[測試][工具] 細粒料篩分析 Fine Aggregate Sieve Analysis

AEML · NTUST

Fine Aggregate Sieve Analysis Tool

中文中文/EnglishEnglish

CNSASTM

mm

= 128

px

拍照範圍建議 / Shooting range planner

mm

9.5 mm (3/8 in.)4.75 mm (No. 4)2.36 mm (No. 8)1.18 mm (No. 16)600 µm (No. 30)300 µm (No. 50)150 µm (No. 100)75 µm (No. 200)

× px

4:33:216:91:1

N

px

9.5 mm (3/8 in.)	g
4.75 mm (No. 4)	g
2.36 mm (No. 8)	g
1.18 mm (No. 16)	g
600 µm (No. 30)	g
300 µm (No. 50)	g
150 µm (No. 100)	g
75 µm (No. 200)	g
	g

AEML, NTUST

1.5 s1.0 s0.75 s0.5 s0.25 s

使用說明書 / User Manual

1. 工具用途

本工具以一張俯拍的粒料照片（照片中放置一枚圓形標準物，預設為新台幣 10 元硬幣），由影像量測各顆粒的尺寸，依 CNS 486 / ASTM C136 的篩號由大至小「虛擬套篩」，計算停留量、停留百分率、累積停留百分率、累積通過百分率、細度模數 (FM) 與標稱最大粒徑，並依 CNS 1240 / ASTM C33 的級配界限判定。也可改用「手動輸入」直接輸入實際篩分析的各篩停留重量（g）。

2. 原理

• 比例尺：實際像素尺寸 μm/px = 標準物直徑 (mm) × 1000 ÷ 硬幣直徑 (px)。修改標準物尺寸時立即重算，不需重新上傳。
• 面積與質量：照片量到的是投影面積（∝ d²），篩分析用的是質量（∝ 體積 ∝ d³）。若直接用面積當停留量（面積法），粗顆粒會被低估、細顆粒高估，FM 會系統性偏低。可改用「估算體積 V ≈ A × 短軸寬」或「V ∝ A^1.5（等效橢球）」以修正。所有方法均假設顆粒比重一致。
• 通過判定（方格網，預設）：將邊長等於篩孔的方格網覆蓋於顆粒上，若顆粒輪廓（凸包）在方格網兩個方向上的投影寬度都 ≤ 篩孔邊長，代表顆粒可移動到某一方格內完全落入，判定通過。為模擬搖晃，每一篩以 0°、30°、45° 三個方向判定；顆粒停留機率 = 停留的角度數 ÷ 3，以該權重計入本篩，其餘權重帶到下一篩繼續判定（每一篩三個角度平均後才往下傳）。
• 通過判定（最小 Feret 寬度）：以顆粒輪廓的凸包，從 0° 到 175° 每 5° 旋轉一次（共 36 個角度）量測卡尺寬度，取最小值；最小寬度 ≤ 篩孔邊長即通過。動畫中每一篩會以間距等於篩孔的平行線（卡尺）逐 5° 旋轉：仍為篩色的顆粒表示到目前角度都還卡住，變為白色表示已在某個角度通過；轉完 175° 時剩下的篩色顆粒即停留在該篩。
• 可信的最小篩號：由硬幣邊緣 10–90% 亮度上升距離估算影像模糊量 σ (px)，N = max(8, ⌈2·max(0.5, σ)/0.2⌉)。篩孔換算像素 ≥ N 的篩為可信。預設所有篩號（9.5 mm 至 75 µm 及底盤）都照常計算，低於解析度的篩在報告中以「⚠ 解析度不足」標示、僅供參考；也可選擇「併入底盤」。低於解析度的極細顆粒可能未被偵測，pan 的量可能偏低。使用者可自訂 N。v1.1 起 σ 只在硬幣邊緣最陡處 ±6 px 內量測並取 25 百分位，避免把硬幣邊緣的斜面、浮雕與陰影誤當成模糊。
• 接觸顆粒：預設以距離轉換 + watershed 分離相接觸的顆粒（鞍點高於較低峰值 70% 者合併，以避免長條顆粒被過度切割）。
• 二值化：預設 Otsu 法自動決定閾值，背景明暗由影像邊框自動判斷，也可自設閾值與顆粒亮暗。小於影像面積一定比例的內部孔洞會被填補（顆粒反光）。

3. 計算與捨入規則

• 停留百分率、累積停留百分率、累積通過百分率報到整數；累積停留百分率以各篩整數停留百分率累加（同範例表）。
• 底盤 = 100 − 其他各篩整數之和；若有 No.200 數據，底盤與 No.200 通過率以未捨入值計算並報到 0.1%（No.200 通過率 ≥ 10% 時報整數）。
• 細度模數 = (No.4、No.8、No.16、No.30、No.50、No.100 累積停留百分率之和) ÷ 100，報到 0.01；若 9.5 mm 篩上有停留，依定義一併計入。
• 標稱最大粒徑 = 累積停留百分率 ≤ 10% 的最小篩號。
• 報告判定：各篩累積通過百分率是否在 CNS 1240 / ASTM C33 界限內（9.5 mm：100；4.75 mm：95–100；2.36 mm：80–100；1.18 mm：50–85；600 μm：25–60；300 μm：5–30；150 μm：0–10）、4.75 mm 至 150 μm 間相鄰兩篩之間的停留量 ≤ 45%、FM 在 2.3–3.1 之間。
• 手動輸入時，欄位留空表示該篩未使用（不列入表格，其材料視為落到下一個有填的篩或底盤）；填 0 表示有使用但停留量為 0（仍列入表格）。比最大使用篩更大的篩視為 100% 通過並畫在圖上。

4. 拍攝與鋪樣建議

• 本工具分析的是單層鋪開的小樣本，不是 CNS 486 / ASTM C136 規定的 500 g 全量試樣，結果代表性受取樣影響。
• 背景：最建議使用背光燈板（A4 LED 描圖燈板，上面可放一片透明壓克力或玻璃），所有顆粒都會變成黑色剪影，不受顆粒顏色深淺影響，並開啟「背光照片模式」。沒有燈板時，用與多數顆粒對比最大的單色無紋理背景；顆粒同時有深色與淺色時，會有一部分顆粒漏測。不要拍砂堆表面。
• 顆粒單層、不重疊，盡量互不接觸；建議至少數百顆（愈多愈好），鋪樣面積約為 A4 的一部分即可，但需確保細顆粒在照片中仍有足夠像素。
• 相機垂直俯拍、對焦清晰、光線均勻；硬幣放在畫面中央附近，以減少鏡頭邊緣變形；硬幣邊緣不要被顆粒遮住。
• 欲評估到 150 μm (No.100)，像素尺寸需約 ≤ 15–19 μm/px（視 N 而定），一般需以微距或近拍分區拍攝。資訊面板會顯示可信的最小篩號。
• 支援 JPG、PNG 與 iPhone 的 HEIC/HEIF：Safari 可直接讀取；其他瀏覽器會自動以 heic-to 1.6.6（支援新款 iPhone HEIC；失敗時改用 heic2any 0.0.4，皆由 jsDelivr CDN 載入）在瀏覽器端轉檔；可直接把 HEIC 檔拖進工具任何位置。照片以原始解析度處理（最長邊至 6000 px），影像只在瀏覽器端處理，不會上傳伺服器。

