/6

D. |e| ≤ B/3

Correct Answer: C. |e| ≤ B/6

Question 9

Why can upward vertical earthquake acceleration be adverse for gravity-dam sliding?

A. It increases concrete density

B. It reduces effective weight and frictional resistance

C. It eliminates hydrodynamic pressure

D. It increases foundation cohesion

Correct Answer: B. It reduces effective weight and frictional resistance

Question 10

Which condition is most fundamental to the feasibility of a slender arch dam?

A. A broad valley with compressible abutments

B. Competent abutments capable of resisting arch thrust

C. A foundation that permits unrestricted sliding

D. Complete absence of contraction joints

Correct Answer: B. Competent abutments capable of resisting arch thrust