4a. 拍攝比例示意圖：分辨 75 µm (No. 200) 的最低要求

以 iPhone 17 Pro 輸出圖檔 5712 × 4284 px 為例。75 µm 篩孔在影像上至少要有 N = 8 個像素（模糊量 σ ≤ 0.8 px 時的最小值），所以像素尺寸必須 ≤ 75 ÷ 8 = 9.38 µm/px；也就是整張照片的實際範圍不得大於 53.6 × 40.2 mm，10 元硬幣（Ø 26.0 mm）在照片上至少要有 2773 px，約佔畫面寬度的一半。一般手機照片 σ 約 1 px（N = 10），建議再拍近一點，範圍約 42.8 × 32.1 mm（7.50 µm/px）。

欲分辨的最小篩號	N = 8：µm/px	最大拍攝範圍 (mm)	硬幣直徑 (px)	硬幣佔畫面寬	N = 10：µm/px	拍攝範圍 (mm)	硬幣直徑 (px)
75 µm (No. 200)	9.38	53.6 × 40.2	2773	48.6 %	7.50	42.8 × 32.1	3467
150 µm (No. 100)	18.75	107.1 × 80.3	1387	24.3 %	15.0	85.7 × 64.3	1733
300 µm (No. 50)	37.5	214.2 × 160.7	693	12.1 %	30.0	171.4 × 128.5	867
600 µm (No. 30)	75.0	428.4 × 321.3	347	6.1 %	60.0	342.7 × 257.0	433

• 這個倍率需使用 iPhone 的微距模式近拍（鏡頭距離數公分），並確認對焦清晰；照片要用原始解析度（5712 × 4284），不可裁切後放大，也不要用「縮小檔案」的分享方式。
• 此範圍內扣除硬幣後可鋪樣的面積有限，適合只拍細顆粒部分；若同時要量 4.75 mm 的粗顆粒，請注意粗顆粒數量會太少。
• 工具在電腦瀏覽器上以原始解析度（最長邊至 6000 px、約 25 MP）處理；iPhone / iPad 的 Safari 受畫布 16 MP 限制，會縮小約 0.81 倍，此時需再拍近約 20%（建議用電腦分析）。
• 實際可信的最小篩號仍以工具量到的 σ 與 N 為準（資訊面板會顯示）。

提示：可展開上方「拍照範圍建議」，依自己的相機、標準物與欲分辨的篩號計算拍攝範圍，並列印實際尺寸取景卡。

5. 操作步驟

1. 選擇適用標準、計算假設與判定準則；選擇標準物尺寸。
2. 上傳照片。工具會自動偵測硬幣（Hough circle），可拖曳圓框內部移動、拖曳圓周調整大小，或按「重新圈選標準物」自行拖曳指定（由圓心拖到邊緣）。
3. 檢查「分類結果」圖層：顆粒依停留篩著色，灰色為被排除的邊界顆粒。可切換「二值化」圖層檢查閾值。
4. 開啟「動畫」可逐篩、逐角度觀看判定過程（可暫停）。
5. 按影像上方「✂ 裁切」後在影像上拖曳矩形，可只分析選定範圍（例如排除托盤邊緣）；按「↺ 取消裁切」恢復全圖。
6. 動畫可播放、暫停、往前／往後格放，並調整每步速率，方便上課展示。
7. 標題下方「⛶ 全螢幕顯示」讓整個工具佈滿螢幕；影像工具列的「⛶ 全螢幕」只放大影像（Esc 或再按一次結束）。
8. 使用背光燈板拍攝時，開啟「背光照片模式」：顆粒自動視為暗色剪影、背景為亮色，會先把燈板亮度不均的情形平坦化，再以剪影亮暗兩峰的中點作為閾值（模糊邊緣的 50% 位置），量到的輪廓最準。半透明顆粒中央的亮點會被自動填補。
9. 若照片中顆粒佔分析面積超過 40%，或出現寬度大於 9.5 mm 的連成一片的區塊，工具會判定為「砂堆照片」，並提醒「照片中顆粒互相堆疊、沒有背景，結果不可信」。
10. 查看報告並輸出 PDF。級配曲線與粒徑分布直方圖下方各有「⬇ 下載 PNG」（高解析度，可直接放入投影片或報告）。
11. 「匯出 Excel」產生兩個工作表：Grading（基本資料、計算假設與級配表）與 Particles（每顆顆粒的位置、面積、最小 Feret 寬度、方格網寬度、停留篩號與各篩停留比例）；「匯出 CSV」為同樣內容的單一 CSV 檔（UTF-8）。Excel 需由 cdnjs 載入 SheetJS 0.18.5，失敗時自動改存 CSV。
12. 「儲存設定」把所有選項、手動輸入值、標準物位置、裁切範圍與結果摘要存成 JSON 檔；「載入設定」可還原，若照片尺寸相同，會自動套用標準物與裁切範圍，方便重現結果或批改作業。
13. 影像分析在背景執行緒（Web Worker）進行，處理時畫面不會凍結，並顯示進度；瀏覽器不支援時自動改在主執行緒執行。
14. 工具以硬幣邊緣配適橢圓檢查俯拍角度：長短軸比 > 1.02（相機傾斜約 11° 以上）時會警告。
15. 電腦版瀏覽器可直接以原始解析度處理 6000 萬像素以上的照片（最長邊 16384 px、上限約 1.2 億像素），約每 1000 萬像素需 0.2 GB 記憶體；手機 Safari 受畫布限制仍會縮小至約 1600 萬像素。
16. 「繪圖方式」預設為 WebGPU 硬體加速，用於影像的縮放、平移與動畫顯示，大型照片會更流暢；瀏覽器不支援時自動改用軟體繪圖。繪圖方式只影響顯示，不影響分析結果。
17. 按基本設定最下方的「⟲ 重新開始」會清除影像、裁切範圍與所有計算結果（設定保留）。

6. PDF 輸出

• jsPDF + html2canvas：把報告畫面轉成圖片再放進 PDF，中文不需嵌入字型，但PDF 內文字無法選取。函式庫由 CDN 載入（jsPDF 2.5.1、html2canvas 1.4.1，cdnjs）。
• 列印 (window.print)：使用瀏覽器的列印功能，可選「另存為 PDF」，文字可選取。
• 自動：優先使用 jsPDF + html2canvas，CDN 載入失敗時改用列印。

7. 限制

• 影像只能量到二維投影，無法得知顆粒厚度；扁平或長條顆粒的通過判定與體積估算有誤差。
• 低於解析度的極細顆粒可能未被偵測，底盤的量可能偏低；顆粒重疊、陰影、反光或背景不均會影響分割結果。
• 本工具為影像估算，不能取代 CNS 486 / ASTM C136 實際試驗。

1. Purpose

This tool takes a top-down photograph of a fine-aggregate sample with a circular reference object (default: a NT$10 coin), measures every particle, "virtually sieves" them through the CNS 486 / ASTM C136 sieve stack from coarse to fine, and reports the amount retained, percentages retained, cumulative percentages retained and passing, fineness modulus (FM) and nominal maximum size, checked against the CNS 1240 / ASTM C33 grading limits. A "manual input" mode accepts measured masses (g) retained on each sieve.

2. Principle

• Scale: pixel size (µm/px) = reference diameter (mm) × 1000 ÷ coin diameter (px). Changing the reference size recalculates immediately; no re-upload is needed.
• Area vs. mass: a photo measures projected area (∝ d²), whereas a sieve analysis uses mass (∝ volume ∝ d³). Using area as the retained amount (area method) under-weights coarse particles and over-weights fine ones, so the FM is systematically low. "Estimated volume V ≈ A × minor width" or "V ∝ A^1.5 (equivalent ellipsoid)" compensate for this. All methods assume a uniform specific gravity.
• Passing criterion – square grid (default): a grid with the sieve opening as its cell size is laid over the particle; if the projected widths of the particle outline (convex hull) along both grid directions are ≤ the opening, the particle can be moved to fall completely within one cell and passes. To simulate shaking, each sieve is evaluated at 0°, 30° and 45°; the retention probability equals the number of retaining angles ÷ 3. That weight is retained on the sieve and the remainder is passed to the next sieve (angles are averaged before passing material down).
• Passing criterion – minimum Feret width: the caliper width of the particle outline (convex hull) is measured every 5° from 0° to 175° (36 angles) and the minimum is taken; the particle passes if it is ≤ the opening. In the animation, parallel caliper lines spaced at the opening rotate in 5° steps for each sieve: particles still in the sieve colour are blocked at every angle so far, white ones have already passed at some angle; those still coloured after 175° are retained.
• Smallest trusted sieve: the image blur σ (px) is estimated from the 10–90 % intensity rise across the coin rim, N = max(8, ⌈2·max(0.5, σ)/0.2⌉). Sieves whose opening is ≥ N px are trusted. By default all sieves (9.5 mm to 75 µm and the pan) are evaluated; sieves below the resolution are marked "⚠ low resolution" in the report (for reference only). Alternatively their material can be merged into the pan. Very fine particles below the resolution may be missed, so the pan may be under-estimated. N can be set by the user. Since v1.1, σ is measured only within ±6 px of the steepest point of the coin rim and the 25th percentile is used, so the bevel, relief and shadow of a real coin are not mistaken for blur.
• Touching particles: separated by default with a distance-transform watershed (peaks whose saddle exceeds 70 % of the lower peak are merged to avoid over-splitting elongated grains).
• Binarization: Otsu threshold by default; the background polarity is detected from the image border. Threshold and particle polarity can be set manually. Small interior holes (specular highlights) are filled.

3. Calculation and rounding

• Percentages are reported to the nearest whole number; cumulative retained percentages are the running sum of the rounded individual percentages (as in the worked example).
• Pan = 100 − sum of the rounded values of the other sieves; when No.200 data exist, the pan and the No.200 passing are computed from unrounded values and reported to 0.1 % (to the whole number if the No.200 passing is ≥ 10 %).
• FM = (sum of cumulative % retained on No.4, No.8, No.16, No.30, No.50, No.100) ÷ 100, reported to 0.01; the 9.5-mm sieve is added by definition only if material is retained on it.
• Nominal maximum size = the smallest sieve with cumulative retained ≤ 10 %.
• Judgment: cumulative passing within the CNS 1240 / ASTM C33 limits (9.5 mm: 100; 4.75 mm: 95–100; 2.36 mm: 80–100; 1.18 mm: 50–85; 600 µm: 25–60; 300 µm: 5–30; 150 µm: 0–10); not more than 45 % retained between any two consecutive sieves from 4.75 mm to 150 µm; FM within 2.3–3.1.
• Manual input: a blank field means the sieve was not used (not listed; its material is counted on the next filled sieve or pan); 0 means the sieve was used with nothing retained (listed). Sieves larger than the largest sieve used are plotted as 100 % passing.

4. Photography and sample spreading

• The tool analyses a small single-layer sample, not the 500-g test portion required by CNS 486 / ASTM C136; representativeness depends on sampling.
• Background: a light box is strongly recommended (A4 LED tracing pad, optionally with a clear acrylic or glass sheet on top) – every particle becomes a dark silhouette regardless of its colour; enable "Backlit photo". Without a light box, use a uniform background with the best contrast to most particles; with mixed dark and light grains some will be missed. Do not photograph the surface of a pile.
• Spread particles in a single, non-overlapping layer, ideally not touching; use at least several hundred particles, while keeping enough pixels for the fine fractions.
• Shoot perpendicular to the surface, in focus, with even lighting; place the coin near the centre of the frame to minimise lens distortion, and keep its rim unobstructed.
• To evaluate down to 150 µm (No.100) the pixel size must be about ≤ 15–19 µm/px (depending on N), which usually requires close-up or macro photos. The information panel shows the smallest trusted sieve.
• JPG, PNG and iPhone HEIC/HEIF are supported: Safari decodes HEIC natively; other browsers convert it in the browser with heic-to 1.6.6 (supports recent iPhone HEIC; heic2any 0.0.4 as fallback, both from jsDelivr CDN). Files can be dropped anywhere on the tool. Photos are processed at original resolution (up to 6000 px on the long side) and never uploaded.

4a. Framing diagram: minimum requirement to resolve 75 µm (No. 200)

Example: iPhone 17 Pro output image of 5712 × 4284 px. A 75-µm opening must span at least N = 8 pixels (the minimum, valid when the blur σ ≤ 0.8 px), so the pixel size must be ≤ 75 ÷ 8 = 9.38 µm/px. The whole photo may therefore cover no more than 53.6 × 40.2 mm, and the NT$10 coin (Ø 26.0 mm) must measure at least 2773 px — about half the frame width. Phone photos typically have σ ≈ 1 px (N = 10), so shooting slightly closer (≈ 42.8 × 32.1 mm, 7.50 µm/px) is recommended.

Smallest sieve to resolve	N = 8: µm/px	Max. field of view (mm)	Coin diameter (px)	Coin / frame width	N = 10: µm/px	Field of view (mm)	Coin diameter (px)
75 µm (No. 200)	9.38	53.6 × 40.2	2773	48.6 %	7.50	42.8 × 32.1	3467
150 µm (No. 100)	18.75	107.1 × 80.3	1387	24.3 %	15.0	85.7 × 64.3	1733
300 µm (No. 50)	37.5	214.2 × 160.7	693	12.1 %	30.0	171.4 × 128.5	867
600 µm (No. 30)	75.0	428.4 × 321.3	347	6.1 %	60.0	342.7 × 257.0	433

• This magnification requires the iPhone macro mode (a few cm from the sample) with sharp focus. Use the original resolution (5712 × 4284); do not crop and enlarge, and do not share a reduced-size copy.
• After the coin, little area is left for particles, so this framing suits the fine fraction; coarse 4.75-mm particles will be too few in such a small field.
• Desktop browsers process the photo at full resolution (up to 6000 px on the long side, ~25 MP). Safari on iPhone / iPad is limited to 16 MP canvases and scales the image by ~0.81, so shoot ~20 % closer there (a computer is recommended).
• The actual smallest trusted sieve is still determined from the measured σ and N (shown in the information panel).

Tip: expand the "Shooting range planner" above to compute the field of view for your own camera, reference and target sieve, and to print a true-scale framing card.

5. Steps

1. Choose the standard, calculation assumption, passing criterion and reference size.
2. Upload the photo. The coin is detected automatically (Hough circle). Drag inside the circle to move it, drag its rim to resize, or press "Redraw reference" and drag from the centre to the rim.
3. Check the "Classified" layer: particles are coloured by the sieve on which they are retained; grey particles are excluded (touching the border). Use the "Binary" layer to check the threshold.
4. Enable "Animation" to watch the sieve-by-sieve, angle-by-angle evaluation (can be paused).
5. Press "✂ Crop" above the image and drag a rectangle to analyse only that region (e.g. to exclude a tray edge); "↺ Reset crop" restores the full image.
6. The animation can be played, paused, stepped backward / forward, and its speed per step adjusted for teaching.
7. "⛶ Full screen (whole tool)" below the title fills the screen with the whole tool; "⛶ Full screen" in the image toolbar enlarges only the image (Esc or press again to exit).
8. With a light box, enable "Backlit photo": particles are treated as dark silhouettes on a bright background, uneven light-box brightness is flattened, and the threshold is set at the midpoint of the silhouette and background peaks (the 50 % position of a blurred edge) for accurate outlines. Bright spots inside translucent grains are filled.
9. If particles cover more than 40 % of the analysed area, or merged blobs wider than 9.5 mm appear, the photo is flagged as a pile: "Particles are piled up with no visible background; the results are not reliable."
10. Review the report and export a PDF. The grading curve and the size histogram each have "⬇ Download PNG" (high resolution, for slides or reports).
11. "Export Excel" creates two sheets: Grading (metadata, assumptions and the grading table) and Particles (position, area, min. Feret width, grid widths, retaining sieve and fractions per sieve for every particle); "Export CSV" writes the same content to one UTF-8 CSV file. Excel uses SheetJS 0.18.5 from cdnjs and falls back to CSV.
12. "Save settings" stores all options, manual inputs, reference circle, crop and a result summary as JSON; "Load settings" restores them and re-applies the reference and crop when the photo size matches, so results can be reproduced or checked.
13. Image analysis runs in a background thread (Web Worker) with a progress bar, so the page does not freeze; it falls back to the main thread when Workers are unavailable.
14. The coin rim is fitted with an ellipse to check the camera angle: an axis ratio > 1.02 (tilt ≳ 11°) raises a warning.
15. Desktop browsers process photos of 60 MP and more at full resolution (up to 16384 px on the long side, ~120 MP), needing about 0.2 GB of memory per 10 MP; mobile Safari is still limited to ~16 MP by its canvas size.
16. "Rendering" defaults to WebGPU hardware acceleration for zooming, panning and animation, which is smoother for large photos; it falls back to software rendering when unsupported. Rendering affects display only, not the results.
17. "⟲ Start over" at the bottom of the General panel clears the image, crop and all results (settings are kept).

6. PDF export

• jsPDF + html2canvas: the report is rendered as an image inside the PDF, so Chinese text needs no embedded font, but the text in the PDF is not selectable. Libraries are loaded from CDN (jsPDF 2.5.1, html2canvas 1.4.1, cdnjs).
• Print (window.print): uses the browser print dialog (choose "Save as PDF"); text remains selectable.
• Auto: jsPDF + html2canvas first, falling back to print if the CDN cannot be loaded.

7. Limitations

• Only 2-D projections are measured; particle thickness is unknown, so flat or elongated particles introduce errors in passing decisions and volume estimates.
• Very fine particles below the resolution may be missed, so the pan may be under-estimated; overlaps, shadows, glare or uneven backgrounds affect segmentation.
• This is an image-based estimate and does not replace an actual CNS 486 / ASTM C136 test.

AEML · NTUST

先進工程材料研究室，國立台灣科技大學營建工程系
Advanced Engineering Materials Laboratory (AEML), Department of Civil and Construction Engineering, National Taiwan University of Science and Technology (NTUST)

https://www.concrete.tw  ·  https://www.concrete.support

v1.1 · 2026 · © 2026 AEML, NTUST. All rights reserved. 免費供教學與非商業使用 / Free for teaching and non-commercial use.

免責聲明：本工具為影像估算，不能取代 CNS 486 / ASTM C136 實際試驗。 / Disclaimer: image-based estimate; does not replace an actual CNS 486 / ASTM C136 test.

AEML, NTUST

混凝土細粒料篩分析工具Fine Aggregate Sieve Analysis Tool

影像式篩分析：以硬幣為比例尺，計算級配、細度模數與標稱最大粒徑（v1.1）Image-based sieve analysis using a coin as scale: grading, fineness modulus and nominal maximum size (v1.1)

適用標準：CNS 486（篩分析）· CNS 386-1（試驗篩）· CNS 1240（混凝土粒料）Standards: CNS 486 (sieve analysis) · CNS 386-1 (test sieves) · CNS 1240 (concrete aggregates)

適用標準：ASTM C136（篩分析）· ASTM E11（試驗篩）· ASTM C33（混凝土粒料）Standards: ASTM C136 (sieve analysis) · ASTM E11 (test sieves) · ASTM C33 (concrete aggregates)

基本設定General

影像分析設定Image analysis

報告與輸出Report & output

上傳粒料照片Upload aggregate photo

手動輸入各篩停留重量 (g)Manual input: mass retained on each sieve (g)

影像資訊與解析度Image info & resolution

語言介面Language

適用標準Standard

輸入方式Input mode

影像分析Image analysis

手動輸入（實測重量）Manual input (measured mass)

計算假設Calculation assumption

面積法Area method

估算體積 V ≈ A × 短軸寬Estimated volume V ≈ A × minor width

估算體積 V ∝ A^1.5（等效橢球）Estimated volume V ∝ A^1.5 (ellipsoid)

短軸寬定義Minor width definition

最小 Feret 寬度Minimum Feret width

等效橢圓短軸Equivalent-ellipse minor axis

通過篩孔判定準則Passing criterion

方格網覆蓋（0°/30°/45°）Square grid (0°/30°/45°)

最小 Feret 寬度 ≤ 篩孔Min. Feret width ≤ opening

標準物尺寸Reference object

1 元（20.0 mm）NT$1 (20.0 mm)

5 元（22.0 mm）NT$5 (22.0 mm)

10 元（26.0 mm）NT$10 (26.0 mm)

50 元（28.0 mm）NT$50 (28.0 mm)

自訂Custom

直徑Diameter

標準物偵測Reference detection

自動 + 手動修正Auto + manual correction

自動（Hough circle）Automatic (Hough circle)

手動拖曳圓框Manual (drag a circle)

二值化閾值Binarization threshold

Otsu 法（自動）Otsu (automatic)

自設User-defined

閾值Threshold

顆粒亮暗Particle polarity

自動（依邊框背景）Auto (from border)

顆粒較亮Particles brighter

顆粒較暗Particles darker

接觸顆粒分離Touching particles

watershed 分離Watershed

不分離No separation

碰到影像邊界的顆粒Particles touching the border

排除Exclude

保留Keep

可信最小篩號 NTrusted-sieve threshold N

自動（由硬幣邊緣模糊估算）Auto (from coin-edge blur)

自訂User-defined

N（篩孔最少像素）N (min. pixels per opening)

開啟動畫Animation

顯示篩分析報告Show sieve analysis report

顯示細度模數計算報告Show fineness modulus report

報告判定Compliance check

PDF 輸出方式PDF method

自動Auto

jsPDF + html2canvasjsPDF + html2canvas

列印 (window.print)Print (window.print)

輸出 PDF 報告Export PDF report

計算Calculate

載入範例（500 g）Load example (500 g)

清除Clear

留空 = 該篩未使用（不列入表格）；填 0 = 有使用但停留量為 0。Blank = sieve not used (not listed); 0 = sieve used, nothing retained.

留空 = 未使用blank = not used

點此選擇或拖曳照片至此（JPG / PNG / HEIC）
照片需含一枚圓形標準物（預設新台幣 10 元硬幣）；影像僅在瀏覽器端處理，不會上傳。Click to choose or drop a photo here (JPG / PNG / HEIC)
The photo must contain a circular reference (default NT$10 coin). Images are processed in your browser only.

⛶ 全螢幕⛶ Full screen

✕ 結束全螢幕✕ Exit full screen

⛶ 全螢幕顯示（整個工具）⛶ Full screen (whole tool)

✕ 結束全螢幕✕ Exit full screen

✂ 裁切✂ Crop

✂ 裁切中：拖曳選取範圍（再按取消）✂ Cropping: drag a box (click to cancel)

↺ 取消裁切（全圖）↺ Reset crop (full image)

請在影像上拖曳出要分析的矩形範圍；範圍外的顆粒不列入計算，碰到範圍邊界的顆粒依「邊界顆粒」設定處理。標準物可在範圍外。Drag a rectangle on the image to set the analysis region. Particles outside are ignored; particles touching its edge follow the border-particle setting. The reference may lie outside.

已設定分析範圍 {0} × {1} px，重新分析中。Analysis region set to {0} × {1} px; re-analysing.

已取消裁切，改為分析全圖。Crop removed; analysing the full image.

請先上傳照片。Upload a photo first.

分析範圍：使用者裁切 {0} × {1} px（左上角 x = {2}, y = {3}）；碰到範圍邊界的顆粒視同邊界顆粒。Analysis region: user crop {0} × {1} px (top-left x = {2}, y = {3}); particles touching its edge are treated as border particles.

分析範圍（裁切）Analysis region (crop)

⏮ 往前格放⏮ Previous step

往後格放 ⏭Next step ⏭

每步Per step

繪圖方式Rendering

WebGPU 硬體加速WebGPU (hardware)

軟體（Canvas 2D）Software (Canvas 2D)

軟體（Canvas 2D）Software (Canvas 2D)

此瀏覽器或裝置不支援 WebGPUWebGPU not available on this browser / device

繪圖方式Rendering

此瀏覽器或裝置無法使用 WebGPU，已自動改用軟體繪圖；分析結果不受影響。WebGPU is not available here; software rendering is used. Results are not affected.

⟲ 重新開始⟲ Start over

確定要清除目前的影像與計算結果，重新開始嗎？（設定會保留）Clear the current image and results and start over? (Settings are kept)

已清除影像與計算結果，請上傳新照片或輸入資料。Image and results cleared. Upload a new photo or enter data.

背光照片模式（燈板剪影）Backlit photo (light-box silhouettes)

剪影亮暗峰中點silhouette mid-level

背光照片模式：顆粒視為暗色剪影、背景為亮色；燈板亮度不均已平坦化。Backlit mode: particles are dark silhouettes on a bright background; uneven light-box brightness is flattened.

二值化閾值：剪影亮暗兩峰中點 = {0}（邊緣 50% 位置）。Threshold: mid-level between silhouette and background peaks = {0} (50 % edge position).

顆粒佔分析面積Particle area fraction

⚠ 照片中顆粒互相堆疊、沒有背景，結果不可信。請取少量樣本單層攤開（最好使用背光燈板）後重拍。⚠ Particles are piled up with no visible background; the results are not reliable. Spread a small sample in a single layer (preferably on a light box) and retake the photo.

判定依據：顆粒佔分析面積 {0}%（單層攤開通常 < 40%）；寬度大於 9.5 mm 的連成一片區塊 {1} 個。Criteria: particles cover {0} % of the analysed area (a single layer is usually < 40 %); {1} merged blob(s) wider than 9.5 mm.

分析完成（{0} 顆，FM = {1}），但照片中顆粒互相堆疊、沒有背景，結果不可信。Done ({0} particles, FM = {1}), but particles are piled up with no background; results are not reliable.

自動偵測標準物的信心較低，請確認黃色圓框是否正好框住硬幣；若不正確，請按「重新圈選標準物」。Low confidence in the automatic reference detection; check that the yellow circle matches the coin, or press "Redraw reference".

已偵測到可能的標準物（直徑 {0} px），但信心較低，請確認黃色圓框是否正確。A possible reference was found (diameter {0} px) with low confidence; please check the yellow circle.

轉換灰階Converting to grey

平滑化Smoothing

偵測標準物Detecting reference

二值化Thresholding

填補孔洞Filling holes

標記顆粒Labelling particles

watershed 分離Watershed

量測顆粒形狀Measuring particles

記憶體不足，無法處理這張照片。請改用電腦版 Chrome / Edge、關閉其他分頁，或先裁切／縮小照片。Out of memory. Use desktop Chrome / Edge, close other tabs, or crop / downsize the photo.

大型影像 {0} MP，以原始解析度處理，約需 {1} GB 記憶體；建議使用電腦版 Chrome / Edge。Large image ({0} MP) processed at full resolution; about {1} GB of memory is needed. Desktop Chrome / Edge recommended.

運算方式Processing

背景執行緒（Web Worker）Background thread (Web Worker)

主執行緒（瀏覽器不支援 Worker）Main thread (Worker unavailable)

硬幣長短軸比Coin axis ratio

相機傾斜約 {0}°camera tilt ≈ {0}°

硬幣呈橢圓（長短軸比 > 1.02），相機可能未垂直俯拍，比例尺在畫面各處不一致。請將相機平行於樣本平面後重拍。The coin appears elliptical (axis ratio > 1.02); the camera may not be perpendicular, so the scale varies across the image. Hold the camera parallel to the sample plane and retake.

⬇ 下載 PNG⬇ Download PNG

PNG 已下載。PNG downloaded.

粒徑分布直方圖Particle size distribution

以最小 Feret 寬度、每 1/4 倍頻（2^0.25）分組；長條為顆粒數，依該粒徑會停留的篩號著色；紅線為各組停留量占總量百分比（依目前計算假設）。灰色區域低於可信解析度。Grouped by minimum Feret width in quarter-octave bins (2^0.25); bars are particle counts coloured by the sieve that would retain that size; the red line is each bin's share of the total amount (current assumption). The grey zone is below the trusted resolution.

低於解析度Below resolution

最小 Feret 寬度 (mm)Minimum Feret width (mm)

顆粒數Number of particles

停留量占比 (%)Share of amount (%)

顆粒數（依篩號著色）Particle count (by sieve)

停留量占比Share of amount

匯出 ExcelExport Excel

匯出 CSVExport CSV

💾 儲存設定💾 Save settings

📂 載入設定📂 Load settings

CSV 已下載（UTF-8，可直接用 Excel 開啟）。CSV downloaded (UTF-8, opens in Excel).

產生 Excel 檔中（首次需下載 SheetJS）…Creating Excel file (downloading SheetJS the first time)…

Excel 已下載（工作表：Grading 級配、Particles 顆粒資料）。Excel downloaded (sheets: Grading, Particles).

無法載入 SheetJS（CDN），已改為下載 CSV。SheetJS could not be loaded from the CDN; a CSV was downloaded instead.

設定已儲存（JSON 檔，含標準物、裁切範圍與結果摘要）。Settings saved (JSON with reference, crop and result summary).

設定已載入。Settings loaded.

設定已載入，並套用到目前照片的標準物與裁切範圍，重新分析中。Settings loaded and applied to the current photo's reference and crop; re-analysing.

設定已載入；請上傳原照片（{0}），會自動套用標準物與裁切範圍。Settings loaded; upload the original photo ({0}) to apply the reference and crop automatically.

設定已載入，但目前照片尺寸與存檔時（{0}）不同，標準物與裁切範圍未套用。Settings loaded, but the current photo size differs from the saved one ({0}); reference and crop were not applied.

無法讀取：這不是本工具的設定檔。Cannot read: not a settings file of this tool.

檔名File

停留百分率（未捨入）% retained (unrounded)

備註Note

編號ID

中心 x (mm)Centre x (mm)

中心 y (mm)Centre y (mm)

投影面積 (mm²)Projected area (mm²)

等面積圓直徑 (mm)Equivalent circle diameter (mm)

最小 Feret 寬度 (mm)Min. Feret width (mm)

等效橢圓短軸 (mm)Equivalent-ellipse minor axis (mm)

方格網 0° 寬度 (mm)Grid width 0° (mm)

方格網 30° 寬度 (mm)Grid width 30° (mm)

方格網 45° 寬度 (mm)Grid width 45° (mm)

停留量權重Weight

主要停留篩號Main retaining sieve

排除原因Excluded

停留比例Fraction on

碰到邊界touches border

碰到標準物touches reference

📐 拍照範圍建議（點擊展開）📐 Shooting range planner (click to expand)

欲分辨的最小篩號Smallest sieve to resolve

相機解析度Camera resolution

600 萬畫素6 MP

1200 萬畫素12 MP

1800 萬畫素18 MP

2400 萬畫素24 MP

3600 萬畫素36 MP

4800 萬畫素48 MP

6000 萬畫素60 MP

自訂寬 × 高Custom width × height

寬 × 高Width × height

長寬比Aspect ratio

預期清晰度 NExpected sharpness N

清晰（N = 8）Sharp (N = 8)

一般手機（N = 10）Typical phone (N = 10)

較模糊（N = 14）Softer (N = 14)

N 為篩孔最少需佔的像素數：N = max(8, ⌈2·max(0.5, σ)/0.2⌉)。實際值以上傳照片後，由硬幣邊緣量到的模糊量 σ 為準。N is the minimum number of pixels across a sieve opening: N = max(8, ⌈2·max(0.5, σ)/0.2⌉). The actual value comes from the blur σ measured on the coin rim after upload.

套用標準物到影像分析Apply reference to image analysis

已將標準物 {0} mm 套用到影像分析設定。Reference {0} mm applied to the image analysis settings.

換算影像尺寸：{0} px（{1} MP）Image size: {0} px ({1} MP)

超過此裝置的處理上限（約 {1} MP），將以 {0} px 處理，以下數值已依此計算。Exceeds this device's processing limit (~{1} MP); the photo will be processed at {0} px and the figures below use that size.

建議拍攝範圍Recommended field of view

最大 {0} mm（N = 8）max. {0} mm (N = 8)

像素尺寸Pixel size

上限 {0} µm/px（N = 8）limit {0} µm/px (N = 8)

硬幣直徑 · 佔畫面寬度Coin diameter · share of frame width

至少 {0} px · {1} %（N = 8）at least {0} px · {1} % (N = 8)

取景提示：讓硬幣約佔畫面寬度的 {0}%（約 {1}），並以此距離或更近拍攝。Framing tip: make the coin about {0} % of the frame width (about {1}) – shoot at this distance or closer.

標準物太大，畫面放不下（硬幣直徑超過畫面短邊 90%）。建議改用較小的標準物、分兩段拍（先用 No.30 篩分粗細），或使用平台掃描器。The reference does not fit in the frame (coin wider than 90 % of the short side). Use a smaller reference, shoot coarse and fine fractions separately (split on No. 30), or use a flatbed scanner.

此範圍內粗顆粒（4.75 mm）數量不足，代表性差（畫面短邊小於 10 × 4.75 mm）。建議分兩段拍：粗料用較大範圍、細料用此範圍。Too few coarse (4.75 mm) particles fit in this field (short side < 10 × 4.75 mm). Shoot in two stages: coarse fraction at a larger field, fine fraction at this one.

4800 萬畫素以上的手機多為四合一感光元件，實際清晰度可能只相當於 N = 12–14，建議 N 選「較模糊」再評估。Phones with 48 MP or more usually use quad-pixel sensors; real sharpness may correspond to N = 12–14, so evaluate with "Softer".

像素尺寸 (µm/px)
N = {0}Pixel size (µm/px)
N = {0}

拍攝範圍 (mm)Field of view (mm)

硬幣直徑 (px)Coin diameter (px)

硬幣佔畫面寬Coin / frame width

標準物放不下reference does not fit

標準物佔畫面短邊 60% 以上，可鋪樣面積很小，顆粒數可能不足。建議改用較小的標準物（例如 1 元 20 mm），或分兩段拍。The reference takes more than 60 % of the short side, leaving little room for particles. Use a smaller reference (e.g. NT$1, 20 mm) or shoot in two stages.

標準物佔畫面過大reference takes most of the frame

粗顆粒不足too few coarse particles

分辨 {0} 所需拍攝範圍（{1} px，依實際比例繪製）Field of view to resolve {0} ({1} px, drawn to scale)

（佔畫面寬 {0}%）({0} % of frame width)

最大拍攝範圍（N = 8）：{0} µm/pxLargest field (N = 8): {0} µm/px

建議範圍（N = {0}）：{1} × {2} mm，{3} µm/pxRecommended (N = {0}): {1} × {2} mm, {3} µm/px

放大：{0} 篩孔Zoom: {0} opening

1 格 = 1 像素 = {0} µm1 cell = 1 pixel = {0} µm

紅框：{0} = {1} pxRed: {0} = {1} px

條件：Requirement:

篩孔像素 ≥ Nopening ≥ N pixels

相機垂直俯拍，硬幣置於畫面中央shoot straight down, coin at the centre

顆粒比例尺（與上圖同比例，mm）：Grain scale (same scale, mm):

藍框：最大拍攝範圍（N = 8）；黃虛線：建議範圍（所選 N）；硬幣與顆粒依實際比例繪製。Blue: largest field (N = 8); yellow dashed: recommended field (selected N); coin and grains drawn to scale.

🖨 列印實際尺寸取景卡🖨 Print true-scale framing card

實際尺寸取景卡True-scale framing card

條件：分辨 {0}，相機 {1} px，N = {2}，標準物 {3} mm → 拍攝範圍 {4} mm，像素尺寸 {5} µm/pxConditions: resolve {0}, camera {1} px, N = {2}, reference {3} mm → field {4} mm, pixel size {5} µm/px

本卡為實際尺寸（1:1）。This card is at true scale (1:1).

拍攝範圍大於 A4，本卡已縮小（{0}），請依比例放大鋪樣範圍。The field is larger than A4; this card is scaled ({0}) – enlarge the spreading area accordingly.

（已轉 90° 以放入 A4）(rotated 90° to fit A4)

外框 = 建議拍攝範圍 {0} mm；虛線圓 = 標準物 Ø {1} mmOuter frame = recommended field {0} mm; dashed circle = reference Ø {1} mm

列印時請選「實際大小 / 100%」，不要選「符合頁面」。印出後用尺量下方比例尺，應為 50 mm。Print at "Actual size / 100 %", not "Fit to page". Check that the scale bar measures 50 mm.

把硬幣放在虛線圓內，樣本單層鋪在外框內，顆粒不重疊（建議使用背光燈板）。Place the coin in the dashed circle and spread the sample in one layer inside the frame, without overlaps (a light box is recommended).

相機垂直俯拍，讓外框剛好填滿畫面（或略小於畫面），即符合建議範圍。Shoot straight down so the frame just fills (or is slightly inside) the picture.

上傳後以工具量到的 σ、N 與可信的最小篩號為準。After upload, the measured σ, N and smallest trusted sieve are authoritative.

放大Zoom in

縮小Zoom out

全圖Fit

平移Pan

分類結果Classified

二值化Binary

原圖Original

重新圈選標準物Redraw reference

尚未上傳照片No photo loaded

滑鼠滾輪縮放、拖曳平移；拖曳黃色圓框內部可移動、拖曳圓周可調整大小。Wheel to zoom, drag to pan; drag inside the yellow circle to move it, drag its rim to resize.

▶ 播放▶ Play

❚❚ 暫停❚❚ Pause

■ 停止■ Stop

最小 Feret 寬度旋轉min. Feret sweep

方格網每 {0} 格畫一條線grid drawn every {0} cells

使用說明書User manual

請上傳照片，或切換為「手動輸入」。Upload a photo, or switch to manual input.

處理中…Working…

讀取影像中…Loading image…

偵測標準物中…Detecting reference…

影像分割與顆粒量測中…Segmenting and measuring particles…

無法讀取此檔案，請選擇影像檔（JPG / PNG）。Cannot read this file; please choose an image (JPG / PNG).

處理失敗：{0}Processing failed: {0}

請在影像上由硬幣圓心拖曳到邊緣，以圈選標準物。Drag from the coin centre to its rim to mark the reference.

可拖曳圓框修正標準物位置與大小。Drag the circle to correct the reference.

已自動偵測標準物（直徑 {0} px）。Reference detected automatically (diameter {0} px).

已自動偵測標準物（直徑 {0} px），如有偏差可拖曳圓框修正。Reference detected (diameter {0} px); drag the circle to correct it if needed.

無法自動偵測標準物，請由硬幣圓心拖曳到邊緣以手動圈選。Reference not found; drag from the coin centre to its rim to mark it.

無法自動偵測標準物。請將「標準物偵測」改為「自動 + 手動修正」或「手動」。Reference not found. Switch reference detection to "Auto + manual" or "Manual".

標準物已設定（直徑 {0} px），重新分析中。Reference set (diameter {0} px); re-analysing.

分析完成：納入 {0} 顆顆粒，FM = {1}。Done: {0} particles included, FM = {1}.

沒有任何可信的篩號（影像解析度不足），請以更近的距離拍攝。No trusted sieve (insufficient resolution); take a closer photo.

輸入值必須為 ≥ 0 的數字（紅框欄位）。Inputs must be numbers ≥ 0 (red fields).

請輸入各篩停留重量，或按「載入範例」。Enter the mass retained on each sieve, or load the example.

計算完成（實測重量），FM = {0}。Calculated (measured mass), FM = {0}.

產生 PDF 中…Generating PDF…

PDF 已下載。PDF downloaded.

無法載入 jsPDF / html2canvas（CDN），請改用「列印」。Cannot load jsPDF / html2canvas from CDN; please use "Print".

CDN 載入失敗，改用瀏覽器列印（可選「另存為 PDF」）。CDN unavailable; using browser print (choose "Save as PDF").

上傳照片後顯示像素尺寸、模糊量與可信的最小篩號。Pixel size, blur and the smallest trusted sieve appear after a photo is loaded.

分析影像Analysed image

標準物Reference

實際像素尺寸Pixel size

邊緣模糊 σEdge blur σ

無法量測，假設 1 pxnot measurable, 1 px assumed

N（篩孔最少像素）N (min. px per opening)

自訂user

可信最小篩孔Smallest reliable opening

可信的最小篩號Smallest trusted sieve

無none

二值化閾值Threshold

顆粒較亮particles brighter

顆粒較暗particles darker

顆粒數Particles

共 {0}；納入 {1}；排除 {2}{0} total; {1} included; {2} excluded

分割耗時Segmentation time

底盤Pan

底盤Bottom tray

合計Total

硬幣直徑小於 100 px，比例尺誤差較大，請靠近拍攝。Coin diameter < 100 px; the scale is uncertain. Take a closer photo.

無法由硬幣邊緣量測模糊量，以 σ = 1 px 估算 N。Coin-edge blur could not be measured; σ = 1 px assumed for N.

低於解析度的篩，其停留量已併入底盤。低於解析度的極細顆粒可能未被偵測，pan 的量可能偏低。Material on sieves below the image resolution has been merged into the pan. Very fine particles below the resolution may be missed, so the pan may be under-estimated.

沒有任何篩孔達到解析度要求。No sieve opening meets the resolution requirement.

納入的顆粒少於 200 顆，結果代表性不足，建議至少數百顆。Fewer than 200 particles included; use at least several hundred particles.

部分計算 FM 的篩未使用或不可信，以上一篩的累積停留百分率代入（FM 為下限值，僅供參考）。Some FM sieves are missing or untrusted; the cumulative value of the next larger sieve was used (FM is a lower bound, for reference only).

gg

mm²mm²

mm³（估算）mm³ (est.)

mm³（∝ A^1.5）mm³ (∝ A^1.5)

——

合格Pass

不合格Fail

未使用，視為 100% 通過not used, taken as 100 % passing

細粒料篩分析報告Sieve Analysis Report – Fine Aggregate

日期Date

標準Standard

輸入方式Input

尚無結果。請上傳照片並完成標準物設定，或使用手動輸入。No results yet. Upload a photo and set the reference, or use manual input.

分析影像（顆粒依停留篩著色；灰色為排除顆粒；黃色虛線為標準物）Analysed image (particles coloured by retaining sieve; grey = excluded; yellow dashed = reference)

非原版：本頁的版權標示或浮水印已被移除或修改。原版工具由 AEML, NTUST 提供（www.concrete.tw）。Unofficial copy: the credit block or watermark of this page has been removed or altered. The original tool is by AEML, NTUST (www.concrete.tw).

計算假設Calculation assumptions

警告Warnings

篩分析結果Sieve analysis

細度模數計算Fineness modulus calculation

報告判定Compliance check

試驗標準：{0}Standards: {0}

計算假設：實測重量（各篩停留重量由使用者輸入）。Calculation basis: measured mass (mass retained on each sieve entered by the user).

假設所有顆粒比重一致，停留量比例等於質量比例。All particles are assumed to have the same specific gravity, so amount ratios equal mass ratios.

計算假設：面積法（體積比例 = 投影面積比例）。注意：面積法會使 FM 系統性偏低。Assumption: area method (volume ratio = projected-area ratio). Note: the area method biases FM low.

計算假設：估算體積 V ≈ A × 短軸寬Assumption: estimated volume V ≈ A × minor width

計算假設：估算體積 V ∝ A^1.5（等效橢球）Assumption: estimated volume V ∝ A^1.5 (equivalent ellipsoid)

通過判定：方格網覆蓋（顆粒可完全落入單一方格者通過），0°、30°、45° 三個方向的停留機率平均後再往下一篩傳遞。Passing criterion: square grid (passes if the particle fits completely in one cell); retention probabilities at 0°, 30° and 45° are averaged before passing material to the next sieve.

通過判定：最小 Feret 寬度（每 5° 旋轉）≤ 篩孔邊長者通過。Passing criterion: minimum Feret width (5° steps) ≤ sieve opening.

接觸顆粒：watershed 分離。Touching particles: separated by watershed.

接觸顆粒：不分離。Touching particles: not separated.

二值化閾值：Otsu 法 = {0}。Threshold: Otsu = {0}.

二值化閾值：自設 = {0}。Threshold: user-defined = {0}.

碰到影像邊界或標準物的顆粒：排除。Particles touching the image border or the reference: excluded.

碰到影像邊界的顆粒：保留。Particles touching the image border: kept.

標準物直徑 {0} mm（{1}）；總樣本量為扣除標準物後的總量。Reference diameter {0} mm ({1}); the total excludes the reference object.

實際像素尺寸 {0} μm/px；N = {1} px；可信的最小篩號：{2}。Pixel size {0} µm/px; N = {1} px; smallest trusted sieve: {2}.

本結果為單層鋪開之小樣本的影像估算，非 500 g 全量試樣。Results are an image-based estimate of a small single-layer sample, not a 500-g test portion.

篩號Sieve

停留量Retained

顆粒數（加權）Particles (weighted)

停留百分率 (%)% Retained

累積停留百分率 (%)Cumulative % retained

過篩百分率 (%)
100 − 停留100 − % retained

累積通過百分率 (%)Cumulative % passing

規範界限 (%)Limits (%)

判定Result

低於影像解析度，停留量併入底盤Below image resolution; merged into pan

百分率報到整數；累積停留百分率以各篩整數累加；底盤 = 100 − 其他各篩整數之和（有 No.200 時底盤與 No.200 通過率以未捨入值報到 0.1%）。Percentages to the nearest whole number; cumulative values are running sums of the rounded values; pan = 100 − sum of the others (with No.200, the pan and No.200 passing are unrounded, reported to 0.1 %).

細度模數允許範圍：2.3–3.1（CNS 1240 與 ASTM C33 相同）。Allowable fineness modulus: 2.3–3.1 (same in CNS 1240 and ASTM C33).

篩號Sieve Size

停留量Weight Retained

停留百分率
(wt. %)Amount Retained (wt. %)

累積停留百分率 (%)Cumulative Amount Retained (%)

累積通過百分率 (%)Cumulative Amount Passing (%)

只加總六個篩（No.4、No.8、No.16、No.30、No.50、No.100）的累積停留百分率。Only sum up those on six sieves (No. 4, No. 8, No. 16, No. 30, No. 50, No. 100).

細度模數 FMFineness modulus

標稱最大粒徑Nominal maximum size

項目Item

結果Value

規定Requirement

級配界限（{0}）— 累積通過百分率Grading limits ({0}) — cumulative % passing

相鄰兩篩間停留量 ≤ 45%（4.75 mm 至 150 μm）Retained between consecutive sieves ≤ 45 % (4.75 mm to 150 µm)

細度模數Fineness modulus

判定結果：全部合格Result: all requirements met

判定結果：已檢查項目均合格，但部分篩未使用或低於解析度，無法完整判定Result: all checked items pass, but some sieves are missing or untrusted

判定結果：不合格Result: does not comply

免責聲明：本工具為影像估算，不能取代 CNS 486 / ASTM C136 實際試驗。Disclaimer: this tool provides an image-based estimate and does not replace an actual CNS 486 / ASTM C136 test.

先進工程材料研究室（AEML），國立台灣科技大學營建工程系 · www.concrete.tw · www.concrete.support · v1.1 · © 2026 AEML, NTUST. All rights reserved. 免費供教學與非商業使用。Advanced Engineering Materials Laboratory (AEML), Dept. of Civil and Construction Engineering, NTUST · www.concrete.tw · www.concrete.support · v1.1 · © 2026 AEML, NTUST. All rights reserved. Free for teaching and non-commercial use.

級配曲線Grading curve

粒徑 (mm)Aggregate size (mm)

累積通過百分率 (%)Percent passing (%)

規範上下限（{0}）Specification limits ({0})

試驗值Test result

未使用的篩（視為 100% 通過）Unused sieve (100 % passing)

FM = {0}（允許 2.3–3.1）FM = {0} (allowed 2.3–3.1)

低於解析度的篩Sieves below resolution

照常計算並標示（全部篩號）Evaluate and flag (all sieves)

併入底盤Merge into pan

⚠ 解析度不足⚠ low res.

低於解析度（僅供參考）Below resolution (reference only)

許多顆粒被判定大於 9.5 mm 或接近硬幣大小，標準物可能偵測錯誤（圈到顆粒）。請檢查黃色圓框是否正好框住 10 元硬幣，必要時按「重新圈選標準物」。Many particles appear larger than 9.5 mm or close to the coin size; the reference may be mis-detected. Check that the yellow circle matches the coin, or press "Redraw reference".

標示「⚠ 解析度不足」的篩，篩孔小於可信解析度 N，仍照常計算但僅供參考；低於解析度的極細顆粒可能未被偵測，pan 的量可能偏低。Sieves marked "⚠ low res." are smaller than the trusted resolution N; they are still evaluated but are for reference only. Very fine particles below the resolution may be missed, so the pan may be under-estimated.

所有篩孔都低於可信解析度，全部結果僅供參考，請靠近拍攝。All sieve openings are below the trusted resolution; all results are for reference only. Take a closer photo.

低於解析度的篩：照常計算並標示（僅供參考）。Sieves below resolution: evaluated and flagged (reference only).

低於解析度的篩：停留量併入底盤。Sieves below resolution: material merged into the pan.

轉換 HEIC 照片中（首次需下載轉檔程式，約 3 MB）…Converting HEIC photo (first time downloads a ~3 MB decoder)…

無法讀取 HEIC 檔（{0}）。請確認網路可連到 cdn.jsdelivr.net，或改用 Safari 開啟，或在 iPhone「設定 › 相機 › 格式」選「最相容」後重拍。Cannot read the HEIC file ({0}). Check that cdn.jsdelivr.net is reachable, use Safari, or set iPhone Settings › Camera › Formats to "Most Compatible".